Quantum Monge-Kantorovich Problem and Transport Distance between Density Matrices
| العنوان: | Quantum Monge-Kantorovich Problem and Transport Distance between Density Matrices |
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| المؤلفون: | Shmuel Friedland, Michał Eckstein, Sam Cole, Karol Życzkowski |
| المصدر: | Physical Review Letters. 129 |
| بيانات النشر: | American Physical Society (APS), 2022. |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Quantum Physics, FOS: Physical sciences, General Physics and Astronomy, Mathematical Physics (math-ph), 81P40, 90C22, 15A69, Quantum Physics (quant-ph), Mathematical Physics |
| الوصف: | A quantum version of the Monge--Kantorovich optimal transport problem is analyzed. The transport cost is minimized over the set of all bipartite coupling states $\rho^{AB}$, such that both of its reduced density matrices $\rho^A$ and $\rho^B$ of dimension $N$ are fixed. We show that, selecting the quantum cost matrix to be proportional to the projector on the antisymmetric subspace, the minimal transport cost leads to a semidistance between $\rho^A$ and $\rho^B$, which is bounded from below by the rescaled Bures distance and from above by the root infidelity. In the single qubit case we provide a semi-analytic expression for the optimal transport cost between any two states and prove that its square root satisfies the triangle inequality and yields an analogue of the Wasserstein distance of order two on the set of density matrices. We introduce an associated measure of proximity of quantum states, called SWAP-fidelity, and discuss its properties and applications in quantum machine learning. Comment: 15 pages including appendices, 4 figures. Version v2 includes a new quantity, SWAP-fidelity, and some applications |
| تدمد: | 1079-7114 0031-9007 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f8c64d219883151afd55357ecbcd50fc https://doi.org/10.1103/physrevlett.129.110402 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....f8c64d219883151afd55357ecbcd50fc |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 10797114 00319007 |
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