Majorization uncertainty relations for mixed quantum states

Author Puchała Z.; Rudnicki Ł.; Krawiec A.; Życzkowski K.
Title Majorization uncertainty relations for mixed quantum states
Journal Journal of Physics A: Mathematical and Theoretical
Year 2018
Status Published
Volume 51
Issue 17
DOI 10.1088/1751-8121/aab66c
URL https://doi.org/10.1088/1751-8121/aab66c
Abstract <p>Majorization uncertainty relations are generalized for an arbitrary mixed quantum state <span style="font-size:129%"><em>ρ</em></span> of a finite size <span style="font-size:129%"><em>N</em></span>. 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 <span style="font-size:129%"><em>ρ</em></span> and the entries of a unitary matrix <span style="font-size:129%"><em>U</em></span> 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.</p>