aqora

A Strengthened Monotonicity Inequality of Quantum Relative Entropy: A Unifying Approach Via Rényi Relative Entropy

Lin Zhang

arXiv:1403.5343Letters in Mathematical PhysicsMar 4, 20169 citations

Quantifying the quantumness of ensembles via generalized α-z-relative rényi entropy

Huaijing Huang, Zhaoqi Wu, Chuanxi Zhu +1 more

International Journal of Theoretical PhysicsJul 12, 20208 citations

Geometric relative entropies and barycentric Rényi divergences

Milán Mosonyi, Gergely Bunth, Péter Vrana

arXiv:2207.14282Linear Algebra and its ApplicationsJun 7, 202413 citations

Rényi–Holevo inequality from α-z-Rényi relative entropies

Diego G. Bussandri, Grzegorz Rajchel-Mieldzioć, Pedro W. Lamberti +1 more

We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the [Formula: see text]-[Formula: see text]-Rényi relative entropies, which comprise known relevant quantities such as the Rényi relative entropy and the sandwiched Rényi relative entropy, we establish the Holevo–Rényi inequality. This result leads to a quantum bound for the [Formula: see text]-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the [Formula: see text]-[Formula: see text]-Rényi relative entropies, which comprise known relevant quantities such as the Rényi relative entropy and the sandwiched Rényi relative entropy, we establish the Holevo–Rényi inequality. This result leads to a quantum bound for the [Formula: see text]-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.

arXiv:2309.04539International Journal of Quantum InformationApr 30, 20242 citations

Symmetric Petz-Rényi relative entropy uncertainty relation

Domingos S. P. Salazar

Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace norm in evaluating their similarity. This fidelity is bounded by a function of the trace norm, a relationship to which we will refer as Holevo's inequality. More broadly, Holevo's fidelity is part of a one-parameter family of symmetric Petz-Rényi relative entropies, which in turn satisfy a Pinsker's-like inequality with respect to the trace norm. Although Holevo's inequality is tight, Pinsker's inequality is loose for this family. We show that the symmetric Petz-Rényi relative entropies satisfy a tight inequality with respect to the trace norm, improving Pinsker's and reproducing Holevo's as a specific case. Additionally, we show how this result emerges from a symmetric Petz-Rényi uncertainty relation, a result that encompasses several relations in quantum and stochastic thermodynamics.Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace norm in evaluating their similarity. This fidelity is bounded by a function of the trace norm, a relationship to which we will refer as Holevo's inequality. More broadly, Holevo's fidelity is part of a one-parameter family of symmetric Petz-Rényi relative entropies, which in turn satisfy a Pinsker's-like inequality with respect to the trace norm. Although Holevo's inequality is tight, Pinsker's inequality is loose for this family. We show that the symmetric Petz-Rényi relative entropies satisfy a tight inequality with respect to the trace norm, improving Pinsker's and reproducing Holevo's as a specific case. Additionally, we show how this result emerges from a symmetric Petz-Rényi uncertainty relation, a result that encompasses several relations in quantum and stochastic thermodynamics.

arXiv:2402.01390Feb 2, 20240 citations

On quantum Renyi entropies: a new definition and some properties.

Martin Müller-Lennert, Frédéric Dupuis, Oleg Szehr +2 more

Jun 13, 201326 citations

Rényi–Holevo inequality from α-z-Rényi relative entropies

Related papers

Rényi–Holevo inequality from α-z-Rényi relative entropies

Related papers