Quantum state discrimination and its applications

Abstract

Quantum state discrimination underlies various applications in quantum information processing tasks. It essentially describes the distinguishability of quantum systems in different states, and the general process of extracting classical information from quantum systems. It is also useful in quantum information applications, such as the characterisation of mutual information in cryptographic protocols, or as a technique to derive fundamental theorems in quantum foundations. It has deep connections to physical principles such as relativistic causality. Quantum state discrimination traces a long history of several decades, starting with the early attempts to formalise information processing of physical systems such as optical communication with photons. Nevertheless, in most cases, optimal strategies of quantum state discrimination remain unsolved, and related applications are valid in some limited cases only. The present review aims to provide an overview on quantum state discrimination, covering some recent progress, and addressing applications in some selected topics. This review serves to strengthen the link between results in quantum state discrimination and quantum information applications, by showing the ways in which the fundamental results are exploited in applications and vice versa.

42 pages, a review article, a preprint in Institute of Mathematical Sciences (2015), thanks to M. Wilde for encouraging, though being late, to submit to arXiv

References in corpus (65)

• Quantum Nonlocality without Entanglement
• Quantum Copying: Beyond the No-Cloning Theorem
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• On the reality of the quantum state
• The operational meaning of min- and max-entropy
• The Quantum Chernoff Bound
• Quantum State Discrimination
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation
• Unambiguous Discrimination Between Linearly-Independent Quantum States
• Tomography of Quantum Operations
• Device-independent tests of classical and quantum dimensions
• Phase covariant quantum cloning
• Statistical distinguishability between unitary operations
• Optimal universal quantum cloning and state estimation
• Asymptotic Error Rates in Quantum Hypothesis Testing
• Optimal Cloning of Pure States, Judging Single Clones
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Quantum channels and their entropic characteristics
• Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding
• Quantum cloning without signaling
• Maximum Confidence Quantum Measurements
• Unambiguous discrimination of mixed states
• Dimension witnesses and quantum state discrimination
• Quantum channels showing superadditivity in capacity
• The no-signaling condition and quantum dynamics
• A Semidefinite Programming Approach to Optimal Unambiguous Discrimination of Quantum States
• Optimal discrimination of mixed quantum states involving inconclusive results
• Accessible information and optimal strategies for real symmetrical quantum sources
• Minimum-error discrimination between three mirror-symmetric states
• Conditions for compatibility of quantum state assignments
• Distinguishability of States and von Neumann Entropy
• Finding optimal strategies for minimum-error quantum-state discrimination
• Maximally epistemic interpretations of the quantum state and contextuality
• Asymptotic quantum cloning is state estimation
• Multiple copy 2-state discrimination with individual measurements
• Structure of minimum-error quantum state discrimination
• Mixed quantum state detection with inconclusive results
• Key distillation from quantum channels using two-way communication protocols
• Conclusive Exclusion of Quantum States
• Optimal discrimination of quantum states with a fixed rate of inconclusive outcomes
• On the Power of Quantum Memory
• State discrimination with error margin and its locality
• Optimal Discrimination of Qubit States - Methods, Solutions, and Properties
• A family of generalized `pretty good' measurements and the minimal-error pure-state discrimination problems for which they are optimal
• Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate
• Optimal State Discrimination in General Probabilistic Theories
• Complete analysis for three-qubit mixed-state discrimination
• Measurement does not always aid state discrimination
• Discrimination with error margin between two states - Case of general occurrence probabilities -
• Quantum information becomes classical when distributed to many users
• No-signaling Principle Can Determine Optimal Quantum State Discrimination
• Optimal bounded-error strategies for projective measurements in non-orthogonal state discrimination
• Distinguishing multi-partite states by local measurements
• Requirement of Dissonance in Assisted Optimal State Discrimination
• Qubit State Discrimination
• Minimum error discrimination problem for pure qubit states
• Helstrom Theorem by No-Signaling Condition
• An asymptotic error bound for testing multiple quantum hypotheses
• Minimum-error multiple state discrimination constrained by the no-signaling principle
• Optimality of minimum-error discrimination by the no-signalling condition
• Optimal Observables for Minimum-Error State Discrimination in General Probabilistic Theories
• The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization
• Distinguishability, Ensemble Steering, and the No-Signaling Principle

Cited by in corpus (190)

• Duality of Quantum Coherence and Path Distinguishability
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Generalization in Quantum Machine Learning: a Quantum Information Perspective
• Non-Hermitian Hamiltonians and no-go theorems in quantum information
• Quantum Algorithmic Measurement
• Statistical Methods for Quantum State Verification and Fidelity Estimation
• The theory of the quantum kernel-based binary classifier
• Optimal verification of general bipartite pure states
• Fast quantum state discrimination with nonlinear PTP channels
• Resource theory of asymmetric distinguishability
• Macroscopic superpositions require tremendous measurement devices
• A hybrid quantum-classical approach to mitigating measurement errors
• Contextual advantages and certification for maximum confidence discrimination
• Pseudomagic Quantum States
• Practical distributed quantum information processing with LOCCNet
• Simulating all quantum measurements using only projective measurements and postselection
• Quantum Sequential Hypothesis Testing
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• Noisy intermediate-scale quantum algorithm for semidefinite programming
• Renyi relative entropies of quantum Gaussian states
• Quantum-enhanced barcode decoding and pattern recognition
• Quantum State Discrimination Using Noisy Quantum Neural Networks
• Quantum advantage for probabilistic one-time programs
• Semi-definite programming and quantum information
• Quantum State Discrimination Using the Minimum Average Number of Copies
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
• Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination
• Implementation of generalized measurements on a qudit via quantum walks
• Implementation of quantum measurements using classical resources and only a single ancillary qubit
• Optimal discrimination of single-qubit mixed states
• Quantum receiver for phase-shift keying at the single photon level
• Quantum data hiding with continuous variable systems
• Optimal sequential measurements for bi-partite state discrimination
• Pseudorandom unitaries are neither real nor sparse nor noise-robust
• Neural Quantum Embedding: Pushing the Limits of Quantum Supervised Learning
• Discriminating mixed qubit states with collective measurements
• Discrimination of Ohmic thermal baths by quantum dephasing probes
• An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results
• Experimental quantum channel discrimination using metastable states of a trapped ion
• Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis
• Quantum state discrimination in a PT-symmetric system
• The Helstrom measurement: A nondestructive implementation
• Experimental quantum state discrimination using the optimal fixed rate of inconclusive outcomes strategy
• Entropic measures of joint uncertainty: effects of lack of majorization
• Ultimate Limits of Thermal Pattern Recognition
• Efficient molecule discrimination in electron microcopy through an optimized orbital angular momentum sorter
• Pseudorandom density matrices
• Measurement-Device-Independent Quantum Coin Tossing
• Variational quantum state discriminator for supervised machine learning
• Exact quantum sensing limits for bosonic dephasing channels
• Maximum confidence measurement for qubit states
• Extracting unambiguous information from a single qubit by sequential observers
• Classification and reconstruction of optical quantum states with deep neural networks
• Optimizing Initial State of Detector Sensors in Quantum Sensor Networks
• The Dynamical Resource Theory of Informational Non-Equilibrium
• Postselected quantum hypothesis testing
• Multiple-shot and unambiguous discrimination of von Neumann measurements
• High-fidelity, multi-qubit generalized measurements with dynamic circuits
• Optimal Trace Distance and Fidelity Estimations for Pure Quantum States
• Preserving Measurements for Optimal State Discrimination over Quantum Channels
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• Tight bounds for antidistinguishability and circulant sets of pure quantum states
• Bound on local minimum-error discrimination of bipartite quantum states
• Experimental Realization of Schumacher's Information Geometric Bell Inequality
• Certified answers for ordered quantum discrimination problems
• Implementation of discrete positive operator valued measures on linear optical systems using cosine-sine decomposition
• Multiple-copy state discrimination of noisy qubits
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Contraction of Private Quantum Channels and Private Quantum Hypothesis Testing
• Quantum Advantages in (n,d)->1 Random Access Codes
• A Structure of Minimum Error Discrimination for Linearly Independent States
• Construction of propagators for divisible dynamical maps
• Perfect discrimination of quantum measurements using entangled systems
• Identification of malfunctioning quantum devices
• Unextendible entangled bases and more nonlocality with less entanglement
• Demonstration of optimal non-projective measurement of binary coherent states with photon counting
• Optimal quantum discrimination of single-qubit unitary gates between two candidates
• Geometry on the manifold of Gaussian quantum channels
• Operational Interpretation of the Choi Rank Through k-State Exclusion
• Nonlocal quantum state ensembles and quantum data hiding
• An invitation to the sample complexity of quantum hypothesis testing
• Quantum State Discrimination for Supervised Classification
• Quantum guessing games with posterior information
• Asymptotic relative submajorization of multiple-state boxes
• Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination
• Process estimation in qubit systems: a quantum decision theory approach
• Coherence based on positive operator-valued measures for standard and concatenated quantum state discrimination with inconclusive results
• An operational definition of quantum information scrambling
• Contextuality witness inspired by optimal state discrimination
• Toward Instance-Optimal State Certification With Incoherent Measurements
• Analytical Bounds for Dynamic Multi-Channel Discrimination
• Pretty simple bounds on quantum state discrimination
• Idler-Free Multi-Channel Discrimination via Multipartite Probe States
• Generalized measurements on qubits in quantum randomness certification and expansion
• Collapse and revival structure of information backflow for a central spin coupled to a finite spin bath
• Biased Random Access Codes
• Quantum $f$-divergences via Nussbaum-Szkoła Distributions and Applications to $f$-divergence Inequalities
• Quantum estimation and remote charge sensing with a hole-spin qubit in silicon
• Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball
• Improving semi-device-independent randomness certification by entropy accumulation
• Quantum multi-anomaly detection
• Bipartite discrimination of independently prepared quantum states as a counterexample to a parallel repetition conjecture
• Unambiguous discrimination of sequences of quantum states
• Quantum Machine Learning for Distributed Quantum Protocols with Local Operations and Noisy Classical Communications
• Component on shell actions of supersymmetric 3-brane I. 3-brane in D=6
• Experimental optimal discrimination of $N$ states of a qubit with fixed rates of inconclusive outcomes
• Protocol for nonlinear state discrimination in rotating condensate
• Pretty good measurement for bosonic Gaussian ensembles
• Compression of Entanglement Improves Quantum Communication
• Information locking and its resource efficient extraction
• Experimentally determining the incompatibility of two qubit measurements
• Bipartite quantum state discrimination and decomposable entanglement witness
• Indirect Measurement for Optimal Quantum Communication Enhanced by Binary Non-standard Coherent States
• Subsystem Trace-Distances of Two Random States
• Single-shot Distinguishability and Anti-distinguishability of Quantum Measurements
• Experimental Test of Contextuality based on State Discrimination with a Single Qubit
• Bound on optimal local discrimination of multipartite quantum states
• Measurement-Protected Quantum Key Distribution
• Five Starter Pieces: Quantum Information Science via Semi-definite Programs
• Quantum communications in continuous variable systems
• Training quantum measurement devices to discriminate unknown non-orthogonal quantum states
• Detectors for local discrimination of sets of generalized Bell states
• Worst-case Quantum Hypothesis Testing with Separable Measurements
• Linear bosonic quantum channels defined by superpositions of maximally distinguishable Gaussian environments
• Locally distinguishing a maximally entangled basis using shared entanglement
• Entanglement witness and nonlocality in confidence of measurement from multipartite quantum state discrimination
• Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
• The pretty bad measurement
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Optimal discrimination of quantum sequences
• A Variational Approach to Unique Determinedness in Pure-state Tomography
• Global restrictions under local state discrimination
• Entanglement witness and multipartite quantum state discrimination
• Any four orthogonal ququad-ququad maximally entangled states are locally markable
• Quantum Approximation of Normalized Schatten Norms and Applications to Learning
• Local simultaneous state discrimination
• Qubit State Discrimination using Post-measurement Information
• Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems
• $\mathcal{P}\mathcal{T}$-Symmetric Quantum Discrimination of Three States
• Single-Copy Certification of Two-Qubit Gates without Entanglement
• Quantum $k$-nearest neighbors algorithm
• Operating Characteristics for Binary Hypothesis Testing in Quantum Systems
• Quantum enhancement of spoofing detection with squeezed states of light
• Multi-channel convolutional neural quantum embedding
• Contextual advantages across two-state discrimination strategies
• Contextuality-enhanced quantum state discrimination under fixed failure probability
• Polaron formation in a spin chain by measurement-induced imaginary Zeeman field
• Minimum-error discrimination of thermal states
• Annihilating and creating nonlocality without entanglement by postmeasurement information
• Towards Quantum Universal Hypothesis Testing
• Quantum state exclusion for group-generated ensembles of pure states
• Programming of channels in generalized probabilistic theories
• Mimicking states with limited resources: passing quantum quiz via global control
• Theory of Single Photon Detection by a Photoreceptive Molecule and a Quantum Coherent Spin Center
• Quantum state identification of qutrits via a nonlinear protocol
• Discrimination and certification of unknown quantum measurements
• Experimental multi-state quantum discrimination through a Quantum network
• Bipartite quantum states admitting a causal explanation
• Entanglement Cost for Steering Assemblages
• Quantum Physics in Space
• Randomness-free Detection of Non-projective Measurements: Qubits & beyond
• Bayesian and Markovian classical feedforward for discriminating qubit channels
• Converting entanglement into ensemble basis-free coherence
• Security of deterministic key distribution with higher-dimensional systems
• Complete analysis to minimum-error discrimination of mixed four qubit states with arbitrary prior probabilities
• Locking and unlocking of quantum nonlocality without entanglement in local discrimination of quantum states
• Multi-player quantum data hiding by nonlocal quantum state ensembles
• Entanglement and Optimal Timing in Discriminating Quantum Dynamical Processes
• Thermodynamic bound on quantum state discrimination
• A Quantum Informational Approach to the Problem of Time
• $\mathcal{P}\mathcal{T}$-Symmetric Quantum State Discrimination for Attack on BB84 Quantum Key Distribution
• Barycentric decomposition for quantum instruments
• Near-optimal coherent state discrimination via continuously labelled non-Gaussian measurements
• Unbounded entanglement-sustaining sequential local quantum state discrimination
• Parallel repetition of local simultaneous state discrimination
• Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States
• Factorizability of optimal quantum sequence discrimination under maximum-confidence measurements
• Discrimination of metric theories
• Structure of quantum measurements implementable with one round of classical communication
• Thermodynamic Constraints on the Emergence of Intersubjectivity in Quantum Systems
• Sharing quantum indistinguishability with multiple parties
• Error-Tolerant Quantum State Discrimination: Optimization and Quantum Circuit Synthesis
• Enhanced Optimal Quantum Communication by Generalized Phase Shift Keying Coherent Signal
• On the distinguishability of geometrically uniform quantum states
• Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes
• Random Exclusion Codes: Quantum Advantages of Single-Shot Communication
• Device-independent quantum state discrimination
• Dynamic LOCC Circuits for Automated Entanglement Manipulation
• Quantum State Discrimination via Repeated Measurements and the Rule of Three
• Online identification of symmetric pure states