Computation of sandwiched relative alpha-entropy of two n-mode gaussian states

Parthasarathy, K. R.

doi:10.48550/arxiv.2109.04062

Cited by 1 publication

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References 10 publications

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“…Recently, Seshadreeshan, Lami and Wilde in [9] and Parthasarathy in [10] studied the Petz-Rényi relative entropy in the infinite dimesnional setting, for the particular case of gaussian states. A related entropic quantity called sandwiched Rényi relative entropy gained prominence in the recent years due to several nice properties satisfied by them, [11,12,13,14,15]. It should be noted that all of these entropic quantities are important in quantum information theory in general and quantum hypothesis testing in particular.…”

Section: Introductionmentioning

confidence: 99%

Quantum $f$-divergences via Nussbaum-Szkoła Distributions with applications to Petz-Rényi and von Neumann Relative Entropy

Androulakis¹,

John²

2022

Preprint

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Let K be a complex separable Hilbert space of finite or infinite dimensions. We prove that the Petz-Rényi relative entropy of any two quantum states ρ and σ on K, denoted by D α (ρ||σ) reduces to the Rényi relative entropy (divergence) of two classical probability measures P and Q obtained from ρ and σ. This leads to a number of new results in the infinite dimensions, and new proofs for some known results in the finite dimensional setting. Our method provides a general framework for proving a quantum counterpart of any result about the classical Rényi divergence involving only two probability distributions. Furthermore, we construct an example to show that the information theoretic definition of the von Neumann relative entropy is different from Araki's definition of relative entropy. This disproves a recent attempt in the literature to prove such a result. All the results proved here are valid in both finite and infinite dimensions and hence can be applied to continuous variable systems as well.

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