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 probability distributions corresponding to measurements with respect to arbitrary two orthogonal bases is derived in terms of the spectrum of ρ 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.
BT - Journal of Physics A: Mathematical and Theoretical DO - 10.1088/1751-8121/aab66c IS - 17 LA - eng N2 -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 probability distributions corresponding to measurements with respect to arbitrary two orthogonal bases is derived in terms of the spectrum of ρ 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.
PY - 2018 SE - 175306 T2 - Journal of Physics A: Mathematical and Theoretical TI - Majorization uncertainty relations for mixed quantum states UR - https://doi.org/10.1088/1751-8121/aab66c VL - 51 ER -