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We study the fuzzy spaces (as special examples of noncommutative manifolds) with their quasicoherent states in order to find their pertinent metrics. We show that they are naturally endowed with two natural 'quantum metrics' which are associated with quantum fluctuations of 'paths'. The first one provides the length the mean path whereas the second one provides the average length of the fluctuated paths. Onto the classical manifold associated with the quasicoherent state (manifold of the mean values of the coordinate observables in the state minimising their quantum uncertainties) these two metrics provides two minimising geodesic equations. Moreover, fuzzy spaces being not torsion free, we have also two different autoparallel geodesic equations associated with two different adiabatic regimes in the move of a probe onto the fuzzy space. We apply these mathematical results to quantum gravity in BFSS matrix models, and to the quantum information theory of a controlled qubit submitted to noises of a large quantum environment. [ABSTRACT FROM AUTHOR]

We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum Rényi divergences starting from a set of monotone quantum relative entropies. Interestingly, despite its central importance in information theory, only two additive and monotone quantum extensions of the classical relative entropy have been known so far, the Umegaki and the Belavkin-Staszewski relative entropies, which are the minimal and the maximal ones, respectively, with these properties. Using the Kubo-Ando weighted geometric means, we give a general procedure to construct monotone and additive quantum relative entropies from a given one with the same properties; in particular, when starting from the Umegaki relative entropy, this gives a new one-parameter family of monotone (even under positive trace-preserving (PTP) maps) and additive quantum relative entropies interpolating between the Umegaki and the Belavkin-Staszewski ones on full-rank states. In a different direction, we use a generalization of a classical variational formula to define multi-variate quantum Rényi quantities corresponding to any finite set of quantum relative entropies (D q x ) x ∈ X and real weights (P (x)) x ∈ X summing to 1, as Q P b , q ((ϱ x) x ∈ X) : = sup τ ≥ 0 ⁡ { Tr τ − ∑ x P (x) D q x (τ ‖ ϱ x) }. We analyze in detail the properties of the resulting quantity inherited from the generating set of quantum relative entropies; in particular, we show that monotone quantum relative entropies define monotone Rényi quantities whenever P is a probability measure. With the proper normalization, the negative logarithm of the above quantity gives a quantum extension of the classical Rényi α -divergence in the 2-variable case (X = { 0 , 1 } , P (0) = α). We show that if both D q 0 and D q 1 are lower semi-continuous, monotone, and additive quantum relative entropies, and at least one of them is strictly larger than the Umegaki relative entropy then the resulting barycentric Rényi divergences are strictly between the log-Euclidean and the maximal Rényi divergences, and hence they are different from any previously studied quantum Rényi divergence. [ABSTRACT FROM AUTHOR]

Our study examines the output states produced by deletion machines, including the Pati-Braunstein (PB) and our proposed deleting machine (DM). We study the specific form of maximally entangled mixed state (MEMS) and Werner state that achieve the highest entanglement for a given level of mixedness. These states are useful in quantum information tasks due to their optimal entanglement for a given mixedness. We considered various entanglement measures (concurrence and negativity) and mixedness measures (linear and von Neumann entropy). We compared the output state of our proposed deletion machine with MEMS and Werner state, finding that our machine creates states with higher mixedness, entanglement in certain input state (α) and entanglement parameter (w, p) ranges. The results indicate that our proposed deletion machine could be effectively utilized in quantum information applications, similar to MEMS and Werner states. [ABSTRACT FROM AUTHOR]

Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical theories, like GR, to quantum mechanics, like in the AdS/CFT correspondence. In this paper, we first make a survey of the most important settings in which geometrical methods have proven useful to quantum information theory. Then we lay down a geometric theory of entanglement by a principle of action, discussing a simple example with two qubits and consequences for a quantum theory of space-time. [ABSTRACT FROM AUTHOR]

One of the fundamental tasks in quantum information theory is quantum data compression, which can be realized via quantum autoencoders that first compress quantum states to low-dimensional ones and then recover to the original ones with a reference state. When taking a pure reference state, there exists an upper bound for the encoding fidelity, which limits the compression of states with high entropy. To overcome the entropy inconsistency, we allow the reference state to be a mixed state and propose a cost function that combines the encoding fidelity and the quantum mutual information. We consider the reference states to be a mixture of maximally mixed states and pure states and propose three strategies for setting the ratio of mixedness. Numerical simulations of different states and experimental implementations on IBM quantum computers illustrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Finite-dimensional entanglement for pure states has been used extensively in quantum information theory. Depending on the tensor product structure, even a set of separable states can show non-intuitive characters. Two situations are well studied in the literature, namely, the unextendible product basis (UPB) by Bennett et al.,4 and completely entangled subspaces explicitly given by Parthasarathy.22 More recently, Boyer et al.,6 Boyer and Mor7 and Liss et al.21 studied spaces which have only finitely many pure product states. We carry this further and consider the problem of perturbing different spaces, such as the orthogonal complement of an UPB and also Parthasarathy’s completely entangled spaces, by taking linear spans with specified product vectors. To this end, we develop methods and theory of variations and perturbations of the linear spans of certain UPBs, their orthogonal complements, and also Parthasarathy’s completely entangled subspaces. Finally, we give examples of perturbations with infinitely many pure product states. [ABSTRACT FROM AUTHOR]

Matrices are built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums or multiplication of matrices are such procedures and a matrix built from these is said to be a separable matrix. A non-separable matrix is a matrix which is not separable and is often referred to as an entangled 'matrix. The matrices built may retain properties of the lower order matrices or may also acquire new desired properties not inherent in the constituents. Here design methods for non-separable matrices of required types are derived. These can retain properties of lower order matrices or have new desirable properties. Infinite series of required type non-separable matrices are constructible by the general methods. Non-separable matrices of required types are required for applications and other uses; they can capture the structure in a unique way and thus perform much better than separable matrices. General new methods are developed with which to construct multidimensional entangled paraunitary matrices; these have applications for wavelet and filter bank design. The constructions are used to design new systems of non-separable unitary matrices; these have applications in quantum information theory. Some consequences include the design of full diversity constellations of unitary matrices, which are used in MIMO systems, and methods to design infinite series of special types of Hadamard matrices. [ABSTRACT FROM AUTHOR]

Within the framework of quantum information theory, the performance of conventional 2-D techniques is often unsatisfactory for the study of Bell states that hold a unique status as maximally entangled states. Therefore, 3-D approaches are increasingly employed to achieve more accurate and detailed analysis, offering improved performance and insights in complex scenarios. Among the diverse background of mixed two-qubit states, certain configurations exhibit unique quantum correlations that harness advanced quantum information processing tasks such as Bell diagonal states. Although, these states may appear superficially simple and exhibit a rich spectrum of correlations. The present research employs a methodology that involves a convex combination of distinct Bell states to generate the entire class of Bell diagonal states. This work explores the time evolution of Bell diagonal states, when exposed to various quantum channels and investigates the dynamics of quantum correlations such as entanglement, discord, and state of separability. Finally, the behaviour of Bell diagonal states is analysed and results are compared between theory and practice. A threedimensional visual approach is used to illustrate a deeper understanding of various quantum features and dynamic behaviour of the Bell diagonal states. [ABSTRACT FROM AUTHOR]

Random tensor models have applications in a variety of fields, such as quantum gravity, quantum information theory, mathematics of modern technologies, etc. and studying their statistical properties, e.g. tensor eigenvalue/vector distributions, is interesting and useful. Recently some tensor eigenvalue/vector distributions have been computed by expressing them as partition functions of 0D quantum field theories. In this paper, using this method, we compute three cases of complex eigenvalue/vector distributions of symmetric order-three random tensors, where the three cases can be characterized by the Lie-group invariances, |$O(N,\mathbb {R})$|⁠ , |$O(N,\mathbb {C})$|⁠ , and |$U(N,\mathbb {C})$|⁠ , respectively. Exact closed-form expressions of the distributions are obtained by computing partition functions of four-fermi theories, where the last case is of the "signed" distribution, which counts the distribution with a sign factor coming from a Hessian matrix. As an application, we compute the injective norm of the complex symmetric order-three random tensor in the large- N limit by computing the edge of the last signed distribution, obtaining agreement with an earlier numerical result in the literature. [ABSTRACT FROM AUTHOR]

Cortical neurons integrate upstream signals and random electrical noise to gate signaling outcomes, leading to statistically random patterns of activity. Yet classically, the neuron is modeled as a binary computational unit, encoding Shannon entropy. Here, the neuronal membrane potential is modeled as a function of inherently probabilistic ion behavior. In this new model, each neuron computes the probability of transitioning from an off-state to an on-state, thereby encoding von Neumann entropy. Component pure states are integrated into a physical quantity of information, and the derivative of this high-dimensional probability distribution yields eigenvalues across the multi-scale quantum system. In accordance with the Hellman–Feynman theorem, the resolution of the system state is paired with a spontaneous shift in charge distribution, so this defined system state instantly becomes the past as a new probability distribution emerges. This mechanistic model produces testable predictions regarding the wavelength of free energy released upon information compression and the temporal relationship of these events to physiological outcomes. Overall, this model demonstrates how cortical neurons might achieve non-deterministic signaling outcomes through a computational process of noisy coincidence detection. [ABSTRACT FROM AUTHOR]

Quantum logic (QL) and fuzzy logic (FL) have been gaining attention nowadays due to its potential to be used in quantum computing and information theory. This paper aims to provide a comprehensive overview of QL models of fuzzy representations viz. fuzzy sets (FSs), interval valued fuzzy sets (IVFSs), intuitionistic fuzzy sets (IFSs) and interval valued intuitionistic fuzzy sets (IVIFSs). These QL models can be used to analyze the behavior of quantum logical systems in a fuzzy environment, which is particularly useful for dealing with uncertainty and imprecision in quantum environment. Furthermore, this paper explores the concept of effect algebras (EAs), which are algebraic structures that provide a natural framework for studying FL. Specifically, it is shown that the family of FS, IVFS, IFS and IVIFS can be organized into an EA if the Lukasiewicz operations are considered. This result is significant because EAs can be used to model a wide range of physical and mathematical systems, including quantum systems, and provide a useful tool for analyzing the properties of FL. [ABSTRACT FROM AUTHOR]

The single-letter characterization of the entanglement-assisted capacity of a quantum channel is one of the seminal results of quantum information theory. In this paper, we consider a modified communication scenario in which the receiver is allowed an additional, "inconclusive" measurement outcome, and we employ an error metric given by the error probability in decoding the transmitted message conditioned on a conclusive measurement result. We call this setting postselected communication and the ensuing highest achievable rates the postselected capacities. Here, we provide a precise single-letter characterization of postselected capacities in the setting of entanglement assistance as well as the more general nonsignaling assistance, establishing that they are both equal to the channel's projective mutual information — a variant of mutual information based on the Hilbert projective metric. We do so by establishing bounds on the one-shot postselected capacities, with a lower bound that makes use of a postselected teleportation-based protocol and an upper bound in terms of the postselected hypothesis testing relative entropy. As such, we obtain fundamental limits on a channel's ability to communicate even when this strong resource of postselection is allowed, implying limitations on communication even when the receiver has access to postselected closed timelike curves. [ABSTRACT FROM AUTHOR]

The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble [IEEE Trans. Inf. Theory 66(9) (2020) 5634]. In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation. Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories. [ABSTRACT FROM AUTHOR]

Convex sets of quantum states and processes play a central role in quantum theory and quantum information. Many important examples of convex sets in quantum theory are spectrahedra, that is, sets of positive operators satisfying affine constraints. These examples include sets of quantum states with given expectation values of a set of observables, sets of multipartite quantum states with given marginals, sets of quantum measurements, channels and multitime quantum processes, as well as sets of higher-order quantum maps and quantum causal structures. This contribution provides a characterization of the extreme points of general spectrahedra, and bounds on the ranks of the corresponding operators. The general results are applied to several special cases, and then used to retrieve classic results such as Choi's characterization of the extreme quantum channels, Parthasarathy's characterization of the extreme quantum states with given marginals and the quantum version of Birkhoff's theorem for qubit unital channels. Finally, we propose a notion of positive operator valued measures (POVMs) with general affine constraints for their normalization, and we characterize the extremal POVMs. [ABSTRACT FROM AUTHOR]

The decays of the B meson into vector mesons, observed during the LHCb experiment, provide an ideal laboratory to investigate particle physics phenomena with quantum information theory methods. In this article, we focus on the decays yielding a pair of ϕ mesons to investigate the presence of entanglement in the spin correlations of the system and quantify the amount of Bell inequality violation it entails. Our results show that the present LHCb data allow access to entanglement and to the Bell inequality violation with a significance exceeding the 5 σ threshold in both the cases. This demonstrates that the strong and electroweak interactions responsible for the B meson decay act as a source of entanglement and the quantum mechanics nature of high-energy phenomena. Particular attention is paid to the assessment of loopholes: deficiencies in the experimental setup which could invalidate the results of the Bell test. [ABSTRACT FROM AUTHOR]

Estimating the overlap between two states is an important task with several applications in quantum information. However, the typical swap test circuit can only measure a sole pair of quantum states at a time. In this study, a recursive quantum circuit is designed to measure overlaps of n quantum states | ϕ 1 〉 , | ϕ 2 〉 , ... | ϕ n 〉 concurrently with O (k 2 k) controlled-swap(CSWAP) gates and O (k) ancillary qubits, where k = ⌈ log n ⌉ . All pairwise overlaps among input quantum states | 〈 ϕ i | ϕ j 〉 | 2 can be obtained in this circuit. Compared with existing scheme for measuring the overlap of multiple quantum states, the circuit provides higher precision and less consumption of ancillary qubits. In addition, some simulation experiments are performed on IBM quantum cloud platform to verify the superiority of this algorithm. [ABSTRACT FROM AUTHOR]

Despite the numerous ways now available to quantify which parts or subsystems of a network are most important, there remains a lack of centrality measures that are related to the complexity of information flows and are derived directly from entropy measures. Here, we introduce a ranking of edges based on how each edge's removal would change a system's von Neumann entropy (VNE), which is a spectral-entropy measure that has been adapted from quantum information theory to quantify the complexity of information dynamics over networks. We show that a direct calculation of such rankings is computationally inefficient (or unfeasible) for large networks, since the possible removal of M edges requires that one compute all the eigenvalues of M distinct matrices. To overcome this limitation, we employ spectral perturbation theory to estimate VNE perturbations and derive an approximate edge-ranking algorithm that is accurate and has a computational complexity that scales as O(MN) for networks with N nodes. Focusing on a form of VNE that is associated with a transport operator e-βL, where L is a graph Laplacian matrix and β> 0 is a diffusion timescale parameter, we apply this approach to diverse applications including a network encoding polarized voting patterns of the 117th U.S. Senate, a multimodal transportation system including roads and metro lines in London, and a multiplex brain network encoding correlated human brain activity. Our experiments highlight situations where the edges that are considered to be most important for information diffusion complexity can dramatically change as one considers short, intermediate, and long timescales β for diffusion. [ABSTRACT FROM AUTHOR]

In quantum information theory, the Schmidt rank is a fundamental measure for the entanglement dimension of a pure bipartite state. Its natural definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces, which does not exist (or at least is not canonically given) if the observable algebras of the local systems are allowed to be general C*-algebras. In this work, we generalize the Schmidt rank to the commuting operator framework where the joint system is not necessarily described by the minimal tensor product but by a general bipartite algebra. We give algebraic and operational definitions for the Schmidt rank and show their equivalence. We analyze bipartite states and compute the Schmidt rank in several examples: the vacuum in quantum field theory, Araki–Woods-Powers states, as well as ground states and translation invariant states on spin chains which are viewed as bipartite systems for the left and right half chains. We conclude with a list of open problems for the commuting operator framework. [ABSTRACT FROM AUTHOR]

Triorthogonal matrices were introduced in quantum information theory in connection with distillation of magic states (Bravyi and Haah in Phys Rev A 86:052329, 2012). We give an algorithm to construct binary triorthogonal matrices from binary self-dual codes. Further, we generalize to this setting the classical coding techniques of shortening and extending. We also give some simple propagation rules. [ABSTRACT FROM AUTHOR]

Estimating nonlinear functions of quantum states, such as the moment tr ( ρ m ) , is of fundamental and practical interest in quantum science and technology. Here we show a quantum-classical hybrid framework to measure them, where the quantum part is constituted by the generalized swap test, and the classical part is realized by postprocessing the result from randomized measurements. This hybrid framework utilizes the partial coherent power of the intermediate-scale quantum processor and, at the same time, dramatically reduces the number of quantum measurements and the cost of classical postprocessing. We demonstrate the advantage of our framework in the tasks of state-moment estimation and quantum error mitigation. [ABSTRACT FROM AUTHOR]

Definition: Integrated Fabry–Perot cavities (IFPCs), often referred to as nanobeams due to their form factor and size, have profoundly modified the landscape of integrated photonics as a new building block for classical and quantum engineering. In this entry, the main properties of IFPCs will be summarized from the classical and quantum point of view. The classical will provide some of the main results obtained in the last decade, whereas the quantum point of view will explore cavity quantum electrodynamics (CQED), which promises to revolutionize the future "quantum internet". [ABSTRACT FROM AUTHOR]

Inspired by a conjecture related to numerical investigations for a quantum channel in a system of large size, we shall study relations between two different entropies of a quantum channel. One of them is defined by Gour and Wilde as the generalization of quantum relative entropy and maximally mixed state. The second one is defined as the difference between the entropy of the Choi state of the quantum channel and a constant number. At first, we show that the latter entropy is an upper boundary of the former entropy. Moreover, we also give a sufficient and necessary condition that the two entropies are equal. That is, if and only if the relative entropy reaches its supremum on the maximal entangled pure state in the former entropy. At last, to study the difference between the two entropies, we expect to find some quantum channels in which their related entropies do not reach their supremum on the maximal entangled pure states for the former entropy. By calculating the two entropies, we find that amplitude-damping channels are desired examples. [ABSTRACT FROM AUTHOR]

We obtain formulas for Petz–Rényi and Umegaki relative entropy from the idea of distribution of a positive self-adjoint operator. Classical results on Rényi and Kullback–Leibler divergences are applied to obtain new results and new proofs for some known results about Petz–Rényi and Umegaki relative entropy. Most important among these, is a necessary and sufficient condition for the finiteness of the Petz–Rényi α -relative entropy. All of the results presented here are valid in both finite and infinite dimensions. In particular, these results are valid for states in Fock spaces and thus are applicable to continuous variable quantum information theory. [ABSTRACT FROM AUTHOR]

In the field of Cryptography, Quantum Key Distribution (QKD) is an application of Quantum Information theory that obtained a great deal of attention in recent years. It allows to establish secret keys between two or more parties, in a much safer way than that implemented by classic cryptography (based on discrete logarithms and factorization of prime numbers). The most promising way of realizing a QKD network (especially over great distances) in the near future is by a constellation of satellites. This paper considers the problem of optimizing the orbits of the satellites in order to maximize the minimum key length shared in a network of ground stations over a fixed amount of time. Different networks of stations are considered and the influence of their geographical disposition on the design and the performance index is highlighted. The networks considered are: a global constellation, a regional European constellation, and two in which there are groups of stations in two different narrow bands of latitude. The effect of Inter-satellite links is then taken into account and how, in some cases, they can improve the performances. Finally the daily performance of the considered constellations are analyzed. [ABSTRACT FROM AUTHOR]

In order to study the corrosion effect of vitamin corrosion inhibitor in reinforced concrete systems, the effects of thiamine (VitB1), nicotinic acid (VitB3), pyridoxine (VitB6) and ascorbic acid (VitC) on steel reinforcement in simulated pore solutions of concrete containing chlorine was investigated using dynamic potential polarization and electrochemical impedance spectroscopy tests. The mechanism of vitamin corrosion inhibition on steel reinforcement was also discussed based on density general function theory with quantum chemical calculations. The results show that VitB6 has the best corrosion inhibition effect in simulated pore solution of concrete containing 0.05 mol/L NaCl because of the strongest bonding stability between its highest occupied molecular orbital and the 3d orbital of iron. All four vitamins have a specific concentration value to achieve the best corrosion inhibition effect IE. At this time, VitB1 and VitB3 are anodic corrosion inhibitors and VitB6 and VitC are mixed corrosion inhibitors. With the increase of vitamin concentration, the IE tends to fluctuate inversely, which is due to the inhibition of cathodic reaction caused by the adsorption of polar groups on steel surface, further aggravating the imbalance between cathode and anode. [ABSTRACT FROM AUTHOR]

Genuine multipartite non‐locality is not only of fundamental interest but also serves as an important resource for quantum information theory. The N$N$‐partite scenario and provide an analytical upper bound on the maximal expectation value of the generalized Svetlichny inequality achieved by an arbitrary N$N$‐qubit system is considered. Furthermore, the constraints on quantum states for which the upper bound is tight are also presented and illustrated by noisy generalized Greenberger‐Horne‐Zeilinger states. Especially, the new techniques proposed to derive the upper bound allow more insights into the structure of the generalized Svetlichny operator and enable us to systematically investigate the relevant properties. As an operational approach, the variation of the correlation matrix defined makes it more convenient to search for suitable unit vectors that satisfy the tightness conditions. Finally, the results give feasible experimental implementations in detecting the genuine multipartite non‐locality and can potentially be applied to other quantum information processing tasks. [ABSTRACT FROM AUTHOR]

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as 'informational entropy'), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same 'modal content'; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks. [ABSTRACT FROM AUTHOR]

This article analyzes the entanglements of feminist commodity activism and state feminism. Feminist commodity activism refers to consumption and commodified communication as modes of feminist political participation. Earlier research on these topics has focused on the business sector and on media and popular culture, largely sidelining the state as a site of feminism. This article addresses the increasingly close relations between consumerism and state politics and asks how feminist commodity activism interacts with state feminism. It draws on two empirical cases in the Nordic welfare state of Finland. The first is Uhana Design, a small-scale fashion business, and its Girl Gang campaign that leans on state feminism. The second is Finland's former leading female politicians' engagements with feminist fashion. By analyzing these cases via three theoretical lenses, business, popular, and state feminism, this article develops the notion of commodified state feminism, paying attention to economic, cultural, and political dimensions of feminist commodity activism and state feminism. It also argues that commodified state feminism is emblematic of the current political context, in which the boundaries between market and politics have become blurred. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the type of monadic bounded L-algebras as L-algebras equipped with two monadic operators, named universal quantifier "∀" and existential quantifier "∃", respectively. First, we investigate the properties of pre-ideals on L-algebras and the pre-ideal generated by a nonempty subset of an L-algebra is defined. Second, we investigate monadic bounded L-algebras and monadic pre-ideals in monadic bounded L-algebras. Moreover, the relation between monadic bounded L-algebras and monadic quantum B-algebras is discussed. Finally, the relations among monadic self-similar L-algebras and other monadic structures are discussed, such as monadic (left) hoops, monadic Wajsberg hoops and monadic MV-algebras. Moreover, we obtain a characterization of monadic bounded L-algebras and monadic bounded self-similar L-algebras by relatively complete subalgebras and m-relatively complete subalgebras, respectively. These results are important to the further study of logical system with monadic operators. [ABSTRACT FROM AUTHOR]

This study investigates the synergy between Classical Machine Learning (CML) and Quantum Machine Learning (QML) in analyzing security datasets, conducting a comparative analysis using models based on QML and CML to evaluate their performance as data sizes and iteration counts increase. The author, specifically, employs popular machine learning methods, including Support Vector Machines (SVM), Neural Networks (NN), and Logistic Regression (LR), to assess these techniques on real-world security datasets, such as network intrusion detection data and malware classification logs. The primary focus is determining the effectiveness and efficiency of QML and CML approaches in handling large-scale security data. Through rigorous experimentation, the study highlights the benefits and drawbacks of both QML and CML, indicating that while QML offers significant speedups in processing times for large datasets due to quantum parallelism, it faces challenges in terms of hardware accessibility and noise sensitivity, while CML methods, though slower with massive data, benefit from mature algorithms and more robust infrastructure. The outcomes provide critical insights into the practicality of applying QML and CML to security-related applications, demonstrating that QML techniques can outperform CML in specific scenarios, such as real-time threat detection, due to their superior computational efficiency. However, the current limitations of quantum hardware suggest that CML remains more practical for many applications in the short term. This work significantly advances the state of the art in Quantum Machine Learning. It offers vital guidance for practitioners and researchers in security data analysis, underscoring the potential of QML to revolutionize security data processing while acknowledging the ongoing need for advancements in quantum computing technology. [ABSTRACT FROM AUTHOR]

The resource theory of imaginarity studies the operational value of imaginary parts in quantum states, operations, and measurements. Here we introduce and study the distillation and conversion of imaginarity in distributed scenario. This arises naturally in bipartite systems where both parties work together to generate the maximum possible imaginarity on one of the subsystems. We give exact solutions to this problem for general qubit states and pure states of arbitrary dimension. We present a scenario that demonstrates the operational advantage of imaginarity: the discrimination of quantum channels without the aid of an ancillary system. We then link this scenario to local operations and classical communications(LOCC) discrimination of bipartite states. We experimentally demonstrate the relevant assisted distillation protocol, and show the usefulness of imaginarity in the aforementioned two tasks. This work examines imaginarity as a resource in quantum information theory. The authors extend the resource theory of imaginarity to distributed scenarios, discuss the operational meaning and its role in channel discrimination. [ABSTRACT FROM AUTHOR]

In this paper, we present a new application of group theory to develop a systematical approach to efficiently compute the Schmidt numbers. The Schmidt number is a natural quantification of entanglement in quantum information theory, but computing its exact value is generally a challenging task even for very concrete examples. We exhibit a complete characterization of all orthogonally covariant k-positive maps. This result generalizes earlier results by Tomiyama (Linear Algebra Appl 69:169–177, 1985). Furthermore, we optimize duality relations between k-positivity and Schmidt numbers under group symmetries. This new approach enables us to transfer the results of k-positivity to the computation of the Schmidt numbers of all orthogonally invariant quantum states. [ABSTRACT FROM AUTHOR]

The group of matrices P 1 of Pauli is a finite 2-group of order 16 and plays a fundamental role in quantum information theory, since it is related to the quantum information on the 1-qubit. Here we show that both P 1 and the Pauli 2-group P 2 of order 64 on 2-qubits, other than in quantum computing, can also appear in dynamical systems which are described by non-self-adjoint Hamiltonians. This will allow us to represent P 1 and P 2 in terms of pseudofermionic operators. [ABSTRACT FROM AUTHOR]

The problem of evaluating the differences between quantum states before and after being affected by errors encoded in unitary transformations is addressed. Standard distance functions, e.g., the Bures length, are not fully adequate for such a task. Weighted distances are instead the appropriate information measures to quantify the distinguishability of multipartite states. Here, the previously introduced weighted Bures length and the newly defined weighted Hilbert‐Schmidt distance are employed to quantify how much single‐qubit Pauli errors alter cluster states. For both types of weighted distances, it is found that different errors of the same dimension change cluster states in a different way, i.e., their detectability is in general different. Indeed, they transform an ideal cluster state into a state whose weighted distances from the input depends on the specific chosen Pauli rotation, as well as the position of the affected qubit in the graph related to the cluster state. As these features are undetected by using standard distances, the study proves the usefulness of weighted distances to monitor key but elusive properties of many‐body quantum systems. [ABSTRACT FROM AUTHOR]

The rate and security of quantum communications between users placed at arbitrary points of a quantum communication network depend on the structure of the network, on its extension and on the nature of the communication channels. In this work we propose a strategy for the optimization of trusted-relays based networks that intertwines classical network approaches and quantum information theory. Specifically, by suitably defining a quantum communication efficiency functional, we identify the optimal quantum communication connections through the network by balancing security and the quantum communication rate. The optimized network is then constructed as the network of the maximal quantum communication efficiency connections and its performance is evaluated by studying the scaling of average properties as functions of the number of nodes and of the network spatial extension. [ABSTRACT FROM AUTHOR]

The present publication considers implementing an online control proctoring system, with the possibility of using methods and models of pattern recognition using algorithmic quantum computing to conduct online exams. The study's object is the protection method within infrastructure proctoring systems in education. The study aims to create a security system for proctoring technology infrastructure in education. The article proposes an alternative approach to building protection systems with an effective recognition model using algorithmic quantum computing in proctoring platforms. This study addresses these issues and proposes a novel approach to generating a random cryptographic key using multimodal biometric technology. A presented quantum algorithm method for computer simulation of the data processing quantum principles allows studying and analysing how the created model for transforming a classical image into a quantum state works. This method also shows the possibilities of quantum information theory in interpreting classical problems or how to optimise the same, taking into account the development of methods for the functioning of models and algorithms for quantum computing, data protection and security of online video communications in a proctoring system in an educational environment. The novelty of this research is expressed primarily in the constant updating and addition of authentication systems using quantum computing in various aspects, including the proctoring system in the educational environment. The practical significance is due to the need in the current situation to attract attention to existing problems in structuring the infrastructure of a monitoring system within planning and coordinating the protection, thereby enhancing learning outcomes by eliminating security flaws using a quantum computing algorithm for pattern recognition. [ABSTRACT FROM AUTHOR]

Quantum Entanglement is one of the key manifestations of quantum mechanics that separate the quantum realm from the classical one. Characterization of entanglement as a physical resource for quantum technology became of uppermost importance. While the entanglement of bipartite systems is already well understood, the ultimate goal to cope with the properties of entanglement of multipartite systems is still far from being realized. This paper covers characterization of multipartite entanglement using algebraic-geometric tools. First, we establish an algorithm to classify multipartite entanglement by k -secant varieties of the Segre variety and ℓ -multilinear ranks that are invariant under Stochastic Local Operations with Classical Communication (SLOCC). We present a fine-structure classification of multiqubit and tripartite entanglement based on this algorithm. Another fundamental problem in quantum information theory is entanglement transformation that is quite challenging regarding to multipartite systems. It is captivating that the proposed entanglement classification by algebraic geometry can be considered as a reference to study SLOCC and asymptotic SLOCC interconversions among different resources based on tensor rank and border rank, respectively. In this regard, we also introduce a new class of tensors that we call persistent tensors and construct a lower bound for their tensor rank. We further cover SLOCC convertibility of multipartite systems considering several families of persistent tensors. [ABSTRACT FROM AUTHOR]

The symplectic eigenvalues play a significant role in the finite-mode quantum information theory, and Williamson's normal form proves to be a valuable tool in this area. Understanding the symplectic spectrum of a Gaussian Covariance Operator is a crucial task. Recently, in 2018, an infinite-dimensional analogue of Williamson's Normal form was discovered, which has been instrumental in studying the infinite-mode Gaussian quantum states. However, most existing results pertain to finite-dimensional operators, leaving a dearth of literature in the infinite-dimensional context. The focus of this article is on employing approximation techniques to estimate the symplectic spectrum of certain infinite-dimensional operators. These techniques are well-suited for a particular class of operators, including specific types of infinite-mode Gaussian Covariance Operators. Our approach involves computing the Williamson's Normal form and deriving bounds for the symplectic spectrum of these operators. As a practical application, we explicitly compute the symplectic spectrum of Gaussian Covariance Operators. Through this research, we aim to contribute to the understanding of symplectic eigenvalues in the context of infinite-dimensional operators, opening new avenues for exploration in quantum information theory and related fields. [ABSTRACT FROM AUTHOR]

Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that a better model consists of random tensor networks with link states that are not maximally entangled, i.e., have non-trivial spectra. In this work, we initiate a systematic study of the entanglement properties of these networks. We employ tools from free probability, random matrix theory, and one-shot quantum information theory to study random tensor networks with bounded and unbounded variation in link spectra, and in cases where a subsystem has one or multiple minimal cuts. If the link states have bounded spectral variation, the limiting entanglement spectrum of a subsystem with two minimal cuts can be expressed as a free product of the entanglement spectra of each cut, along with a Marchenko–Pastur distribution. For a class of states with unbounded spectral variation, analogous to semiclassical states in quantum gravity, we relate the limiting entanglement spectrum of a subsystem with two minimal cuts to the distribution of the minimal entanglement across the two cuts. In doing so, we draw connections to previous work on split transfer protocols, entanglement negativity in random tensor networks, and Euclidean path integrals in quantum gravity. [ABSTRACT FROM AUTHOR]

Both bosons and fermions satisfy a strong version of Leibniz's Principle of the Identity of Indiscernibles (PII), and so are ontologically on a par with respect to the PII. This holds for non-entangled, non-product states and for physically entangled states—as it has been established in previous work. In this paper, the Leibniz strategy is completed by including the (bosonic) symmetric product states. A new understanding of Pauli's Exclusion Principle is provided, which distinguishes bosons from fermions in a peculiar ontological way. Finally, the program as a whole is defended against substantial objections. [ABSTRACT FROM AUTHOR]

In this article, we investigate meandric systems having one shallow side: the arch configuration on that side has depth at most two. This class of meandric systems was introduced and extensively examined by I. P. Goulden, A. Nica, and D. Puder [Int. Math. Res. Not. IMRN 2020 (2020), 983-1034]. Shallow arch configurations are in bijection with the set of interval partitions. We study meandric systems by using moment-cumulant transforms for noncrossing and interval partitions, corresponding to the notions of free and Boolean independence, respectively, in non-commutative probability. We obtain formulas for the generating series of different classes of meandric systems with one shallow side by explicitly enumerating the simpler, irreducible objects. In addition, we propose random matrix models for the corresponding meandric polynomials, which can be described in the language of quantum information theory, in particular that of quantum channels. [ABSTRACT FROM AUTHOR]

Introduction: The sustainable development of China's food system is an essential requirement for realizing the digital transformation of agriculture and rural areas and the main target for the big release of agricultural and rural digitalization dividends and the scale of feedback. What are the current trends of change in China's agricultural and rural digitization and sustainable development of the food system? Have they achieved a high level of coordinated development? What are the factors constraining their coordinated development? Methods: This work is based on 30 Chinese provincial administrative areas from 2011 to 2020. We adopt the entropy weight method to calculate the comprehensive development index of the agricultural and rural digitization and food system sustainability, respectively. The coupling degree and coupling coordination degree of the two systems are calculated by applying the coupling coordination degree model. The obstacle degree model was used to diagnose the obstacles constraining the coupling and coordinated development of the coupled systems. Results: This study found that the development index of China's provincial agricultural and rural digitization and food system sustainability increased gradually from 2011 to 2020. The coupling of the two systems is mainly in the high-level coupling stage, but the coupling coordination degree is primarily in the low and medium coupling coordination intervals. These results are heterogeneous across China's four geographic regions: east, center, west, and northeast. The level of rural digital platform construction and rural digital industrialization is the most essential indicator-level and element-level barriers to agricultural and rural digitalization, respectively. Per capita food possession and food stability are, respectively, the most critical indicator-level and elementlevel barriers to the food system sustainability. Discussion: The research in this work contributes to a comprehensive understanding of the evolutionary trends in agriculture and rural digitalization and the food system sustainability in the country as a whole and within the country. Although the two systems have not achieved a high level of coordinated development, the coupling degree and coupled coordination degree show a positive feedback relationship. The analysis of the obstacle factors helps to recognize the main bottlenecks constraining the coupled and coordinated development of the systems at a more specific level. [ABSTRACT FROM AUTHOR]

Quantum noise has always been an important issue in the field of quantum information transmission. As the localization of quantum noise, local quantum Bernoulli noises (LQBNs) have attracted extensive attention in recent years. In this paper, the quantum conditional entropy based on LQBNs is deeply discussed, and a new definition of quantum conditional entropy is given. Then we find that this quantum conditional entropy has some basic properties such as concavity, conditional reduced entropy and unitary invariance. This research is of great significance to the field of quantum information, which can help us to understand the influence of local quantum noises on quantum information transmission. [ABSTRACT FROM AUTHOR]

Maximum distance separable (MDS) quantum error-correcting codes (QECCs) and MDS entanglement-assisted QECCs (EAQECCs) play significant roles in quantum information theory. In this paper, we construct several new families of MDS QECCs and MDS EAQECCs by utilizing Hermitian self-orthogonal generalized Reed–Solomon codes. These newly obtained MDS QECCs contain some known classes of MDS QECCs as subclasses and some of them have larger minimum distance. In addition, many q-ary MDS QECCs and MDS EAQECCs in our constructions have length exceeding q + 1 and minimum distance surpassing q 2 + 1 . [ABSTRACT FROM AUTHOR]

Quantum coherence and quantum correlations are important components of quantum information theory, which play important roles in quantum information processing. In this paper, we quantify correlations from coherence. The correlations relative to channels via metric-adjusted skew information are put forward. The corresponding results are suitable for special channels, such as positive operator-valued measurements (POVMs), projection measurements and von Neumann measurements. In addition, we discuss the dynamics of quantum correlations in the Bell-diagonal state relative to some classical channels via metric-adjusted skew information. The typical two are the Werner state and the isotropic state. We find that some separable states in entanglement resources theory possess correlations. It also shows quantum channels will disturb quantum states and have a great influence on the correlations. The correlations relative to different channels via different versions of metric-adjusted skew information have their advantages. This has inspired one to study the problem of the existence and action of various quantum correlations in quantum theory to be easily applied to experiments. [ABSTRACT FROM AUTHOR]

According to information theories of legislative organizations, legislators depend on policy expertise from committees to make decisions. Expertise may also be derived from knowledge held by individual legislators, typically knowledge from their professional backgrounds. Research has shown that legislators sponsor (or patron) bills related to their professional backgrounds and other legislators defer to their expertise. Moreover, bills sponsored by legislators with professional expertise are more likely to advance through the legislative process. This paper considers the role of information derived from professional background on the patronage and passage of healthrelated legislation in the Virginia General Assembly. In so doing, the paper takes a unique approach. Whereas most studies classify legislators in terms of their professional field, this analysis probes more deeply by assessing the effects of a legislators' current or former occupations within their professional field. This paper finds that occupational background is even more influential than the professional field of a legislator on bill patronage and bill passage. The effects of occupational background hold up against alternative explanations such as committee membership, majority party status, or gender in determining bill patronage and passage rates. [ABSTRACT FROM AUTHOR]

Entanglement in many‐body systems may display quantum phase transition signatures, and analogous insights are emerging in the study of work fluctuations. Here, the fermionic superfluid‐to‐insulator transition (SIT) is considered and related to its entanglement properties and its work distribution statistics. Using the attractive fermionic Hubbard model with randomly distributed impurities, the work distribution is analyzed under two quench protocols triggering the SIT. In the first, the concentration of impurities is increased; in the second, the impurities' disorder strength is varied. The results indicate that, at criticality, the entanglement is minimized while the average work is maximized. This study demonstrates that, for this state, density fluctuations vanish at all orders, resulting in all central moments of the work probability distribution being precisely zero. For systems undergoing a precursor to the transition (short chains with finite impurity potential) numerical results confirm these predictions, with higher moments further from the ideal results. For both protocols, at criticality, the system absorbs the most energy with almost no penalty in terms of fluctuations: ultimately this feature can be used to implement a quantum critical battery. The impact of temperature on this critical behaviour is also investigated and shown to favor work extraction for high enough temperatures. [ABSTRACT FROM AUTHOR]