Related papers: On the metric property of quantum Wasserstein divergences

On the metric property of quantum Wasserstein divergences

URL: http://arxiv.org/abs/2402.13150v3
Date: Mon, 12 Aug 2024 17:15:42 GMT
Title: On the metric property of quantum Wasserstein divergences
Authors: Gergely Bunth, József Pitrik, Tamás Titkos, Dániel Virosztek,
Abstract summary: Quantum Wasserstein divergences are modified versions of quantum Wasserstein defined by channels. We prove triangle inequality for quantum Wasserstein divergences for every quantum system described by a separable Hilbert space.
Score: 1.8749305679160366
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Quantum Wasserstein divergences are modified versions of quantum Wasserstein distances defined by channels, and they are conjectured to be genuine metrics on quantum state spaces by De Palma and Trevisan. We prove triangle inequality for quantum Wasserstein divergences for every quantum system described by a separable Hilbert space and any quadratic cost operator under the assumption that a particular state involved is pure, and all the states have finite energy. We also provide strong numerical evidence suggesting that the triangle inequality holds in general, for an arbitrary choice of states.

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