One-Shot Decoupling |
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Authors: | Frédéric Dupuis Mario Berta Jürg Wullschleger Renato Renner |
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Affiliation: | 1. Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland 2. Department of Computer Science and Operations Research, Université de Montréal, Montreal, QC, Canada 3. McGill University, Montreal, QC, Canada
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Abstract: | If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost) completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing the mapping that describes the evolution of A. The criterion applies to arbitrary such mappings in the general one-shot setting. Furthermore, the criterion is tight for mappings that satisfy certain natural conditions. One-shot decoupling has a number of applications both in physics and information theory, e.g., as a building block for quantum information processing protocols. As an example, we give a one-shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption/production. |
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