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We address the problem of coherent state discrimination in the presence of phase diffusion. We investigate the role of the HYbrid Near-Optimum Receiver (HYNORE) we proposed in [J. Opt. Soc. Am. B40 (2023) 705] in the task of mitigating the noise impact. We prove the HYNORE to be a robust receiver, outperforming the Displacement Photon-Number-Resolving (DPNR) receiver and beating the standard quantum limit in particular regimes. We introduce the maximum tolerable phase noise σ max as a figure of merit for the receiver robustness and show that HYNORE increases its value with respect to the DPNR receiver. [ABSTRACT FROM AUTHOR]

Nonlinear mean field dynamics enables quantum information processing operations that are impossible in linear one‐particle quantum mechanics. In this approach, a register of bosonic qubits (such as neutral atoms or polaritons) is initialized into a symmetric product state |ψ⟩⊗n$| \psi \rangle ^{ \! \otimes n }$ through condensation, then subsequently controlled by varying the qubit‐qubit interaction. An experimental implementation of quantum state discrimination, an important subroutine in quantum computation, with a toroidal Bose–Einstein condensate is proposed. The condensed bosons here are atoms, each in the same superposition of angular momenta 0 and ℏ$\hbar$, encoding a qubit. A nice feature of the protocol is that only a readout of individual quantized circulation states (not superpositions) is required. [ABSTRACT FROM AUTHOR]

Different classifier functions can be defined in the framework of a quantum approach to machine learning. While the fidelity-classifier is based on a measure of similarity between quantum states, other classifiers refer to the possibility of an empirical discrimination between different states. An important example is represented by the Helstrom-classifier that has been successfully applied to some empirical simulations, for instance to the study of bio-medical images. An interesting case is represented by the evaluation of clonogenic assays: a technique whose aim is measuring the survival-degree of in vitro-cell cultures, based on the ability of a single cell to grow and to form a colony. In this field a quantum approach allows us to increase the classification-accuracy, in comparison with the corresponding results that are currently obtained in the case of most classical approaches. Some open problems and some possible further developments are mentioned in the conclusion of the article. [ABSTRACT FROM AUTHOR]

The fundamental quantum mechanical features forbid non-orthogonal quantum states to be distinguished accurately through a single-shot measurement. Using parity-time ( P T ) quantum mechanics, however, a perfect state discrimination with certainty can be implemented. Here, we experimentally implement quantum state discrimination for photonic single-qubit states by executing post-selected gates and loss-based non-unitary evolutions in the P T -symmetric system, providing a relatively superior strategy for state discrimination in non-Hermitian systems. We also unveil the origin of P T quantum state discrimination by embedding the P T dynamics into a higher-level system under unitary dynamics. This experimental work demonstrates the key principle of P T quantum state discrimination and opens a door of other effective approaches in the P T -symmetric quantum mechanics. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the unambiguous correct discrimination of three multi-copy quantum states with equal a priori probability. The measurement operators include the success operators and the correct operators. Using this scenario, we introduce the concept of the relative average correct probability, as a function of the average success probability. Based on the analysis of the relative average correct probability, the problem given in Chefles (Phys Rev A 64:062305, 2001) are solved completely. [ABSTRACT FROM AUTHOR]

Consider a quantum system prepared in a state chosen from a known set, the aim of quantum state discrimination is to perform a measurement on the system which can determine that a subset of the possible preparation procedures have been prepared. However, the aim of quantum state exclusion is to perform a measurement on the system which can conclusively rule that a subset of the possible preparation procedures have not taken place. For classical states, probabilities of error in discrimination and exclusion are always equal. For quantum states, we point out that probabilities of error in discrimination and exclusion are still equal in two-state ensembles, however they are no longer equal in multiple-state ensembles. More specifically, the error-probability of discrimination is not less than the error-probability of exclusion. [ABSTRACT FROM AUTHOR]

We investigate minimum-error (ME) discrimination for mixed qubit states using a geometric approach. By analyzing positive operator-valued measure (POVM) solutions and introducing Lagrange operator Γ , we develop a four-step structured instruction to find Γ for N mixed qubit states. Our method covers optimal solutions for two, three, and four mixed qubit states, including a novel result for four qubit states. We introduce geometric-based POVM classes and non-decomposable subsets for constructing optimal solutions, enabling us to find all possible answers for the general problem of minimum-error discrimination for N mixed qubit states with arbitrary a priori probabilities. [ABSTRACT FROM AUTHOR]

In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination.

Models of nonlinear quantum computation based on deterministic positive trace‐preserving (PTP) channels and evolution equations are investigated. The models are defined in any finite Hilbert space, but the main results are for dimension N=2$ N \! = \! 2$. For every normalizable linear or nonlinear positive map ϕ on bounded linear operators X, there is an associated normalized PTP channel ϕ(X)/tr[ϕ(X)]$ \phi (X) / {\rm tr}[\phi (X)]$. Normalized PTP channels include unitary mean field theories, such as the Gross–Pitaevskii equation for interacting bosons, as well as models of linear and nonlinear dissipation. They classify into four types, yielding three distinct forms of nonlinearity whose computational power are explored. In the qubit case, these channels support Bloch ball torsion and other distortions studied previously, where it has been shown that such nonlinearity can be used to increase the separation between a pair of close qubit states, suggesting an exponential speedup for state discrimination. Building on this idea, the authors argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a novel phase where a pair of attracting fixed points create an intrinsically fault‐tolerant nonlinear state discriminator. [ABSTRACT FROM AUTHOR]

We investigate the unambiguous correct discrimination strategy of a set of linearly independent equidistant real quantum states and three sets of three linearly independent states. The measurement operators include the success and correct operators, and can gain more information about the input states than by using the conventional unambiguous discrimination strategy. Five examples are given to demonstrate the efficiency of the unambiguous correct discrimination strategy. [ABSTRACT FROM AUTHOR]

We investigate the unambiguous correct discrimination strategy for discriminating a set of nonorthogonal symmetric qudit states. Restricting to linearly independent and equally likely pure symmetric qudit states, we construct the optimal positive operator valued measure that the measuring operators consist of the success and correct operators. Our strategy can produce the relative average correct probability in correctly identifying each state in the set when the value of the average success probability is optimal as that in the standard unambiguous discrimination strategy. Three examples are given to demonstrate the efficiency of the unambiguous correct discrimination strategy. [ABSTRACT FROM AUTHOR]

Grover's unstructured quantum search algorithm gives a quadratic speedup over classical linear search, provided that multiple accesses to the oracle are possible. In this paper, we show that in dealing with NP-complete decision-version problems, the quantum computing paradigm still outperforms classical computation, even if only one invocation of the oracle is allowed. The superiority of the quantum approach under such a restrictive condition can often be maintained even if a simple measurement strategy is chosen. A quantum decider utilizing only Hadamard gates and measurements in the computational basis has a better chance of discriminating between a problem with solution(s) and one without, when compared to the best separation achieved by a classical decider. In addition, the simple quantum measurement strategy is remarkably close to the optimal discriminating measurement, which itself is considerably more complex to devise and implement. If we further require the decider to be unambiguous (any definitive answer must be error-free), then a general positive operator-valued measurement can be devised to classify a problem as unsolvable, with some probability, after one consultation of the oracle. Such a feature remains impossible for a classical decider, even after any less than exhaustive oracle invocations. The inherent probabilistic nature of quantum mechanics seems to be at the heart of the advantage quantum computing exhibits over classical computation, in the context of deciding NP-complete problems based on a single oracle query. [ABSTRACT FROM AUTHOR]

In the context of quantum-inspired machine learning, remarkable mathematical tools for solving classification problems are given by some methods of quantum state discrimination. In this respect, quantum-inspired classifiers based on nearest centroid and Helstrom discrimination have been efficiently implemented on classical computers. We present a local approach combining the kNN algorithm to some quantum-inspired classifiers. [ABSTRACT FROM AUTHOR]

Few-electron states confined in quantum-dot arrays are key objects in quantum computing. The discrimination between these states is essential for the readout of a (multi-)qubit state, and can be achieved through a measurement of the quantum capacitance within the gate-reflectometry approach. For a system controlled by several gates, the dependence of the measured capacitance on the direction of the oscillations in the voltage space is captured by the quantum capacitance matrix. Herein, we apply this tool to study a double quantum dot coupled to three gates, which enable the tuning of both the bias and the tunneling between the two dots. Analytical solutions for the two-electron case are derived within a Hubbard model, showing the overall dependence of the quantum capacitance matrix on the applied gate voltages. In particular, we investigate the role of the tunneling gate and reveal the possibility of exploiting interdot coherences in addition to charge displacements between the dots. Our results can be directly applied to double-dot experimental setups, and pave the way for further applications to larger arrays of quantum dots. [ABSTRACT FROM AUTHOR]

Abstract Quantum incompatibility is a fundamental property in quantum physics and is considered as a resource in quantum information processing tasks. Here, we construct a framework based on the incompatibility witness originated from quantum state discrimination. In this framework, we discuss the geometrical properties of the witnesses with noisy mutually unbiased bases and construct a quantifier of quantum incompatibility associated with geometrical information. Furthermore, we explore the incompatibility of a pair of positive operator valued measurements, which only depends on the information of measurements, and discuss the incompatibility of measurements which can be discriminated by mutually unbiased bases. Finally, if we take a resource-theory perspective, the new-defined quantifier can characterize the resource of incompatibility. This geometrical framework gives the evidence that vectors can be utilized to describe resourceful incompatibility and make a step to explore geometrical features of quantum resources.

In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination. [ABSTRACT FROM AUTHOR]

Quantum incompatibility is a fundamental property in quantum physics and is considered as a resource in quantum information processing tasks. Here, we construct a framework based on the incompatibility witness originated from quantum state discrimination. In this framework, we discuss the geometrical properties of the witnesses with noisy mutually unbiased bases and construct a quantifier of quantum incompatibility associated with geometrical information. Furthermore, we explore the incompatibility of a pair of positive operator valued measurements, which only depends on the information of measurements, and discuss the incompatibility of measurements which can be discriminated by mutually unbiased bases. Finally, if we take a resource-theory perspective, the new-defined quantifier can characterize the resource of incompatibility. This geometrical framework gives the evidence that vectors can be utilized to describe resourceful incompatibility and make a step to explore geometrical features of quantum resources. [ABSTRACT FROM AUTHOR]

Port-based teleportation (PBT) is a protocol in which Alice teleports an unknown quantum state to Bob using measurements on a shared entangled multipartite state called the port state and forward classical communication. In this paper, we give an explicit proof that the so-called pretty good measurement, or square-root measurement, is optimal for the PBT protocol with independent copies of maximally entangled states as the port state. We then show that the very same measurement remains optimal even when the port state is optimized to yield the best possible PBT protocol. Hence, there is one particular pretty good measurement achieving the optimal performance in both cases. The following well-known facts are key ingredients in the proofs of these results: (i) the natural symmetries of PBT, leading to a description in terms of representation-theoretic data; (ii) the operational equivalence of PBT with certain state discrimination problems, which allows us to employ duality of the associated semidefinite programs. Along the way, we rederive the representation-theoretic formulas for the performance of PBT protocols proved in Studziński et al. (Sci Rep 7(1):1–11, 2017) and Mozrzymas et al. (N J Phys 20(5):053006, 2018) using only standard techniques from the representation theory of the unitary and symmetric groups. Providing a simplified derivation of these beautiful formulas is one of the main goals of this paper. [ABSTRACT FROM AUTHOR]

Complementarity plays a central role in the conceptual development of quantum mechanics, and also provides practical applications in quantum information technologies. How to properly quantify it is an important problem in quantum foundations, and there exists different types of complementarity relations. In this paper, a complementarity relation is established with the robustness of asymmetry. Specifically, the two complementary aspects are quantified by applying the robustness of asymmetry corresponding to two cyclic groups whose generators are linked by the Fourier matrix. This complementarity relation is compared with known results and considered in other perspectives, especially its operational meaning regarding quantum state discrimination. We conclude that the internal asymmetry of quantum states is closely related to other fundamental concepts, such as complementarity and coherence, and it is possible to quantitatively investigate complementarity and quantum state discrimination using the robustness of asymmetry. [ABSTRACT FROM AUTHOR]

We consider a quantum-classical (q-c) channel associated with quantum observable and a function on the set of results which defines a subordinate observable. We describe this situation as a combination of two quantum channels, where the output of the first channel is the classical outcome of the subordinate observable and quantum state which can be measured to yield the measurement result of the original channel. We also show that, under certain conditions, the states after the first channel in the given decomposition provide better quantum properties than the classical output of the original q-c channel. [ABSTRACT FROM AUTHOR]

We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification.

Quantum state discrimination depicts the general progress of extracting classical information from quantum systems. We show that quantum state discrimination can be realized in a measurement device-independent scenario using tools of self-testing results. That is, the states can be discriminated credibly with the untrusted experiment devices by the correspondence between quantum correlations and states. In detail, we show that two states that are not conjugate with each other can be discriminated without additional trusted input states, and the discrimination of others require a kind of trusted inputs. Further we show the guessing probability analysis of this protocol for minimum error discrimination, which is acceptable based on numerical results. • Quantum state discrimination can be realized measurement device-independently. • The devices are treated as black boxes and the quantum state discrimination is realized without knowing precise form of measurements. • The trust of devices can be removed to improve security and experimental errors can be treated at the level of observed statistics. [ABSTRACT FROM AUTHOR]

The guesswork of a quantum ensemble quantifies the minimum number of guesses needed in average to correctly guess the state of the ensemble, when only one state can be queried at a time. Here, we derive analytical solutions of the guesswork problem subject to a finite set of conditions, including the analytical solution for any qubit ensemble with uniform probability distribution. As explicit examples, we compute the guesswork for any qubit regular polygonal and polyhedral ensemble. [ABSTRACT FROM AUTHOR]

We consider the optimal discrimination of nonorthogonal qubit states with post-measurement information and provide an analytic structure of the optimal measurements. We also show that there is always a null optimal measurement when post-measurement information is given. Further, in discriminating four states using post-measurement information, we analytically provide the optimal probability of correct guessing and show that the uniqueness of optimal measurement is equivalent to the non-existence of non-null optimal measurement with post-measurement information. [ABSTRACT FROM AUTHOR]

We address a continuous-variable quantum key distribution protocol employing quaternary phase-shift-keying of coherent states and a non-Gaussian measurement inspired by quantum receivers minimizing the error probability in a quantum-state-discrimination scenario. We consider a pure-loss quantum wiretap channel, in which a possible eavesdropper is limited to collect the sole channel losses. We perform a characterization of state-discrimination receivers and design an optimized receiver maximizing the asymptotic secure key rate (SKR), namely the key-rate optimized receiver (KOR), comparing its performance with respect to the pretty good measurement and the heterodyne-based protocol. We show that the KOR increases the SKR for metropolitan-network distances. Finally, we also investigate the implementations of feasible schemes, such as the displacement feed-forward receiver, obtaining an increase in the SKR in particular regimes.

In quantum state discrimination, the observers are given a quantum system and aim to verify its state from the two or more possible target states. In the local quantum state marking as an extension of quantum state discrimination, there are N composite quantum systems and N possible orthogonal target quantum states. Distant Alice and Bob are asked to correctly mark the states of the given quantum systems via local operations and classical communication. Here we investigate the local state marking with N $4\otimes4$ systems, N = 4, 5, 6, and 7. Therein, Alice and Bob allow for three local operations: measuring the local observable either σ _z or σ _x simultaneously, and entanglement swapping. It shows that, given arbitrary four $4\otimes4$ systems, Alice and Bob can perform the perfect local quantum state marking. In the N = 5, 6 cases, they can perform perfect local state marking with specific target states. We conjecture the impossibility of the local quantum state marking given any seven target states since Alice and Bob cannot fulfill the task in the simplest case.

Quantum key distribution (QKD) is a quantum technology which creates a common secret key between two distant users without any technological and computational assumptions about the eavesdropper. Nevertheless, not all the QKD protocols have tight upper and lower security bounds, thus the study of eavesdropping strategies and countermeasures is important. Using large number of symmetric coherent states is one of possible technologies in quantum key distribution against unambiguous state discrimination (USD) attack. Here we propose an attack based on heterodyne measurement, which is relatively simple for practical implementation and which becomes more powerful than USD attack when the number of states in the protocol is large enough. We study the performance of this attack for various symmetric coherent states QKD protocol parameters and for various distances between the legitimate users. [ABSTRACT FROM AUTHOR]

Few-electron states confined in quantum-dot arrays are key objects in quantum computing. The discrimination between these states is essential for the readout of a (multi-)qubit state, and can be achieved through a measurement of the quantum capacitance within the gate-reflectometry approach. For a system controlled by several gates, the dependence of the measured capacitance on the direction of the oscillations in the voltage space is captured by the quantum capacitance matrix. Herein, we apply this tool to study a double quantum dot coupled to three gates, which enable the tuning of both the bias and the tunneling between the two dots. Analytical solutions for the two-electron case are derived within a Hubbard model, showing the overall dependence of the quantum capacitance matrix on the applied gate voltages. In particular, we investigate the role of the tunneling gate and reveal the possibility of exploiting interdot coherences in addition to charge displacements between the dots. Our results can be directly applied to double-dot experimental setups, and pave the way for further applications to larger arrays of quantum dots.

The quantum state discrimination problem is to distinguish between non-orthogonal quantum states. This problem has many applications in quantum information theory, quantum communication and quantum cryptography. In this paper, a quantum algorithm using weak measurement and partial negation will be proposed to solve the quantum state discrimination problem using a single copy of an unknown qubit. The usage of weak measurement makes it possible to reconstruct the qubit after measurement since the superposition will not be destroyed due to measurement. The proposed algorithm will be able to determine, with high probability of success, the state of the unknown qubit and whether it is encoded in the Hadamard or the computational basis by counting the outcome of the successive measurements on an auxiliary qubit. [ABSTRACT FROM AUTHOR]

Complementarity plays a central role in the conceptual development of quantum mechanics, and also provides practical applications in quantum information technologies. How to properly quantify it is an important problem in quantum foundations, and there exists different types of complementarity relations. In this paper, a complementarity relation is established with the robustness of asymmetry. Specifically, the two complementary aspects are quantified by applying the robustness of asymmetry corresponding to two cyclic groups whose generators are linked by the Fourier matrix. This complementarity relation is compared with known results and considered in other perspectives, especially its operational meaning regarding quantum state discrimination. We conclude that the internal asymmetry of quantum states is closely related to other fundamental concepts, such as complementarity and coherence, and it is possible to quantitatively investigate complementarity and quantum state discrimination using the robustness of asymmetry.

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The complementarity (upper bound) and uncertainty relations (lower bound) of the coherence via skew information under mutually unbiased bases (MUBs) are studied. The complementarity relation for the geometric measure of coherence is also obtained based on the relation between the coherence via skew information and the geometric measure of coherence. As applications, two tighter upper bounds are presented on the minimum error probabilities that discriminate a set of pure states with the least square measurement, which improve the results of Xiong et al. (Phys Rev A 98:032324, 2018). [ABSTRACT FROM AUTHOR]

Symmetric coherent states are of interest in quantum cryptography, since for such states there is an upper bound for unambiguous state discrimination (USD) probability, which is used to resist USD attack. But it is not completely clear what an eavesdropper can do for shorter channel length, when USD attack in not available. We consider the task of generalized discrimination between symmetric coherent states and construct an operation which enlarges the information content of the states with fixed failure probability. We apply this transformation to develop a zero-error eavesdropping strategy for quantum cryptography on symmetric coherent states. [ABSTRACT FROM AUTHOR]

The quantum steganalysis faces more challenges than classical steganalysis owing to the support of quantum mechanical principles such as Heisenberg uncertainty principle and non-cloning theorem. In this paper, a novel quantum steganalysis protocol based on pure state is proposed, which adheres to the fundamental fact that classical steganography tends to change the probability distribution of the carrier, and the physical properties that the unknown quantum state discrimination process is sensitive to the distribution in quantum state discrimination. After utilizing accurate calculation on the geometric coherence and 1/2-affinity coherence to obtain the probability that the transmitted quantum states can be correctly discriminated, effective detection on covert communication can be achieved by comparing the detected distribution with theoretical distribution. Meanwhile, steganographic detection rate and false alarm rate are introduced as two significant performance evaluation parameters of quantum steganalysis. In this paper, the quantum steganalysis and performance evaluation targeting the BB84-based quantum steganography proposed by Martin are given in detail. The geometric coherence and 1/2-affinity coherence change substantially when the steganographic embedding rate is above 0.2, and a high steganographic detection rate and a low false alarm rate can be obtained according to the proposed protocol. Besides, the impact on QKD efficiency can be controlled by adjusting the detection rate or adopting sampling detection strategy. It proves that the proposed protocol has a satisfactory quantum steganalysis performance. [ABSTRACT FROM AUTHOR]

Lattice states are a class of quantum states that naturally generalize the fundamental set of Bell states. We apply recent results from quantum error correction and from one-way local operations and classical communication (LOCC) theory that are built on the structure theory of operator systems and operator algebras, to develop a technique for the construction of relatively small sets of lattice states not distinguishable by one-way LOCC schemes. We also present examples, show the construction extends to generalized Pauli states, and compare the construction to other recent work. [ABSTRACT FROM AUTHOR]

In this work, we consider the preservation of a measurement for quantum systems interacting with an environment. Namely, a method of preserving an optimal measurement over a channel is devised, what we call channel coding of a quantum measurement in that operations are applied before and after a channel in order to protect a measurement. A protocol that preserves a quantum measurement over an arbitrary channel is shown only with local operations and classical communication without the use of a larger Hilbert space. Therefore, the protocol is readily feasible with present day’s technologies. Channel coding of qubit measurements is presented, and it is shown that a measurement can be preserved for an arbitrary channel for both i) pairs of qubit states and ii) ensembles of equally probable states. The protocol of preserving a quantum measurement is demonstrated with IBM quantum computers. [ABSTRACT FROM AUTHOR]

By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix. Given a string of qubits representing a series of trials, one can measure them individually and determine the state with a certain confidence. We show that there is an improved strategy which measures the qubits after entangling them, which leads to a greater confidence. This strategy is demonstrated on the simulation facility of IBM quantum computers. [ABSTRACT FROM AUTHOR]

We consider the problem of correctly classifying a given quantum two-level system (qubit) which is known to be in one of two equally probable quantum states. We assume that this task should be performed by a quantum machine which does not have at its disposal a complete classical description of the two template states, but can only have partial prior information about their level of purity and mutual overlap. Moreover, similarly to the classical supervised learning paradigm, we assume that the machine can be trained by $n$ qubits prepared in the first template state and by $n$ more qubits prepared in the second template state. In this situation, we are interested in the optimal process which correctly classifies the input qubit with the largest probability allowed by quantum mechanics. The problem is studied in its full generality for a number of different prior information scenarios and for an arbitrary size $n$ of the training data. Finite size corrections around the asymptotic limit $n\rightarrow \infty $ are derived. When the states are assumed to be pure, with known overlap, the problem is also solved in the case of d-level systems. [ABSTRACT FROM AUTHOR]

We studied the mutual information and quantum discord that Alice and Bob share when Bob implements a discrimination with a fixed rate of inconclusive outcomes (FRIO) onto two pure non-orthogonal quantum states, generated with arbitrary a priori probabilities. FRIO discrimination interpolates between minimum error (ME) and unambiguous state discrimination (UD). ME and UD are well known discrimination protocols with several applications in quantum information theory. FRIO discrimination provides a more general framework where the discrimination process together with its applications can be studied. In this setting, we compared the performance of optimum probability of discrimination, mutual information, and quantum discord. We found that the accessible information is obtained when Bob implements the ME strategy. The most (least) efficient discrimination scheme is ME (UD), from the point of view of correlations that are lost in the initial state and remain in the final state, after Bob’s measurement.

The Jensen–Shannon divergence has been successfully applied as a segmentation tool for symbolic sequences, that is to separate the sequence into subsequences with the same symbolic content. In this work, we propose a method, based on the Jensen–Shannon divergence, for segmentation of what we call quantum generated sequences , which consist in symbolic sequences generated from measuring a quantum system. For one-qubit and two-qubit systems, we show that the proposed method is adequate for segmentation. • Jensen–Shannon divergence as a segmentation tool for symbolic sequences. • Quantum generated sequences: symbolic sequences generated from measuring a quantum system. • Generalized method for segmentation of quantum generated sequences. • Successful segmentation results for one-qubit and two-qubit systems. [ABSTRACT FROM AUTHOR]

We consider the problem of discriminating qubit states that are sent over a quantum channel and derive a necessary and sufficient condition for an optimal measurement to be preserved by the channel. We apply the result to the characterization of optimal measurement preserving (OMP) channels for a given qubit ensemble, e.g., a set of two states or a set of multiple qubit states with equal a priori probabilities. Conversely, we also characterize qubit ensembles for which a given channel is OMP, such as unitary and depolarization channels. Finally, we show how the sets of OMP channels for a given ensemble can be constructed.

The commonly adopted projective measurements are invalid in the specified task of quantum state discrimination when the discriminated states are superposition of planar-position basis states whose complex-number probability amplitudes have the same magnitude but different phases. Therefore we propose a corresponding scheme via weak-value measurement and examine the feasibility of this scheme. Furthermore, the role of the weak-value measurement in quantum state discrimination is analyzed and compared with one in quantum state tomography in this Letter. [ABSTRACT FROM AUTHOR]

Quantum computing is a significant computing capability which is superior to classical computing because of its superposition feature. Distinguishing several quantum states from quantum algorithm outputs is often a vital computational task. In most cases, the quantum states tend to be non-orthogonal due to superposition; quantum mechanics has proved that perfect outcomes could not be achieved by measurements, forcing repetitive measurement. Hence, it is important to determine the optimum measuring method which requires fewer repetitions and a lower error rate. However, extending current measurement approaches mainly aiming at quantum cryptography to multi-qubit situations for quantum computing confronts challenges, such as conducting global operations which has considerable costs in the experimental realm. Therefore, in this study, we have proposed an optimum subsystem method to avoid these difficulties. We have provided an analysis of the comparison between the reduced subsystem method and the global minimum error method for two-qubit problems; the conclusions have been verified experimentally. The results showed that the subsystem method could effectively discriminate non-orthogonal two-qubit states, such as separable states, entangled pure states, and mixed states; the cost of the experimental process had been significantly reduced, in most circumstances, with acceptable error rate. We believe the optimal subsystem method is the most valuable and promising approach for multi-qubit quantum computing applications. [ABSTRACT FROM AUTHOR]

We investigate the optimum strategy for state discrimination of two pure states when the probability of inconclusive answers is fixed. By varying a given rate of inconclusive probabilities, the strategy optimally interpolates between Unambiguous and Minimum-Error discrimination, the two standard approaches to quantum state discrimination. We derive the explicit expressions of all the probabilities using an ancillary system and introducing unitary transformations which act on the input states and produce the output measured on the ancilla. By exploring physically accessible transformation acting on the input states, we present an optical scheme to implement the state discrimination. [ABSTRACT FROM AUTHOR]

We study the realization of a 2-D positive operator-valued measure (POVM) by local operations and classical communication (LOCC). We derive that any POVM on a 2-D Hilbert space in which each party’s space is finite dimensional can be realized by one-way LOCC. This implies that any optimal discrimination of quantum states spanning such a 2-D Hilbert space is possible by one-way LOCC, regardless of the optimality criterion used and how entangled the states are. [ABSTRACT FROM PUBLISHER]

This study considers the minimum error discrimination of two quantum states in terms of a two-party zero-sum game, whose optimal strategy is a minimax strategy. A minimax strategy is one in which a sender chooses a strategy for a receiver so that the receiver may obtain the minimum information about quantum states, but the receiver performs an optimal measurement to obtain guessing probability for the quantum ensemble prepared by the sender. Therefore, knowing whether the optimal strategy of the game is unique is essential. This is because there is no alternative if the optimal strategy is unique. This paper proposes the necessary and sufficient condition for an optimal strategy of the sender to be unique. Also, we investigate the quantum states that exhibit the minimum guessing probability when a sender’s minimax strategy is unique. Furthermore, we show that a sender’s minimax strategy and a receiver’s minimum error strategy cannot be unique if one can simultaneously diagonalize two quantum states, with the optimal measurement of the minimax strategy. This implies that a sender can confirm that the optimal strategy of only a single side (a sender or a receiver but not both of them) is unique by preparing specific quantum states.