Search

We review some recent results on the mathematical foundations of a quantum theory over a scalar field that is a quadratic extension of the non-Archimedean field of p -adic numbers. In our approach, we are inspired by the idea — first postulated in [I. V. Volovich, p -adic string, Class. Quantum Grav. 4 (1987) L83–L87] — that space, below a suitably small scale, does not behave as a continuum and, accordingly, should be modeled as a totally disconnected metrizable topological space, ruled by a metric satisfying the strong triangle inequality. The first step of our construction is a suitable definition of a p -adic Hilbert space. Next, after introducing all necessary mathematical tools — in particular, various classes of linear operators in a p -adic Hilbert space — we consider an algebraic definition of physical states in p -adic quantum mechanics. The corresponding observables, whose definition completes the statistical interpretation of the theory, are introduced as SOVMs, a p -adic counterpart of the POVMs associated with a standard quantum system over the complex numbers. Interestingly, it turns out that the typical convex geometry of the space of states of a standard quantum system is replaced, in the p -adic setting, with an affine geometry; therefore, a symmetry transformation of a p -adic quantum system may be defined as a map preserving this affine geometry. We argue that, as a consequence, the group of all symmetry transformations of a p -adic quantum system has a richer structure with respect to the case of standard quantum mechanics over the complex numbers. [ABSTRACT FROM AUTHOR]

Quantum mechanics is arguably our most successful physical theory, yet the nature of the quantum state still constitutes an ongoing controversy. This paper proposes, articulates, and defends a metaphysical interpretation of the quantum state that is fictionalist in spirit since it regards quantum states as representing a fictional ontology. Such an ontology is therefore not physical, and yet it provides a reference for the language used in quantum mechanics and has explanatory power. In this sense, this view, akin to Allori’s recent account of wavefunctionalism, combines elements of the representationalist and anti-representationalist camps and aims to be the best of both worlds. [ABSTRACT FROM AUTHOR]

We present a criterion to establish the local continuity of the relative entropy of resource, i.e. the relative entropy distance to the set of free states, in any quantum resource theory. Several basic corollaries of this criterion are presented. Applications to the relative entropy of entanglement in multipartite quantum systems are considered. It is shown, in particular, that local continuity of any relative entropy of multipartite entanglement follows from local continuity of the quantum mutual information. [ABSTRACT FROM AUTHOR]

In a recent paper (Found Phys 54:14, 2024), Carcassi, Oldofredi and Aidala concluded that the ψ -ontic models defined by Harrigan and Spekkens cannot be consistent with quantum mechanics, since the information entropy of a mixture of non-orthogonal states are different in these two theories according to their information theoretic analysis. In this paper, I argue that this no-go theorem for ψ -ontic models is false by explaining the physical origin of the von Neumann entropy in quantum mechanics. [ABSTRACT FROM AUTHOR]

The focus of this Visualization Viewpoints article is to provide some background on quantum computing (QC), to explore ideas related to how visualization helps in understanding QC, and examine how QC might be useful for visualization with the growth and maturation of both technologies in the future. In a quickly evolving technology landscape, QC is emerging as a promising pathway to overcome the growth limits in classical computing. In some cases, QC platforms offer the potential to vastly outperform the familiar classical computer by solving problems more quickly or that may be intractable on any known classical platform. As further performance gains for classical computing platforms are limited by diminishing Moore's Law scaling, QC platforms might be viewed as a potential successor to the current field of exascale-class platforms. While present-day QC hardware platforms are still limited in scale, the field of quantum computing is robust and rapidly advancing in terms of hardware capabilities, software environments for developing quantum algorithms, and educational programs for training the next generation of scientists and engineers. After a brief introduction to QC concepts, the focus of this article is to explore the interplay between the fields of visualization and QC. First, visualization has played a role in QC by providing the means to show representations of the quantum state of single-qubits in superposition states and multiple-qubits in entangled states. Second, there are a number of ways in which the field of visual data exploration and analysis may potentially benefit from this disruptive new technology though there are challenges going forward.

General methods of local continuity analysis of characteristics of infinite-dimensional composite quantum systems are considered. A new approximation technique for obtaining local continuity conditions for various characteristics of quantum systems is proposed and described in detail. This technique is used to prove several general results (a Simon-type dominated convergence theorem, a theorem on the preservation of continuity under convex mixtures, etc.). Local continuity conditions are derived for the following characteristics of composite quantum systems: the quantum conditional entropy, the quantum (conditional) mutual information, the one-way classical correlation and its regularization, the quantum discord and its regularization, the entanglement of formation and its regularization, and the constrained Holevo capacity of a partial trace and its regularization. [ABSTRACT FROM AUTHOR]

We obtain a representation of the set of quantum states in terms of barycenters of nonnegative normalized finitely additive measures on the unit sphere of a Hilbert space . For a measure on , we find conditions in terms of its properties under which the barycenter of this measure belongs to the set of extreme points of the family of quantum states and to the set of normal states. The unitary elements of a unital -algebra are characterized in terms of extreme points. We also study extreme points of the unit ball of a normed ideal operator space on . If for some unitary operator , then for all unitary operators . In addition, we construct quantum correlations corresponding to singular states on the algebra of all bounded operators in a Hilbert space. [ABSTRACT FROM AUTHOR]

There are many tricky optimization problems in real life, and metaheuristic algorithms are the most effective way to solve optimization problems at a lower cost. The dung beetle optimization algorithm (DBO) is a more innovative algorithm proposed in 2022, which is affected by the action of dung beetles such as ball rolling, foraging, and reproduction. Therefore, A dung beetle optimization algorithm is proposed based on quasi-oppositional learning and Q-learning (QOLDBO). First, the quantum state update idea is cleverly integrated into quasi-oppositional learning to increase the randomness of the generated population. And the best behavior pattern is selected by adding Q-learning in the rolling stage to improve the search effect. In addition, the variable spiral local domain method is proposed to make up for the shortage of developing only around the neighborhood optimum. For the optimal solution of each iteration, the dimensional adaptive Gaussian variation is selected and the optimal solution is retained. Experimental performance tests show that QOLDBO performs well in both benchmark test functions and CEC 2017. Simultaneously, the validity of the algorithm is verified on several classical practical application engineering problems.

Using density functional theory in the noncollinear approximation, the behavior of quantum states of hole qubits in a Ge/Co:ZnO system was studied in this work. A detailed analysis of the electronic structure and the distribution of total charge density and hole states was carried out. It was shown that in the presence of holes, the energetically more favorable quantum state is the state |0˃, in contrast to the state |1˃ when there is no hole in the system. The favorability of hole states was found to be dependent on the polarity of the applied electric field. [ABSTRACT FROM AUTHOR]

We consider a quasi-classical version of the Alicki–Fannes–Winter technique widely used for quantitative continuity analysis of characteristics of quantum systems and channels. This version allows us to obtain continuity bounds under constraints of different types for quantum states belonging to subsets of a special form that can be called “quasi-classical”. Several applications of the proposed method are described. Among others, we obtain the universal continuity bound for the von Neumann entropy under the energy-type constraint which in the case of one-mode quantum oscillator is close to the specialized optimal continuity bound presented recently by Becker, Datta and Jabbour. We obtain semi-continuity bounds for the quantum conditional entropy of quantum-classical states and for the entanglement of formation in bipartite quantum systems with the rank/energy constraint imposed only on one state. Semi-continuity bounds for entropic characteristics of classical random variables and classical states of a multi-mode quantum oscillator are also obtained. [ABSTRACT FROM AUTHOR]

There are many tricky optimization problems in real life, and metaheuristic algorithms are the most effective way to solve optimization problems at a lower cost. The dung beetle optimization algorithm (DBO) is a more innovative algorithm proposed in 2022, which is affected by the action of dung beetles such as ball rolling, foraging, and reproduction. Therefore, A dung beetle optimization algorithm is proposed based on quasi-oppositional learning and Q-learning (QOLDBO). First, the quantum state update idea is cleverly integrated into quasi-oppositional learning to increase the randomness of the generated population. And the best behavior pattern is selected by adding Q-learning in the rolling stage to improve the search effect. In addition, the variable spiral local domain method is proposed to make up for the shortage of developing only around the neighborhood optimum. For the optimal solution of each iteration, the dimensional adaptive Gaussian variation is selected and the optimal solution is retained. Experimental performance tests show that QOLDBO performs well in both benchmark test functions and CEC 2017. Simultaneously, the validity of the algorithm is verified on several classical practical application engineering problems. [ABSTRACT FROM AUTHOR]

The continuous progress of the network and big data has brought far-reaching influence and potential opportunities to traditional painting design, and at the same time, it continues to shape the content and form of its artistic style. This paper employs the quantum image enhancement algorithm to transform the traditional painting image into a quantum pure state. Subsequently, it segments each pixel to extract edge information, thereby constructing the traditional painting image state. Next, we employ the quantum image color enhancement algorithm to amplify the color aesthetics of the extracted image state, thereby fostering innovation. Finally, this paper proposes an innovative approach to traditional painting styles using quantum information technology. This paper proposes a quantum image enhancement algorithm that outperforms the classical program in all quality indicators after processing traditional painting images, thereby establishing a theoretical foundation for future research. The study found that traditional paintings made with the help of a quantum image enhancement algorithm have a higher quality of art style innovation and artistic value. The study also found that both types of works, plants (4.37 points) and myths (4.50 points), got higher scores on the tests. This paper brings a fresh perspective to the creation of traditional painting art, paving the way for a more intelligent and diverse future for this genre.

We consider methods for obtaining local lower bounds on characteristics of quantum (resp. classical) systems, i.e., lower bounds valid in the trace norm -neighborhood of a given state (resp. probability distribution). Our basic tool is the quasi-classical modification of the Alicki–Fannes–Winter technique which gives faithful one-side continuity bounds with the rank/energy constraint imposed on only one of the two quantum states (resp. probability distributions). We also propose a new universal method that allows us to obtain easy computable faithful local lower bounds on many important characteristics of quantum (resp. classical) systems. The main attention is paid to infinite-dimensional systems. [ABSTRACT FROM AUTHOR]

Quantum codes are crucial building blocks of quantum computers. With a self-dual quantum code is attached, canonically, a unique stabilised quantum state. Improving on a previous publication, we show how to determine the coefficients on the basis of kets in these states. Two important ingredients of the proof are algebraic graph theory and quadratic forms. The Arf invariant, in particular, plays a significant role. [ABSTRACT FROM AUTHOR]

A quantum stochastic product is defined as a binary operation on the convex set of quantum states that preserves the convex structure. We discuss a class of group-covariant, associative stochastic products, the twirled products, having remarkable connections with quantum measurement theory and with the theory of open quantum systems. By extending this binary operation from the density operators to the full Banach space of trace class operators, one obtains a Banach algebra. In the case where the covariance group is the group of phase-space translations, one has a quantum convolution algebra. The expression of the quantum convolution in terms of Wigner distributions and of the associated characteristic functions is analyzed. [ABSTRACT FROM AUTHOR]

The properties of an initial-boundary value problem for a nonlinear Schödinger equation including terms with a delay of the time argument in the nonlinear potential or in whole part of the nonlinear term are studied. Conditions of local and global existence or arising of a gradient blow up phenomenon are obtained. The relation of a gradient blow up phenomenon with a self-focusing and a destruction of a pure quantum state are described. We consider an evolution of a quantum state generated by a solution of a nonlinear Schrödinger equation as a curve in the set of pure quantum states. We introduce the regularization procedure, which defines a continuation of a solution through the moment of blow up by a curve in the set of quantum states with the transition into the set of mixed states. [ABSTRACT FROM AUTHOR]

We propose a model of a quantum N -dimensional system (quNit) based on a quadratic extension of the non-Archimedean field of p-adic numbers. As in the standard complex setting, states and observables of a p-adic quantum system are implemented by suitable linear operators in a p-adic Hilbert space. In particular, owing to the distinguishing features of p-adic probability theory, the states of an N -dimensional p-adic quantum system are implemented by p-adic statistical operators, i.e., trace-one selfadjoint operators in the carrier Hilbert space. Accordingly, we introduce the notion of selfadjoint-operator-valued measure (SOVM)—a suitable p-adic counterpart of a POVM in a complex Hilbert space—as a convenient mathematical tool describing the physical observables of a p-adic quantum system. Eventually, we focus on the special case where N = 2 , thus providing a description of p-adic qubit states and 2-dimensional SOVMs. The analogies—but also the non-trivial differences—with respect to the qubit states of standard quantum mechanics are then analyzed. [ABSTRACT FROM AUTHOR]

Using density functional theory in the noncollinear approximation, the behavior of quantum states of hole qubits in a Ge/Co:ZnO system was studied in this work. A detailed analysis of the electronic structure and the distribution of total charge density and hole states was carried out. It was shown that in the presence of holes, the energetically more favorable quantum state is the state |0˃, in contrast to the state |1˃ when there is no hole in the system. The favorability of hole states was found to be dependent on the polarity of the applied electric field.

We consider the task of communicating a generic bivariate function of two classical correlated sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. We first propose a coding scheme based on asymptotically good algebraic structured codes, in particular, nested coset codes, and provide a set of sufficient conditions for the reconstruction of the function of the sources over a CQ-MAC. The proposed technique enables the decoder to recover the desired function without recovering the sources themselves. We further improve this by employing a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes. This coding scheme allows exploiting the symmetric structure common amongst the sources and also leverage the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources whose function can be reconstructed over any given CQ-MAC, and identify examples demonstrating the same. We provide these conditions in terms of single-letter quantum information-theoretic quantities. [ABSTRACT FROM AUTHOR]

In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob’s side. We investigate the efficiency of our scheme discussing both deterministic and probabilistic case, where parties share maximally entangled states. It turns out that the new scheme gives better performance than various variants of the optimal PBT protocol used for the same task. All the results are presented in group-theoretic manner depending on such quantities like dimensions and multiplicities of irreducible representations in the Schur-Weyl duality. The presented analysis was possible by considering the algebra of permutation operators acting on $n$ systems distorted by the action of partial transposition acting on more than one subsystem. Considering its action on the $n-$ fold tensor product of the Hilbert space with finite dimension, we present construction of the respective irreducible matrix representations, which are in fact matrix irreducible representations of the Walled Brauer Algebra. I turns out that the introduced formalism, and symmetries beneath it, appears in many aspects of theoretical physics and mathematics - theory of anti ferromagnetism, aspects of gravity theory or in the problem of designing quantum circuits for special task like for example inverting an unknown unitary. [ABSTRACT FROM AUTHOR]

The link between classical and quantum theories is discussed in terms of extensional and intensional viewpoints. The paper aims to bring evidence that classical and quantum probabilities are related by intensionalization, which means that by abandoning sets from classical probability one should obtain quantum theory. Unlike the extensional concept of a set, the intensional probability is attributed to the quantum ensemble, which is contextually dependent. The contextuality offers a consistent realization of the measurement problem, which should require the existence of the time operator. The time continuum by Brouwer has satisfied such a requirement, which makes it fundamental to mathematical physics. The statistical model it provides has been proven tremendously useful in a variety of applications. [ABSTRACT FROM AUTHOR]

We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two orthogonal quantum states of a $n_{A}\times n_{B}$ bipartite quantum system can be discriminated via local measurements with an error probability no larger than $\frac {1}2 \left ({1 - \frac {1}{c \min \{n_{A}, n_{B}\}} }\right)$ , where $1\leq c\leq 2\sqrt {2}$ is a universal constant, and our bound scales provably optimally with the local dimensions $n_{A},n_{B}$. Mathematically, this is achieved by showing that the distinguishability norm $\|\cdot \|_{ \mathrm {LO}}$ associated with local measurements satisfies that $\|\cdot \|_{1}\leq 2\sqrt {2} \min \{n_{A},n_{B}\} \|\cdot \|_{ \mathrm {LO}}$ , where $\|\cdot \|_{1}$ is the trace norm. [ABSTRACT FROM AUTHOR]

In this paper, we establish an interesting duality between two different quantum information-processing tasks, namely, classical source coding with quantum side information, and channel coding over classical-quantum channels. The duality relates the optimal error exponents of these two tasks, generalizing the classical results of Ahlswede and Dueck [IEEE Trans. Inf. Theory, 28(3):430–443, 1982]. We establish duality both at the operational level and at the level of the entropic quantities characterizing these exponents. For the latter, the duality is given by an exact relation, whereas for the former, duality manifests itself in the following sense: an optimal coding strategy for one task can be used to construct an optimal coding strategy for the other task. Along the way, we derive a bound on the error exponent for classical-quantum channel coding with constant composition codes which might be of independent interest. Finally, we consider the task of variable-length classical compression with quantum side information, and a duality relation between this task and classical-quantum channel coding can also be established correspondingly. Furthermore, we study the strong converse of this task, and show that the strong converse property does not hold even in the i.i.d. scenario. [ABSTRACT FROM AUTHOR]

For stochastic quantum systems with measurement feedback, this article proposes a rapid switching control scheme based on state space partition and realizes the rapid stabilization of an eigenstate of an observable operator. Meanwhile, we apply the proposed scheme to the preparation of typical entangled states in multiqubit systems. In view of the convergence obstacle caused by the symmetric structure of the state space, especially in the case with degenerate observable operators, we first partition the state space into a subset containing the target state and its complement to distinguish the target state from its antipodal points, and then design the corresponding control laws in these two subsets, respectively, by using different Lyapunov functions. The interaction Hamiltonians are also constructed to drive the system state to the desired subset first, and further to the target state. In particular, the control law designed in the undesired subset guarantees the strictly monotonic descent of the corresponding Lyapunov function, which makes the system trajectory switch between the two subsets at most twice and has the potential to speed up the convergence process. We also prove the stability of the closed-loop system with the proposed switching control law based on the stochastic Lyapunov stability theory. By applying the proposed switching control scheme to a three-qubit system, we achieve the preparation of a GHZ state and a $W$ state. [ABSTRACT FROM AUTHOR]

Quantum communications is a promising technology that will play a fundamental role in the design of future networks. In fact, significant efforts are being undertaken by both the quantum physics and the classical communications communities on developing new architectures, solutions, and practical implementations of quantum communication networks (QCNs). Although these efforts led to various advances in today's technologies, there still exists a non-trivial gap between the research efforts of the two communities on designing and optimizing the performance of QCNs. For instance, most prior works by the classical communications community ignore important quantum physics-based constraints when designing QCNs. For example, many existing works on entanglement distribution do not account for the decoherence of qubits inside quantum memories and, thus, their designs become impractical since they assume an infinite lifetime of quantum states. In this article, we bring forth a novel analysis of the performance of QCNs in a physics-informed manner, by relying on the quantum physics principles that underly the different components of QCNs. The need for the physics-informed approach is then assessed and its fundamental role in designing practical QCNs is analyzed across various open research areas. Moreover, we identify novel physics-informed performance metrics and controls that enable QCNs to leverage the state-of-theart advancements in quantum technologies to enhance their performance. Finally, we analyze multiple pressing challenges and open research directions in QCNs that must be treated using a physics-informed approach to lead practically viable results. Ultimately, this work attempts to bridge the gap between the classical communications and the quantum physics communities in the area of QCNs to foster the development of the future communication networks toward the quantum Internet. [ABSTRACT FROM AUTHOR]

The preparation of a quantum superposition is the key to the success of many quantum algorithms and quantum machine learning techniques. The preparation of an incomplete or a non-uniform quantum superposition with certain properties is a non-trivial task. In this paper, an $n$ -qubits variational quantum circuit using partial negation and controlled partial negation operators is proposed to prepare a quantum superposition from a given space of probability distributions. The speed of the preparation process and the accuracy of the prepared superposition has special importance to the success of any quantum algorithm. The proposed method can be used to prepare the required quantum superposition in $\mathscr {O}(n)$ steps and with high accuracy when compared with relevant methods in literature.

We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality conditions depend on the channel considered and on an auxiliary state defined on the output space of the channel. For certain $N$ -qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect and, therefore, they feature the smallest error probability among all codes of the same blocklength and cardinality. [ABSTRACT FROM AUTHOR]

We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the context of quantum computing, it corresponds to the least possible amount of data to define and describe a quantum circuit or quantum computer program. Our Kolmogorov complexity of unitary transformation is built upon Kolmogorov "qubit complexity" of Berthiaume, W. Van Dam and S. Laplante via mapping from unitary transformations to unnormalized density operators, which are subsequently "purified" into unnormalized vectors in Hilbert space. We discuss the optimality of our notion of Kolmogorov complexity in a broad sense. [ABSTRACT FROM AUTHOR]

Quantum blockchain is expected to offer an alternative to classical blockchain to resist malicious attacks laughed by future quantum computers. Although a few quantum blockchain schemes have been constructed, their efficiency is low and unable to meet application requirements due to the fact that they lack of a suitable consensus mechanism. To tackle this issue, a consensus mechanism called quantum delegated proof of stake (QDPoS) is constructed by using quantum voting to provide fast decentralization for the quantum blockchain scheme at first. Then an efficient scheme is proposed for quantum blockchain based on QDPoS, where the classical information is initialized as a part of each single quantum state and these quantum states are entangled to form the chain. Compared with previous methods, the designed quantum blockchain scheme is more complete and carried out with higher efficiency, which greatly contributes to better adapting to the challenges of the quantum era. [ABSTRACT FROM AUTHOR]

We describe a generalized version of the result called quantum Dini lemma that was used previously for analysis of local continuity of basic correlation and entanglement measures. The generalization consists in considering sequences of functions instead of a single function. It allows to expand the scope of possible applications of the method. We prove two general dominated convergence theorems and the theorem about preserving local continuity under convex mixtures. By using these theorems we obtain several convergence conditions for the quantum relative entropy and for the mutual information of a quantum channel considered as a function of a pair (channel, input state). [ABSTRACT FROM AUTHOR]

We have successfully fabricated single-layer (SL) 1T-VSe 2 /Bi 2 Se 3 heterostructures using molecular beam epitaxy (MBE), which exhibits uniform moiré patterns on the heterostructure surface. Scanning tunneling microscopy/spectroscopy (STM/STS) reveals a notable quantum state near the Fermi energy, robust across the entire moiré lattice. This quantum state peak shifts slightly across different domain ranges, suggesting an elastic strain dependence in SL VSe 2 , confirmed by geometric phase analysis (GPA) simulations. Density functional theory (DFT) calculations indicate that the enhanced quantum state results from charge redistribution between the substrate and the epifilm with the orbitals of Se atoms in the deformed VSe 2 playing a dominant role.

Quantum codes are crucial building blocks of quantum computers. With a self-dual quantum code is attached, canonically, a unique stabilised quantum state. Improving on a previous publication, we show how to determine the coefficients on the basis of kets in these states. Two important ingredients of the proof are algebraic graph theory and quadratic forms. The Arf invariant, in particular, plays a significant role.

Quantum Key Distribution (QKD) is a promising technology that provides proven unconditional security based on fundamentals of quantum physics, especially for point-to-point communications. It could be applied in large-scale optical networks for long-distance key provisioning mainly by three relaying methods: quantum-repeater-based QKD, trusted-relay-based QKD, and measurement-device-independent QKD (MDI-QKD). However, quantum-repeater-based QKD is still under study because of the immature technologies such as the preliminary quantum memory. The trusted-relay-based QKD is vulnerable since insecurity of non-ideal single-photon sources and detectors cannot be ignored in practical applications. On the other hand, for MDI-QKD, there exists a limitation on its key rate under long-distance communications. According to these limitations, embedding protocols like MDI-QKD into the existing trusted-relay-based QKD secured optical networks (QKD-ON) with usage of untrusted relays is a promising key-provisioning scheme. In this paper, we study such partially-trusted relay scenarios and focus on its routing of keys in different kinds of typical network topologies. A partially-trusted-relay-based QKD method is described, which can allow a pair of optical nodes sharing secret keys under the coexistence of trusted relays and untrusted relays. The secret-key provisioning with collaborative routing (SKP-CR) algorithm is proposed to search for the optimal key-relay routing path. We perform the simulations with different proportion of trusted relays versus untrusted relays, initial secret keys in the quantum key pools (QKPs), and traffic load. The simulations verify that the SKP-CR algorithm can significantly outperform the conventional trusted-relay-based scheme in terms of key-distribution success rate with an improvement of up to 62% with a mesh topology. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of learning an unknown quantum circuit of a certain structure. If the unknown target is an $n$ -qubit Clifford circuit, we devise an efficient algorithm to reconstruct its circuit representation by using $O(n^{2})$ queries to it. For decades, it has been unknown how to handle circuits beyond the Clifford group since the stabilizer formalism cannot be applied in this case. Herein, we study quantum circuits of $T$ -depth one on the computational basis. We show that the output state of a $T$ -depth one circuit can be represented by a stabilizer pseudomixture with a specific algebraic structure. Using Pauli and Bell measurements on copies of the output states, we can generate a hypothesis circuit that is equivalent to the unknown target circuit on computational basis states as input. If the number of $T$ gates of the target is of the order $O({\log n})$ , our algorithm requires $O(n^{2})$ queries to it and produces its equivalent circuit representation on the computational basis in time $O(n^{3})$. Using further additional $O(4^{3n})$ classical computations, we can derive an exact description of the target for arbitrary input states. Our results greatly extend the previously known facts that stabilizer states can be efficiently identified based on the stabilizer formalism. [ABSTRACT FROM AUTHOR]

In the literature on the interpretation of quantum mechanics, not many works attempt to adopt a proactive perspective aimed at seeing how different interpretations can enrich each other through a productive dialogue. In particular, few proposals have been devised to show that different approaches can be clarified by comparing them, and can even complement each other, improving or leading to a more fertile overall approach. The purpose of this paper is framed within this perspective of complementation and mutual enrichment. In particular, the Relational Quantum Mechanics (RQM) and the Modal-Hamiltonian Interpretation (MHI) are compared, highlighting their differences and points of contact. The final purpose is to show that, in spite of their disagreements, they are not contradictory but, on the contrary, they can be made compatible from an overarching perspective and can even complement each other in a fruitful way. [ABSTRACT FROM AUTHOR]

Classification of remotely sensed images (RSIs) is prerequisite for further applications. Of the existing RSI classification algorithms, the self-organizing mapping (SOM) neural network is considered as one of the most effective unsupervised classification algorithms. However, the traditional SOM only considers the Euclidean distance between neurons, which cannot reflect the correlation characteristics of neurons. For this reason, a radical algorithm, called “pixel entanglement (PE) through self-organizing pixel entanglement neural network (SOPENN)” is proposed in this article. First, the pixels in an RSI are considered as called “quantum pixels,” and all of the pixels in a RSI are considered as called “quantum pixel array”; then PE coefficient is proposed to mine the quantum entanglement relationship of quantum pixels on the array space; finally, a self-organizing neural network (SONN) is established to stimulate the PE behavior between quantum pixels. The theory mentioned above is applied in RSI classification to verify the performance of the SOPENN through four study areas. The experimental results demonstrate that: 1) the classification accuracy of SOPENN model proposed in this article averagely increases 8.42% when compared with the traditional unsupervised classification methods, Iterative Selforganizing Data Analysis (ISODATA), K-means, and SOM; and Kappa coefficient (KC) averagely increases 0.14; and 2) the classification accuracy and KC from the proposed SOPENN model reached the same level when compared with the supervised classification (support vector machine (SVM) model) in four study areas. [ABSTRACT FROM AUTHOR]

We consider the most general finite-dimensional quantum mechanical information source, which is given by a quantum system $A$ that is correlated with a reference system $R$. The task is to compress $A$ in such a way as to reproduce the joint source state $\rho ^{AR}$ at the decoder with asymptotically high fidelity. This includes Schumacher’s original quantum source coding problem of a pure state ensemble and that of a single pure entangled state, as well as general mixed state ensembles. Here, we determine the optimal compression rate (in qubits per source system) in terms of the Koashi-Imoto decomposition of the source into a classical, a quantum, and a redundant part. The same decomposition yields the optimal rate in the presence of unlimited entanglement between compressor and decoder, and indeed the full region of feasible qubit-ebit rate pairs. [ABSTRACT FROM AUTHOR]

A quantum-state-based technique for change detection and analysis is presented. The method establishes a framework for change detection based on quantum states’ entanglement concept. The approach is applicable to quantum sensing (QS) (i.e., low field intensity, photon pairs) but is contingent to feasibility of quantum implementations and measurements. The main objective in this work is to develop a new change detection technique for classical radar/synthetic aperture radar (SAR) remote sensing that is inspired by quantum illumination (QI) and exploits the underlying characteristics and mathematical analogy between quantum-states and radar scatter-field-states. The described application of QI concept to develop a quantum signal processing (QSP) algorithm for classical radar/SAR data exploitations introduces a new change detection approach for SAR multi-pol exploitations. [ABSTRACT FROM AUTHOR]

In blind compression of quantum states, a sender Alice is given a specimen of a quantum state $\rho $ drawn from a known ensemble (but without knowing what $\rho $ is), and she transmits sufficient quantum data to a receiver Bob so that he can decode a near perfect specimen of $\rho $. For many such states drawn iid from the ensemble, the asymptotically achievable rate is the number of qubits required to be transmitted per state. The Holevo information is a lower bound for the achievable rate, and is attained for pure state ensembles, or in the related scenario of entanglement-assisted visible compression of mixed states wherein Alice knows what state is drawn. In this paper, we prove a general and robust lower bound on the achievable rate for ensembles of classical states, which holds even in the least demanding setting when Alice and Bob share free entanglement and a constant per-copy error is allowed. We apply the bound to a specific ensemble of only two states and prove a near-maximal separation (saturating the dimension bound in leading order) between the best achievable rate and the Holevo information for constant error. This also implies that the ensemble is incompressible – compression does not reduce the communication cost by much. Since the states are classical, the observed incompressibility is not fundamentally quantum mechanical. We lower bound the difference between the achievable rate and the Holevo information in terms of quantitative limitations to clone the specimen or to distinguish the two classical states. [ABSTRACT FROM AUTHOR]