Conditional Mutual Information and Quantum Steering

Abstract

Quantum steering has recently been formalized in the framework of a resource theory of steering, and several quantifiers have already been introduced. Here, we propose an information-theoretic quantifier for steering called intrinsic steerability, which uses conditional mutual information to measure the deviation of a given assemblage from one having a local hidden-state model. We thus relate conditional mutual information to quantum steering and introduce monotones that satisfy certain desirable properties. The idea behind the quantifier is to suppress the correlations that can be explained by an inaccessible quantum system and then quantify the remaining intrinsic correlations. A variant of the intrinsic steerability finds operational meaning as the classical communication cost of sending the measurement choice and outcome to an eavesdropper who possesses a purifying system of the underlying bipartite quantum state that is being measured.

v2: 17 pages, 1 figure, minor changes, accepted for publication in Physical Review A

References in corpus (5)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Quantum steering ellipsoids, extremal physical states and monogamy
• The information-theoretic costs of simulating quantum measurements

Cited by in corpus (16)

• Quantum Steering
• Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
• Fundamental limits on key rates in device-independent quantum key distribution
• Distillation of quantum steering
• Conditional quantum one-time pad
• Relative entropy of steering: On its definition and properties
• Multipartite Intrinsic Non-Locality and Device-Independent Conference Key Agreement
• Distance-based resource quantification for sets of quantum measurements
• Quantifying Quantum Steering with Limited Resources: A Semi-supervised Machine Learning Approach
• Classical and quantum parts of conditional mutual information for open quantum systems
• Revealing the quantitative relation between simultaneous correlations in complementary bases and quantum steering for two-qubit Bell diagonal states
• Quantum conditional mutual information of W state in non-inertial frames
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• Measurement-device-independent measure of steerability and witnesses for all steerable resources
• Cooperation and dependencies in multipartite systems
• No-local-broadcasting theorem for non-signalling behaviours and assemblages