TY - JOUR
T1 - Convexity of quantum χ2-divergence
AU - Hansen, Frank
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/6/21
Y1 - 2011/6/21
N2 - The general quantum χ2-divergence has recently been introduced by Temme et al. [Temme K, Kastoryano M, Ruskai M, Wolf M, Verstrate F (2010) J Math Phys 51:122201] and applied to quantum channels (quantum Markov processes). The quantum χ2-divergence is not unique, as opposed to the classical χ2-divergence, but depends on the choice of quantum statistics. It was noticed that the elements in a particular one-parameter family χα2(ρ,σ) of quantum χ2-divergences are convex functions in the density matrices (ρ,σ), thus mirroring the convexity of the classical χ2(p,q)-divergence in probability distributions (p,q). We prove that any quantum χ2-divergence is a convex function in its two arguments.
AB - The general quantum χ2-divergence has recently been introduced by Temme et al. [Temme K, Kastoryano M, Ruskai M, Wolf M, Verstrate F (2010) J Math Phys 51:122201] and applied to quantum channels (quantum Markov processes). The quantum χ2-divergence is not unique, as opposed to the classical χ2-divergence, but depends on the choice of quantum statistics. It was noticed that the elements in a particular one-parameter family χα2(ρ,σ) of quantum χ2-divergences are convex functions in the density matrices (ρ,σ), thus mirroring the convexity of the classical χ2(p,q)-divergence in probability distributions (p,q). We prove that any quantum χ2-divergence is a convex function in its two arguments.
KW - Monotone metric
KW - Operator monotone function
KW - Quantum mechanics
UR - http://www.scopus.com/inward/record.url?scp=79959924254&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79959924254&partnerID=8YFLogxK
U2 - 10.1073/pnas.1106423108
DO - 10.1073/pnas.1106423108
M3 - Article
C2 - 21642538
AN - SCOPUS:79959924254
VL - 108
SP - 10078
EP - 10080
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
SN - 0027-8424
IS - 25
ER -