Bunth, Gergely and Pitrik, József and Titkos, Tamás and Virosztek, Dániel (2024) Metric property of quantum Wasserstein divergences. PHYSICAL REVIEW A, 110 (2). ISSN 2469-9926
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Abstract
Quantum Wasserstein divergences are modified versions of quantum Wasserstein distances defined by channels and they have been 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.
| Item Type: | Article |
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| Additional Information: | Export Date: 20 March 2025; Cited By: 0; Correspondence Address: G. Bunth; HUN-REN, Alfréd Rényi Institute of Mathematics, Budapest, Reáltanoda Utca 13-15, 1053, Hungary; email: bunth.gergely@renyi.hu; J. Pitrik; HUN-REN, Alfréd Rényi Institute of Mathematics, Budapest, Reáltanoda Utca 13-15, 1053, Hungary; email: pitrik.jozsef@renyi.hu; T. Titkos; HUN-REN, Alfréd Rényi Institute of Mathematics, Budapest, Reáltanoda Utca 13-15, 1053, Hungary; email: titkos.tamas@renyi.hu; D. Virosztek; HUN-REN, Alfréd Rényi Institute of Mathematics, Budapest, Reáltanoda Utca 13-15, 1053, Hungary; email: virosztek.daniel@renyi.hu |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 23 Feb 2026 08:23 |
| Last Modified: | 23 Feb 2026 08:23 |
| URI: | https://real.mtak.hu/id/eprint/234821 |
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