Von Neumann entropy and majorization

TY - JOUR

T1 - Von Neumann entropy and majorization

AU - Busch, Paul

AU - Li, Yuan

N1 - © 2013, Elsevier Inc. This is an author produced version of the paper published in Journal of Mathematical Analysis and Applications. Uploaded in accordance with the publisher's self-archiving policies.

PY - 2013/12/1

Y1 - 2013/12/1

N2 - We consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalization of a theorem due to Uhlmann, extending it to infinite dimensional Hilbert spaces. Finally we show that for any quantum channel Φ, one has S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometric operator V such that Φ(ρ)=VρV*.

AB - We consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalization of a theorem due to Uhlmann, extending it to infinite dimensional Hilbert spaces. Finally we show that for any quantum channel Φ, one has S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometric operator V such that Φ(ρ)=VρV*.

KW - quantum operations

KW - von Neumann entropy

U2 - 10.1016/j.jmaa.2013.06.019

DO - 10.1016/j.jmaa.2013.06.019

M3 - Article

VL - 408

SP - 384

EP - 393

JO - Journal of mathematical analysis and applications

JF - Journal of mathematical analysis and applications

SN - 0022-247X

IS - 1

ER -