The sandwiched rényi divergence and quantum positive evidence order in infinite-dimensional hilbert space. Issue 2 (October 2021)

• Record Type: Journal Article
• Authors: Li, Yuan; Gao, Shuhui; Hao, Hongyan
• Is Part Of: Reports on mathematical physics. Volume 88:Issue 2(2021)
• Page Start: 175
• Page End: 193
• Publication Date: 2021-10
• Subjects: partial orders -- quantum Rényi divergence -- quantum states; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(21)00068-9
• Languages: English
• ISSNs: 0034-4877

Abstract

Abstract : The aim of this note is to extend some main results of the sandwiched Rényi divergence and quantum positive evidence order from finite- to the infinite-dimensional separable Hilbert spaces. We first define sandwiched Rényi divergence D α (ρ||ρ) for α > 1 in separable Hilbert space and consider the positivity, monotonicity and limitation of D α (ρ||σ) (α → ∞). Then we give some sufficient and necessary conditions of σ ⊑ ρ with respect to the quantum positive evidence order, where σ and ρ are quantum states.