One-Shot Decoupling

By Frédéric Dupuis, Mario Berta, Jürg Wullschleger, Renato Renner. 2010

160 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/6473d5f67bf2feddd9e9b5e7f1901824038907ef

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Exponential Decay of Correlations Implies Area Law (2012, methodology): “Part 2 of the lemma, in turn, is a novel relation: Since one might have H ν max(C) ≥ 3H δ max(B) but H δ min(A|B) ≤ 0, it shows that even in situations where one cannot establish EPR pairs between two parties thus decoupling the third purifying party (which can only happen when H δ min(A|B) > 0 [58]”