Informationally restricted quantum correlations

Abstract

Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content of the quantum communication, rather than on its Hilbert-space dimension. Specifically, we explore the extent of classical and quantum correlations given an upper bound on the one-shot accessible information. We provide a characterisation of the set of classical correlations and show that quantum correlations are stronger than classical ones. We also show that limiting information rather than dimension leads to stronger quantum correlations. Moreover, we present device-independent tests for placing lower bounds on the information given observed correlations. Finally, we show that quantum communication carrying $\log d$ bits of information is at least as strong a resource as $d$-dimensional classical communication assisted by pre-shared entanglement.

References in corpus (28)

• The information bottleneck method
• Contextuality for preparations, transformations, and unsharp measurements
• Non-locality and Communication Complexity
• Device-independent tests of classical and quantum dimensions
• Semi-device-independent security of one-way quantum key distribution
• Preparation contextuality powers parity-oblivious multiplexing
• A self-testing quantum random number generator
• Experimental estimation of the dimension of classical and quantum systems
• Quantum Random Access Codes using Single $d$-level Systems
• Semi-device independent random number expansion without entanglement
• MHz-rate semi-device-independent quantum random number generators based on unambiguous state discrimination
• Experimental Device-independent Tests of Classical and Quantum Dimensions
• Self-testing quantum states and measurements in the prepare-and-measure scenario
• Semi-device-independent framework based on natural physical assumptions
• Entanglement assisted random access codes
• Bounding the set of finite dimensional quantum correlations
• Optimal bounds for parity-oblivious random access codes
• Characterising the correlations of prepare-and-measure quantum networks
• (4,1)-Quantum Random Access Coding Does Not Exist
• Smooth Max-Information as One-Shot Generalization for Mutual Information
• Device-Independent Tests of Entropy
• Communication games reveal preparation contextuality
• Secrecy in prepare-and-measure CHSH tests with a qubit bound
• Spatial versus Sequential Correlations for Random Access Coding
• Convexity and Operational Interpretation of the Quantum Information Bottleneck Function
• Complementarity between entanglement-assisted and quantum distributed random access code
• Higher dimensional communication complexity problems: classical protocols vs quantum ones based on Bell's Theorem or prepare-transmit-measure schemes
• The Magical Number Seven: An Unexpected Dimensional Threshold in Quantum Communication Complexity

Cited by in corpus (24)

• Semidefinite programming relaxations for quantum correlations
• Entanglement-assisted quantum communication with simple measurements
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Entanglement detection with imprecise measurements
• Informationally restricted correlations: a general framework for classical and quantum systems
• Semi-device-independent framework based on restricted distrust in prepare-and-measure experiments
• Entanglement in prepare-and-measure scenarios: many questions, a few answers
• Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness
• Semi-device-independent certification of entanglement in superdense coding
• Quantum prescriptions are more ontologically distinct than they are operationally distinguishable
• Almost qudits in the prepare-and-measure scenario
• Bounding and simulating contextual correlations in quantum theory
• Self-testing in prepare-and-measure scenarios and a robust version of Wigner's theorem
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Unbounded quantum advantage in communication complexity measured by distinguishability
• Prepare-and-measure scenarios with photon-number constraints
• Information capacity of quantum communication under natural physical assumptions
• Theory-independent randomness generation from spatial symmetries
• Absolute dimensionality of quantum ensembles
• Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension
• The role of entanglement in energy-restricted communication and randomness generation
• Quantum description of reality is epistemically incomplete
• Limits of Classical correlations and Quantum advantages under (Anti-)Distinguishability constraints in Multipartite Communication
• Quantum inputs in the prepare-and-measure scenario and stochastic teleportation