Majorization uncertainty relations for mixed quantum states

Puchała, Zbigniew; Rudnicki, Łukasz; Krawiec, Aleksandra; Życzkowski, Karol

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Majorization uncertainty relations for mixed quantum states

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Rudnicki, Łukasz
Quantumness, Tomography, Entanglement, and Codes, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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引用

Puchała, Z., Rudnicki, Ł., Krawiec, A., & Życzkowski, K. (2018). Majorization uncertainty relations for mixed quantum states. Journal of Physics A: Mathematical and Theoretical, 51(17), 175306.

引用: https://hdl.handle.net/21.11116/0000-0002-9879-B

要旨

Majorization uncertainty relations are generalized for an arbitrary mixed quantum state ρ of a finite size N . In particular, a lower bound for the sum of two entropies characterizing the probability distributions corresponding to measurements with respect to two arbitrary orthogonal bases is derived in terms of the spectrum of ρ and the entries of a unitary matrix U relating both bases. The results obtained can also be formulated for two measurements performed on a single subsystem of a bipartite system described by a pure state, and consequently expressed as an uncertainty relation for the sum of conditional entropies.