Abstract
It is known that the maximum classical mutual information that can be achieved between measurements on a pair of quantum systems can drastically underestimate the quantum mutual information between those systems. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might only yield outcomes essentially independent of each other. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. As such, the effect might be relevant to statistical mechanics or black hole physics. Previous work on information locking had always assumed a uniform message. In this article, we assume only a min-entropy bound on the message and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. As a cryptographic application of these results, we exhibit a quantum key distribution protocol that is “secure” if the eavesdropper’s information about the secret key is measured using the accessible information but in which leakage of even a logarithmic number of key bits compromises the secrecy of all the others.
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Acknowledgments
Andreas Winter has independently established some locking results for generic unitary transformations. We would like to thank Jonathan Oppenheim for helpful discussions and the Mittag-Leffler Institute for its kind hospitality. This research was supported by the Canada Research Chairs program, the Perimeter Institute, CIFAR, CFI, FQRNT’s INTRIQ, MITACS, NSERC, ORF, ONR through grant N000140811249, QuantumWorks, and the Swiss National Science Foundation through grant no. 200021-119868.
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Dupuis, F., Florjanczyk, J., Hayden, P., Leung, D. (2014). The Locking-Decoding Frontier for Generic Dynamics. In: Bacon, D., Martin-Delgado, M., Roetteler, M. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2011. Lecture Notes in Computer Science(), vol 6745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54429-3_3
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DOI: https://doi.org/10.1007/978-3-642-54429-3_3
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