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

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Cited by in corpus (124)

• Statistical Methods for Quantum State Verification and Fidelity Estimation
• The theory of the quantum kernel-based binary classifier
• Fast quantum state discrimination with nonlinear PTP channels
• Contextual advantages and certification for maximum confidence discrimination
• Pseudomagic Quantum States
• Semi-definite programming and quantum information
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
• Implementation of generalized measurements on a qudit via quantum walks
• Linear optics and photodetection achieve near-optimal unambiguous coherent 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
• Experimental quantum channel discrimination using metastable states of a trapped ion
• Experimental quantum state discrimination using the optimal fixed rate of inconclusive outcomes strategy
• Quantum state discrimination in a PT-symmetric system
• Variational quantum state discriminator for supervised machine learning
• Pseudorandom density matrices
• Exact quantum sensing limits for bosonic dephasing channels
• Maximum confidence measurement for qubit states
• Extracting unambiguous information from a single qubit by sequential observers
• The Dynamical Resource Theory of Informational Non-Equilibrium
• Postselected quantum hypothesis testing
• Optimizing Initial State of Detector Sensors in Quantum Sensor Networks
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• Optimal Trace Distance and Fidelity Estimations for Pure Quantum States
• High-fidelity, multi-qubit generalized measurements with dynamic circuits
• Tight bounds for antidistinguishability and circulant sets of pure quantum states
• Bound on local minimum-error discrimination of bipartite quantum states
• Contraction of Private Quantum Channels and Private Quantum Hypothesis Testing
• Experimental Realization of Schumacher's Information Geometric Bell Inequality
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Perfect discrimination of quantum measurements using entangled systems
• A Structure of Minimum Error Discrimination for Linearly Independent States
• Demonstration of optimal non-projective measurement of binary coherent states with photon counting
• An invitation to the sample complexity of quantum hypothesis testing
• Operational Interpretation of the Choi Rank Through k-State Exclusion
• Nonlocal quantum state ensembles and quantum data hiding
• Quantum State Discrimination for Supervised Classification
• Quantum guessing games with posterior information
• 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
• Quantum $f$-divergences via Nussbaum-Szkoła Distributions and Applications to $f$-divergence Inequalities
• An operational definition of quantum information scrambling
• Biased Random Access Codes
• Collapse and revival structure of information backflow for a central spin coupled to a finite spin bath
• Quantum estimation and remote charge sensing with a hole-spin qubit in silicon
• Generalized measurements on qubits in quantum randomness certification and expansion
• Contextuality witness inspired by optimal state discrimination
• Improving semi-device-independent randomness certification by entropy accumulation
• Quantum Machine Learning for Distributed Quantum Protocols with Local Operations and Noisy Classical Communications
• Experimental optimal discrimination of $N$ states of a qubit with fixed rates of inconclusive outcomes
• Unambiguous discrimination of sequences of quantum states
• Quantum multi-anomaly detection
• Bound on optimal local discrimination of multipartite quantum states
• Experimental Test of Contextuality based on State Discrimination with a Single Qubit
• Indirect Measurement for Optimal Quantum Communication Enhanced by Binary Non-standard Coherent States
• Experimentally determining the incompatibility of two qubit measurements
• Detectors for local discrimination of sets of generalized Bell states
• Single-shot Distinguishability and Anti-distinguishability of Quantum Measurements
• Compression of Entanglement Improves Quantum Communication
• Bipartite quantum state discrimination and decomposable entanglement witness
• Subsystem Trace-Distances of Two Random States
• Quantum communications in continuous variable systems
• Information locking and its resource efficient extraction
• Pretty good measurement for bosonic Gaussian ensembles
• Five Starter Pieces: Quantum Information Science via Semi-definite Programs
• Protocol for nonlinear state discrimination in rotating condensate
• Training quantum measurement devices to discriminate unknown non-orthogonal quantum states
• Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems
• Local simultaneous state discrimination
• Quantum enhancement of spoofing detection with squeezed states of light
• Locally distinguishing a maximally entangled basis using shared entanglement
• Quantum Approximation of Normalized Schatten Norms and Applications to Learning
• 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
• Any four orthogonal ququad-ququad maximally entangled states are locally markable
• The pretty bad measurement
• A Variational Approach to Unique Determinedness in Pure-state Tomography
• Optimal discrimination of quantum sequences
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Qubit State Discrimination using Post-measurement Information
• Operating Characteristics for Binary Hypothesis Testing in Quantum Systems
• Entanglement witness and multipartite quantum state discrimination
• Global restrictions under local state discrimination
• Multi-channel convolutional neural quantum embedding
• Theory of Single Photon Detection by a Photoreceptive Molecule and a Quantum Coherent Spin Center
• Experimental multi-state quantum discrimination through a Quantum network
• Contextuality-enhanced quantum state discrimination under fixed failure probability
• Contextual advantages across two-state discrimination strategies
• Bipartite quantum states admitting a causal explanation
• Towards Quantum Universal Hypothesis Testing
• Quantum state exclusion for group-generated ensembles of pure states
• Discrimination and certification of unknown quantum measurements
• Mimicking states with limited resources: passing quantum quiz via global control
• Programming of channels in generalized probabilistic theories
• Annihilating and creating nonlocality without entanglement by postmeasurement information
• Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes
• Parallel repetition of local simultaneous state discrimination
• Device-independent quantum state discrimination
• Multi-player quantum data hiding by nonlocal quantum state ensembles
• Near-optimal coherent state discrimination via continuously labelled non-Gaussian measurements
• Randomness-free Detection of Non-projective Measurements: Qubits & beyond
• $\mathcal{P}\mathcal{T}$-Symmetric Quantum State Discrimination for Attack on BB84 Quantum Key Distribution
• On the distinguishability of geometrically uniform quantum states
• Entanglement and Optimal Timing in Discriminating Quantum Dynamical Processes
• Security of deterministic key distribution with higher-dimensional systems
• Converting entanglement into ensemble basis-free coherence
• Enhanced Optimal Quantum Communication by Generalized Phase Shift Keying Coherent Signal
• Bayesian and Markovian classical feedforward for discriminating qubit channels
• Random Exclusion Codes: Quantum Advantages of Single-Shot Communication
• Discrimination of metric theories
• Unbounded entanglement-sustaining sequential local quantum state discrimination
• Thermodynamic Constraints on the Emergence of Intersubjectivity in Quantum Systems
• Locking and unlocking of quantum nonlocality without entanglement in local discrimination of quantum states
• Dynamic LOCC Circuits for Automated Entanglement Manipulation
• Complete analysis to minimum-error discrimination of mixed four qubit states with arbitrary prior probabilities
• Factorizability of optimal quantum sequence discrimination under maximum-confidence measurements
• Structure of quantum measurements implementable with one round of classical communication
• Sharing quantum indistinguishability with multiple parties
• Error-Tolerant Quantum State Discrimination: Optimization and Quantum Circuit Synthesis
• Thermodynamic bound on quantum state discrimination
• Barycentric decomposition for quantum instruments
• A Quantum Informational Approach to the Problem of Time
• Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States