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arXiv · 1709.10294

Majorization uncertainty relations for mixed quantum states

Zbigniew Puchała·Łukasz Rudnicki·Aleksandra Krawiec·Karol Życzkowski
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Abstract

Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to measurements with respect to arbitrary two orthogonal bases is derived in terms of the spectrum of $\rho$ and the entries of a unitary matrix $U$ relating both bases. The obtained results 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 uncertainty relation for the sum of conditional entropies.

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Zbigniew Puchała, Łukasz Rudnicki, Aleksandra Krawiec, Karol Życzkowski. 2017-09-29. Majorization uncertainty relations for mixed quantum states. https://doi.org/10.1088/1751-8121/aab66c

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