Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 328, Issue 1, Pages 251-284Publisher
SPRINGER
DOI: 10.1007/s00220-014-1990-4
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Funding
- Swiss National Science Foundation [200021-119868, 200020-135048, PP00P2-128455, 20CH21-138799]
- National Centre of Competence in Research 'Quantum Science and Technology (QSIT)'
- European Research Council [258932]
- Canada's NSERC
- German Science Foundation [CH 843/2-1]
- Swiss State Secretariat for Education and Research [MP1006]
- UK EPSRC [EP/E04297X/1]
- Canada-France NSERC-ANR
- Engineering and Physical Sciences Research Council [EP/E04297X/1] Funding Source: researchfish
- EPSRC [EP/E04297X/1] Funding Source: UKRI
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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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