The α–z Rényi relative entropies are a two-parameter family of Rényi relative entropies that are quantum generalizations of the classical α-Rényi relative entropies. In the work [Adv. Math. 365, 107053 (2020)], we decided the full range of (α, z) for which the data processing inequality (DPI) is valid. In this paper, we give algebraic conditions for the equality in DPI. For the full range of parameters (α, z), we give necessary conditions and sufficient conditions. For most parameters, we give equivalent conditions. This generalizes and strengthens the results of Leditzky et al. [Lett. Math. Phys. 107, 61–80 (2017)].The α–z Rényi relative entropies are a two-parameter family of Rényi relative entropies that are quantum generalizations of the classical α-Rényi relative entropies. In the work [Adv. Math. 365, 107053 (2020)], we decided the full range of (α, z) for which the data processing inequality (DPI) is valid. In this paper, we give algebraic conditions for the equality in DPI. For the full range of parameters (α, z), we give necessary conditions and sufficient conditions. For most parameters, we give equivalent conditions. This generalizes and strengthens the results of Leditzky et al. [Lett. Math. Phys. 107, 61–80 (2017)].

arXiv:2007.06644Journal of Mathematical PhysicsOct 1, 202012 citations

Reverse of the Ruskai-Stillinger bounds for the quantum relative entropy

Mina Sadeghinezhad, Hamed Najafi

Linear Algebra and its ApplicationsJun 1, 20260 citations

A new proof for monotonicity of sandwiched Renyi relative entropy

wang you le, Luo Maokang, DENG Ke

Itis well known that in quantum information quantum relative is monotonically decreasing under the completely positive and trace-preserving maps. For a new proposed sandwiched R\'enyi quantum relative, a map that is linear trace-preserving and whose Hilber-Schmidt adjoint map satisfies Schwarz inequality, monotonicity still holds. We give a new proof of monotonicity of sandwiched R\'enyi relative entropy for $\alpha\in[\frac{1}{2},1)$ . The proof is based on complex interplotation techniques, which already has been used to prove monotonicity under trace-preserving and positive map for $\alpha\in(1,\infty)$ .Itis well known that in quantum information quantum relative is monotonically decreasing under the completely positive and trace-preserving maps. For a new proposed sandwiched R\'enyi quantum relative, a map that is linear trace-preserving and whose Hilber-Schmidt adjoint map satisfies Schwarz inequality, monotonicity still holds. We give a new proof of monotonicity of sandwiched R\'enyi relative entropy for $\alpha\in[\frac{1}{2},1)$. The proof is based on complex interplotation techniques, which already has been used to prove monotonicity under trace-preserving and positive map for $\alpha\in(1,\infty)$.

Jan 1, 20180 citations

An Ergodic Theorem for the Quantum Relative Entropy

Igor Bjelaković, Rainer Siegmund‐Schultze

arXiv:quant-ph/0306094Communications in Mathematical PhysicsMay 25, 200421 citations

\alpha\in[\frac{1}{2},1)

. The proof is based on complex interplotation techniques, which already has been used to prove monotonicity under trace-preserving and positive map for

\alpha\in(1,\infty)