Quantum Wasserstein distance based on an optimization over separable states
arXiv:2209.09925 · doi:10.22331/q-2023-10-16-1143
Abstract
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. We extend our results to a family of generalized quantum Fisher information quantities.
25 pages including 2 figures, quantumarticle; v3: typos corrected, presentation improved, further calculations added
References in corpus (21)
- Entanglement detection
- Quantum metrology from a quantum information science perspective
- A complete family of separability criteria
- Entanglement Certification From Theory to Experiment
- Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations
- Entanglement of assistance and multipartite state distillation
- Metric adjusted skew information
- Detecting multipartite entanglement
- Tutorial: Optical quantum metrology
- Evaluation of convex roof entanglement measures
- Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
- Entanglement Detection in Optical Lattices of Bosonic Atoms with Collective Measurements
- QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB
- Exchange Symmetry and Multipartite Entanglement
- Quantum Fisher Information as the Convex Roof of Variance
- Monotonicity of the quantum 2-Wasserstein distance
- A unified approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information
- Ricci curvature for metric-measure spaces via optimal transport
- Isometric rigidity of Wasserstein tori and spheres
- Quantum Wasserstein isometries on the qubit state space
- Towards Optimal Transport for Quantum Densities
Cited by in corpus (6)
- Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach
- Quantum Optimal Transport: Quantum Channels and Qubits
- On the metric property of quantum Wasserstein divergences
- Isometries of the qubit state space with respect to quantum Wasserstein distances
- Quantum Wasserstein distance between unitary operations
- Critical Scaling of the Quantum Wasserstein Distance