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QI: Fachverband Quanteninformation
QI 29: Quantum Information: Concept and Methods II
QI 29.10: Vortrag
Donnerstag, 21. März 2024, 17:30–17:45, HFT-TA 441
Quantum Wasserstein distance based on an optimization over subsets of physical quantum states — •Géza Tóth1,2,3,4 and József Pitrik4,5,6 — 1Theoretical Physics and EHU Quantum Center, University of the Basque Country UPV/EHU, ES-48080 Bilbao, Spain — 2Donostia International Physics Center (DIPC), ES-20080 San Sebastián, Spain — 3IKERBASQUE, Basque Foundation for Science, ES-48011 Bilbao, Spain — 4Wigner Research Centre for Physics, HU-1525 Budapest, Hungary — 5Alfréd Rényi Institute of Mathematics, HU-1053 Budapest, Hungary — 6Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, HU-1111 Budapest, Hungary
We define the quantum Wasserstein distance such that the optimization of the coupling is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that the self-distance is related to the quantum Fisher information. We present a transport map corresponding to an optimal bipartite separable state. We discuss how the quantum Wasserstein distance introduced is connected to criteria detecting quantum entanglement. We define variance-like quantities that can be obtained from the quantum Wasserstein distance by replacing the minimization over quantum states by a maximization. Besides separable states, we consider other relevant subsets of physical quantum states. We extend our results to a family of generalized quantum Fisher information quantities.
[1] G. Tóth and J. Pitrik, Quantum 7, 1143 (2023); arXiv:2209.09925.