Identifying the Information Gain of a Quantum Measurement

Abstract

We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the measurement, if sufficient shared randomness is available. This result generalizes Winter's measurement compression theorem for fixed independent and identically distributed inputs [Winter, CMP 244 (157), 2004] to arbitrary inputs, and more importantly, it identifies the quantum mutual information of a measurement as the information gained by performing it, independent of the input state on which it is performed. Our result is a generalization of the classical reverse Shannon theorem to quantum-to-classical channels. In this sense, it can be seen as a quantum reverse Shannon theorem for quantum-to-classical channels, but with the entanglement assistance and quantum communication replaced by shared randomness and classical communication, respectively. The proof is based on a novel one-shot state merging protocol for "classically coherent states" as well as the post-selection technique for quantum channels, and it uses techniques developed for the quantum reverse Shannon theorem [Berta et al., CMP 306 (579), 2011].

v2: new result about non-feedback measurement simulation, 45 pages, 4 figures

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• Quantum Darwinism
• Quantum information can be negative
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• Quantum Fluctuation Theorem under Continuous Measurement and Feedback
• Two-stage Estimation for Quantum Detector Tomography: Error Analysis, Numerical and Experimental Results
• A Resource Theory of Quantum Measurements
• Dissipation, dephasing and quantum Darwinism in qubit systems with random unitary interactions
• Global triplewise information trade-off in quantum measurement
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• Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off
• Quantum-proof randomness extractors via operator space theory
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• Channel Simulation: Finite Blocklengths and Broadcast Channels
• The information capacity of entanglement-assisted continuous variable measurement
• Verifying detailed fluctuation relations for discrete feedback-controlled quantum dynamics
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• Correlation measures of a quantum state and information characteristics of a quantum channel
• On lower semicontinuity of the quantum conditional mutual information and its corollaries
• General framework of quantum complementarity from a measurement-based perspective