2010/11/07 by Frédéric Dupuis, Jan Florjanczyk, Patrick Hayden +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Cryptography #Decoding methods #Entropy (arrow of time) #Information leakage #Information theory #Information-theoretic security #Logarithm #Mathematics #Mutual information #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum information #Quantum mechanics #Quantum mutual information #Statistical physics #Statistics #Von Neumann entropy #quant-ph
paper · pdf · doi:10.1098/rspa.2013.0289
published as Proc. R. Soc. A 8 November 2013 vol. 469 no. 2159 · 32 pages, 2 figures
arxiv created 2010/11/07 · openalex publication_date 2013/09/18 · arxiv updated 2014/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is known that the maximum classical mutual information, which can be achieved between measurements on pairs of quantum systems, can drastically underestimate the quantum mutual information between them. 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 yield only 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. While previous works had always assumed a uniform message, we assume only a min-entropy bound and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. Finally, we exhibit a quantum key distribution protocol that is 'secure' in the sense of accessible information but in which leakage of even a logarithmic number of bits compromises the secrecy of all others.