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Open Quantum Systems Decoherence

Optimal Transport of a Free Quantum Particle and its Shape Space Interpretation

arXiv
Authors: Bernadette Lessel

Year

2025

Paper ID

16064

Status

Preprint

Abstract Read

~2 min

Abstract Words

116

Citations

N/A

Abstract

A solution of the free Schrödinger equation is investigated by means of Optimal transport. The curve of probability measures μt this solution defines is shown to be an absolutely continuous curve in the Wasserstein space W2\(mathbb{R}3\). The optimal transport map from μt to μs, the cost for this transport (i.e. the Wasserstein distance) and the value of the Fisher information along μt are being calculated. It is finally shown that this solution of the free Schrödinger equation can naturally be interpreted as a curve in so-called Shape space, which forgets any positioning in space but only describes properties of shapes. In Shape space, μt continues to be a shortest path geodesic.

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  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
  • It adds a 2025 reference point for readers tracking recent quantum research.
  • A solution of the free Schrödinger equation is investigated by means of Optimal transport.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2512.06940 [2] arXiv https://arxiv.org/abs/2512.06940 [3] Publisher https://arxiv.org/abs/2512.06940

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