Quantum Wasserstein distance for Gaussian states

• URL: http://arxiv.org/abs/2512.17809v1
• Date: Fri, 19 Dec 2025 17:13:55 GMT
• Title: Quantum Wasserstein distance for Gaussian states
• Authors: Anaelle Hertz, Mohammad Ahmadpoor, Oleksandr Dzhenzherov, Augusto Gerolin, Khabat Heshami,
• Abstract summary: We give a general formula for the Wasserstein distance of order 2 between any two one-mode Gaussian states.<n>This opens the path to directly compare various known distance measures with the Wasserstein distance through their closed-form solutions.
• Score: 12.174346896225153
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Optimal transport between classical probability distributions has been proven useful in areas such as machine learning and random combinatorial optimization. Quantum optimal transport, and the quantum Wasserstein distance as the minimal cost associated with transforming one quantum state to another, is expected to have implications in quantum state discrimination and quantum metrology. In this work, following the formalism introduced in [De Palma, G. and Trevisan, D. Ann. Henri Poincaré, {\bf 22} (2021), 3199-3234] to compute the optimal transport plan between two quantum states, we give a general formula for the Wasserstein distance of order 2 between any two one-mode Gaussian states. We discuss how the Wasserstein distance between classical Gaussian distributions and the quantum Wasserstein distance by De Palma and Trevisan for thermal states can be recovered from our general formula for Gaussian states. This opens the path to directly compare various known distance measures with the Wasserstein distance through their closed-form solutions.

Related papers

• Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances [70.94157767200342]
  We propose a fast estimation method based on regressing Wasserstein distance on sliced Wasserstein distances.<n>We show that accurate models can be learned from a small number of distribution pairs.<n>Our method consistently provides a better approximation of Wasserstein distance than the state-of-the-art Wasserstein embedding model, Wasserstein Wormhole.
  arXiv  Detail & Related papers  (2025-09-24T19:30:53Z)
• Wasserstein Distances on Quantum Structures: an Overview [0.0]
  Theory of optimal transport of probability measures has wide-ranging applications across a number of different fields.<n>Quantum Wasserstein distances have led to a broad range of developments in the quantum setting.<n>This review is written for those interested in quantum optimal transport in coming from both the fields of classical optimal transport and of quantum information theory.
  arXiv  Detail & Related papers  (2025-06-11T14:39:33Z)
• Wasserstein distances and divergences of order $p$ by quantum channels [1.8749305679160366]
  We introduce a non-quadratic generalization of the quantum mechanical optimal transport problem.<n> Relying on this general machinery, we introduce $p$-Wasserstein distances and divergences.<n>We prove triangle inequality for Wasserstein divergences under the sole assumption that an arbitrary one of the states involved is pure.
  arXiv  Detail & Related papers  (2025-01-14T12:29:05Z)
• One-Shot Min-Entropy Calculation Of Classical-Quantum States And Its Application To Quantum Cryptography [21.823963925581868]
  We develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state.<n>It offers an alternative tight finite-data analysis for the BB84 quantum key distribution scheme.<n>It gives the best finite-key bound known to date for a variant of device independent quantum key distribution protocol.
  arXiv  Detail & Related papers  (2024-06-21T15:11:26Z)
• Bounding the rotating wave approximation for coupled harmonic oscillators [34.82692226532414]
  We study the validity of the rotating wave approximation of an ideal system composed of two harmonic oscillators evolving with a quadratic Hamiltonian and arbitrarily strong interaction.<n>We are able to fully quantify the deviation of arbitrary pure Gaussian states that evolve through different dynamics from a common quantum state.
  arXiv  Detail & Related papers  (2024-03-22T16:51:53Z)
• Quantum simulation of Maxwell's equations via Schr\"odingersation [27.193565893837356]
  We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schr"odingersation approach. Instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework.
  arXiv  Detail & Related papers  (2023-08-16T14:52:35Z)
• Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr\"odinger Equation [56.9919517199927]
  "Wasserstein Quantum Monte Carlo" (WQMC) uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.
  arXiv  Detail & Related papers  (2023-07-06T17:54:08Z)
• Rate-Limited Quantum-to-Classical Optimal Transport in Finite and Continuous-Variable Quantum Systems [11.152271223282463]
  We consider the rate-limited quantum-to-classical optimal transport in terms of output-constrained rate-distortion coding. We develop a coding framework for continuous-variable quantum systems by employing a clipping projection and a dequantization block. For the Gaussian quantum systems, we derive an analytical solution for rate-limited Wasserstein distance of order 2.
  arXiv  Detail & Related papers  (2023-05-17T07:16:20Z)
• Quantum Wasserstein distance based on an optimization over separable states [0.0]
  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.
  arXiv  Detail & Related papers  (2022-09-20T18:01:33Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• The Quantum Wasserstein Distance of Order 1 [16.029406401970167]
  We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposed distance is invariant with respect to permutations of the qudits and unitary operations acting on one qudit. We also propose a generalization of the Lipschitz constant to quantum observables.
  arXiv  Detail & Related papers  (2020-09-09T18:00:01Z)
• Gaussian conversion protocols for cubic phase state generation [104.23865519192793]
  Universal quantum computing with continuous variables requires non-Gaussian resources. The cubic phase state is a non-Gaussian state whose experimental implementation has so far remained elusive. We introduce two protocols that allow for the conversion of a non-Gaussian state to a cubic phase state.
  arXiv  Detail & Related papers  (2020-07-07T09:19:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.