Quantum random access codes and incompatibility of measurements

Abstract

We prove that quantum random access code (QRAC) performs better than its classical counterpart only when incompatible quantum measurements are used in the decoding task. As a consequence, evaluating the average success probability for QRAC provides a semi-device independent test for the detection of quantum incompatibility. We further demonstrate that any incompatible pair of projective measurements gives an advantage over all classical strategies. Finally, we establish a connection between the maximal average success probability for QRAC and earlier quantities introduced to assess incompatibility.

References in corpus (31)

• Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
• An Invitation to Quantum Incompatibility
• Joint measurability of generalized measurements implies classicality
• Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
• One-to-one mapping between steering and joint measurability problems
• Quantifying quantum resources with conic programming
• All sets of incompatible measurements give an advantage in quantum state discrimination
• Quantum Random Access Codes using Single $d$-level Systems
• Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
• Quantum Incompatibility Witnesses
• Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
• Notes on Joint Measurability of Quantum Observables
• Self-testing mutually unbiased bases in the prepare-and-measure scenario
• A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
• Comparing the degrees of incompatibility inherent in probabilistic physical theories
• Quantifying measurement incompatibility of mutually unbiased bases
• Incompatibility robustness of quantum measurements: a unified framework
• Robustness of incompatibility for quantum devices
• (4,1)-Quantum Random Access Coding Does Not Exist
• Coexistence of qubit effects
• Coexistence of qubit effects
• Connections Between Mutually Unbiased Bases and Quantum Random Access Codes
• Adaptive strategy for joint measurements
• Maximally incompatible quantum observables
• Experimentally feasible semi-device-independent certification of $4$ outcome POVMs
• Incompatible measurements in a class of general probabilistic theories
• Foundations of quantum theory and quantum information applications
• Device-independent tests of structures of measurement incompatibility
• Operational foundations of complementarity and uncertainty relations
• Compatibility of quantum measurements and inclusion constants for the matrix jewel
• Device independent witness of arbitrary dimensional quantum systems employing binary outcome measurements

Cited by in corpus (35)

• Incompatible measurements in quantum information science
• Experimental characterisation of unsharp qubit observables and sequential measurement incompatibility via quantum random access codes
• Kirkwood-Dirac nonclassicality, support uncertainty and complete incompatibility
• Semi-device-independent framework based on restricted distrust in prepare-and-measure experiments
• Measurement incompatibility and quantum advantage in communication
• Device-independent quantification of measurement incompatibility
• Widening the sharpness modulation region of an entanglement-assisted sequential quantum random access code: Theory, experiment, and application
• Compatibility of Generalized Noisy Qubit Measurements
• Classification of incompatibility for two orthonormal bases
• On the compatibility of quantum instruments
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Quantum measurement incompatibility in subspaces
• Characterizing and quantifying the incompatibility of quantum instruments
• Adaptive advantage in entanglement-assisted communications
• Improvement in quantum communication using quantum switch
• Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
• Quantum Advantages in (n,d)->1 Random Access Codes
• Interplays between classical and quantum entanglement-assisted communication scenarios
• Distributed quantum incompatibility
• Incompatibility of quantum instruments
• Quantum Random Access Code in Noisy Channels
• Simple and general bounds on quantum random access codes
• Random access test as an identifier of nonclassicality
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Two instances of random access code in the quantum regime
• Can a qudit carry more information than a dit?
• Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations
• High-dimensional multi-input quantum random access codes and mutually unbiased bases
• Quantum Random Access Codes Implementation for Resource Allocation and Coexistence with Classical Telecommunication
• Distance-based measures and Epsilon-measures for measurement-based quantum resources
• Random Exclusion Codes: Quantum Advantages of Single-Shot Communication
• Gottesman-Knill Limit on One-way Communication Complexity: Tracing the Quantum Advantage down to Magic Resources
• Comparing quantum incompatibility of device sets from an operational perspective
• Robust device-independent characterization of sharpness and incompatibility of unsharp instruments