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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2017 Volume 138, Pages 99–124 (Mi into217)

This article is cited in 13 papers

Quantum mappings and characterization of entangled quantum states

S. N. Filippov

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: We review quantum mappings used in problems of characterization of entanglement of two-part and multi-particle systems. Together with positive and $n$-tensorial constant positive mappings, we consider physical dynamical processes that lead to quantum channels that break entanglement, annihilate entanglement, dissociate entanglement of multi-particle states, and prohibit distillation of output states. We introduce a new class of absolutely disentangling channels that provide absolutely separable states at the output, and also characterize a new class of entanglement-imposing channels whose output states are entangled. We present states that are most resistant to loss of entanglementand prove that they may differ from maximally entangled states.

Keywords: quantum channel, positive mapping, quantum entanglement, multi-particle entanglement.

UDC: 530.145, 519.72

MSC: 81P40, 47N50


 English version:
Journal of Mathematical Sciences (New York), 2019, 241:2, 210–236

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