Quantum f-Divergences via Nussbaum-Szkola distributions with applications to gaussian states
ORAL
Abstract
We generalize the Nussbaum and Szkola distributions [Ann. Statist., vol. 37, no. 2, pp. 1040–1057, (2009)] to infinite dimensions, and we show that the quantum f-divergence of two quantum states on arbitrary dimensional Hilbert space is equal to the classical f-divergence of the corresponding Nussbaum-Szkola distributions. The method that we use for our derivation is the study of the spectral decomposition of the relative modular operator in a general setting. We give applications to gaussian states by studying a conjecture that was formulated by Seshadreeshan, Lami and Wilde [J. Math. Phys. 59, 072204 (2018)]. The talk is based on joint works with Tiju Cherian John.
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Publication: 1) G. Androulakis, T. Ch. John, "Quantum f-divergences via Nussbaum-Szkola Distributions with applications to Petz-Rényi and von Neumann Relative Entropy", Submitted for publication. Can be viewed at: https://arxiv.org/abs/2203.01964v2, <br>2) G. Androulakis, T. Ch. John, "Petz-Rényi Relative Entropy of Thermal States and their real Displacements" in preparation.<br>3) G. Androulakis, T. Ch. John "Continuous Nussbaum-Szkola distributions", in preparation.
Presenters
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George Androulakis
University of South Carolina
Authors
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George Androulakis
University of South Carolina
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Tiju Cherian John
University of South Carolina