Simple and general bounds on quantum random access codes

Abstract

Random access codes are a type of communication task that is widely used in quantum information science. The optimal average success probability that can be achieved through classical strategies is known for any random access code. However, only a few cases are solved exactly for quantum random access codes. In this paper, we provide bounds for the fully general setting of n independent variables, each selected from a d-dimensional classical alphabet and encoded in a D-dimensional quantum system subject to an arbitrary quantum measurement. The bound recovers the exactly known special cases, and we demonstrate numerically that even though the bound is not tight overall, it can still yield a good approximation.

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References in corpus (32)

• Quantum cryptography: Public key distribution and coin tossing
• Information Causality as a Physical Principle
• Semi-device-independent security of one-way quantum key distribution
• Preparation contextuality powers parity-oblivious multiplexing
• Dimension witnesses and quantum state discrimination
• Quantum Random Access Codes using Single $d$-level Systems
• Self-testing quantum states and measurements in the prepare-and-measure scenario
• Entanglement assisted random access codes
• Self-testing mutually unbiased bases in the prepare-and-measure scenario
• Self-testing non-projective quantum measurements in prepare-and-measure experiments
• Sequential random access codes and self-testing of quantum measurement instruments
• (4,1)-Quantum Random Access Coding Does Not Exist
• Experimental characterisation of unsharp qubit observables and sequential measurement incompatibility via quantum random access codes
• Semi-device-independent self-testing of unsharp measurements
• Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
• Semidefinite programming relaxations for quantum correlations
• Connections Between Mutually Unbiased Bases and Quantum Random Access Codes
• Characterizing finite-dimensional quantum behavior
• Secrecy in prepare-and-measure CHSH tests with a qubit bound
• Quantum random access codes and incompatibility of measurements
• Experimental Demonstration of Sequential Quantum Random Access Codes
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Spatial versus Sequential Correlations for Random Access Coding
• Experimentally feasible semi-device-independent certification of $4$ outcome POVMs
• Measurement incompatibility and quantum advantage in communication
• Almost qudits in the prepare-and-measure scenario
• Improved Classical and Quantum Random Access Codes
• Quantum Random Access Codes for Boolean Functions
• Widening the sharpness modulation region of an entanglement-assisted sequential quantum random access code: Theory, experiment, and application
• Quantum Advantages in (n,d)->1 Random Access Codes
• A general bound for the dimension of quantum behaviours in the prepare-and-measure scenario
• Quantum Random Access Code in Noisy Channels

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• Quantum stochastic communication via high-dimensional entanglement
• Translating Bell Non-Locality to Prepare-and-Measure Scenarios under Dimensional Constraints
• Random Exclusion Codes: Quantum Advantages of Single-Shot Communication
• Quantum inputs in the prepare-and-measure scenario and stochastic teleportation