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Some properties and applications of the new quantum f-divergences

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arxiv 2501.03799 v1 pith:QA6M62GO submitted 2025-01-07 quant-ph cs.ITmath.IT

Some properties and applications of the new quantum f-divergences

classification quant-ph cs.ITmath.IT
keywords divergencespropertiesquantumsomeapplicationsdivergenceinequalitiesinvestigate
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Recently, a new definition for quantum $f$-divergences was introduced based on an integral representation. These divergences have shown remarkable properties, for example when investigating contraction coefficients under noisy channels. At the same time, many properties well known for other definitions have remained elusive for the new quantum $f$-divergence because of its unusual representation. In this work, we investigate alternative ways of expressing these quantum $f$-divergences. We leverage these expressions to prove new properties of these $f$-divergences and demonstrate some applications. In particular, we give a new proof of the achievability of the quantum Chernoff bound by establishing a strengthening of an inequality by Audenaert et al. We also establish inequalities between some previously known Renyi divergences and the new Renyi divergence. We further investigate some monotonicity and convexity properties of the new $f$-divergences, and prove inequalities between these divergences for various functions.

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Cited by 6 Pith papers

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