Dimension witnesses and quantum state discrimination

Abstract

Dimension witnesses allow one to test the dimension of an unknown physical system in a device-independent manner, that is, without placing assumptions about the functioning of the devices used in the experiment. Here we present simple and general dimension witnesses for quantum systems of arbitrary Hilbert space dimension. Our approach is deeply connected to the problem of quantum state discrimination, hence establishing a strong link between these two research topics. Finally, our dimension witnesses can distinguish between classical and quantum systems of the same dimension, making them potentially useful for quantum information processing.

arXiv comment5 pages

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Cited by in corpus (96)

• Quantum state discrimination and its applications
• Certifying the dimension of classical and quantum systems in a prepare-and-measure scenario with independent devices
• Semi-device-independent framework based on natural physical assumptions
• Bounding the quantum dimension with contextuality
• Bounding the set of finite dimensional quantum correlations
• Self-testing non-projective quantum measurements in prepare-and-measure experiments
• Operational relevance of resource theories of quantum measurements
• Quantum cryptography: key distribution and beyond
• Learning models of quantum systems from experiments
• Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
• Semidefinite programming relaxations for quantum correlations
• Maximum violations of the quantum-witness equality
• Witnessing irreducible dimension
• Experimental Tests of Classical and Quantum Dimensions
• Characterizing finite-dimensional quantum behavior
• Device-independent certification of high-dimensional quantum systems
• Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses
• Bound on Ergotropic Gap for Bipartite Separable States
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Leggett-Garg macrorealism and the quantum nondisturbance conditions
• Testing dimension and non-classicality in communication networks
• Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• Device-independent certification of Hilbert space dimension using a family of Bell expressions
• Informationally restricted correlations: a general framework for classical and quantum systems
• Entanglement in prepare-and-measure scenarios: many questions, a few answers
• Semi-device-independent certification of entanglement in superdense coding
• Memory cost of temporal correlations
• Quantum State Discrimination Using the Minimum Average Number of Copies
• A new device-independent dimension witness and its experimental implementation
• Sharing nonlocality in quantum network by unbounded sequential observers
• Genuine temporal correlations can certify the quantum dimension
• Optimal quantum state discrimination via nested binary measurements
• Optimal discrimination of single-qubit mixed states
• A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations
• Shared randomness and device-independent dimension witnessing
• Compressibility of positive semidefinite factorizations and quantum models
• Device-independent self-testing of unsharp measurements
• Self-testing in prepare-and-measure scenarios and a robust version of Wigner's theorem
• Compounds of symmetric informationally complete measurements and their application in quantum key distribution
• Semi-Device Independent Quantum Money
• Device-independent dimension tests in the prepare-and-measure scenario
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Simulating extremal temporal correlations
• Sharing preparation contextuality in Bell experiment by arbitrary pair of sequential observers
• Certifying sets of quantum observables with any full-rank state
• Quantum Process Identification: A Method for Characterizing Non-Markovian Quantum Dynamics
• Ticking-clock performance enhanced by nonclassical temporal correlations
• Entanglement Verification of Hyperentangled Photon Pairs
• Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Certifying dimension of quantum systems by sequential projective measurements
• Certifying the Classical Simulation Cost of a Quantum Channel
• A general bound for the dimension of quantum behaviours in the prepare-and-measure scenario
• Connector tensor networks: a renormalization-type approach to quantum certification
• Prepare-and-measure scenarios with photon-number constraints
• Unbounded quantum advantage in communication complexity measured by distinguishability
• Structure of dimension-bounded temporal correlations
• An invitation to the sample complexity of quantum hypothesis testing
• Optimal classical and quantum real and complex dimension witness
• Information capacity of quantum communication under natural physical assumptions
• Evidence-based certification of quantum dimensions
• Simple and general bounds on quantum random access codes
• Bound entangled states are useful in prepare-and-measure scenarios
• Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
• Towards Necessary and sufficient state condition for violation of a multi-settings Bell inequality
• Semi-device-independent certification of quantum non-Markovianity using sequential Random Access Codes
• Precise certification of a qubit space
• Connecting XOR and XOR* games
• Minimal scheme for certifying three-outcome qubit measurements in the prepare-and-measure scenario
• Experimental Test of Contextuality based on State Discrimination with a Single Qubit
• Null dimension witness based on single measurements
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Quantum null-hypothesis device-independent Schmidt rank witness
• Quantum dimension witness with a single repeated operation
• Characterizing high-dimensional quantum contextuality
• Witnessing environment dimension through temporal correlations
• Global restrictions under local state discrimination
• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension
• Robust certification of quantum instruments through a sequential communication game
• Extracting the physical sector of quantum states
• Dimensionality Distinguishers
• Bounding conditional entropy of bipartite states with Bell operators
• Graph-theoretic approach to dimension witnessing
• Semi-device-independent randomness certification on discretized continuous-variable platforms
• Operationally classical simulation of quantum states
• Detecting quantum resources in a semi-device independent framework
• Quantum inputs in the prepare-and-measure scenario and stochastic teleportation
• Cross-platform certification of the qubit space with a minimal number of parameters
• Quantum dimension test using the uncertainty principle
• Device-independent quantum state discrimination
• Device-independent dimension leakage null test on qubits at low operational cost
• Random Exclusion Codes: Quantum Advantages of Single-Shot Communication
• Unbounded entanglement-sustaining sequential local quantum state discrimination
• Quantum Random Access Codes Implementation for Resource Allocation and Coexistence with Classical Telecommunication