2019/07/24 by Keiji Matsumoto, Matsumoto, Keiji
Computer Science · Mathematics · #FOS: Physical sciences #Mathematical Inequalities and Applications #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1907.10604
openalex publication_date 2019/07/24 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
Consider a classical system, which is in the state described by probability distribution p or q, and embed these classical informations into quantum system by a physical map Γ, ρ=Γ(p) and σ=Γ(q). Intuitively, the pair \pρM,pσM\ of the distributions of the data of the measurement M on the pair \ρ,σ\ should contain strictly less information than the pair \p,q\ provided the pair \ρ,σ\ is non-commutative. Indeed, this statement had been shown if the information is measured by f-divergence such that f is operator convex. In the paper, the statement is extended to the case where f is strictly convex. Also, we disprove the assertion for the total variation distance \Vert p-q\Vert1, the f-divergence with f(r)=|1-r|: if \ρ,σ\ satisfies some not very restrictive conditions, \Vert pρM-pσM\Vert1 equals \Vert p-q\Vert1. Here we present sufficient condition for general case, and necessary and sufficient condition for qubit states.