Defines Boltzmann-Wasserstein distance on quantum theories via optimal W2 transport of Boltzmann-weighted spectra, equates it to thermal correlators, and constructs a Schwinger-Keldysh wormhole saddle that reproduces the spectral optimum.
De Palma and D
3 Pith papers cite this work, alongside 6 external citations. Polarity classification is still indexing.
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abstract
We propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a transport cost. Our proposal is the first where the transport plans between quantum states are in natural correspondence with quantum channels, such that the transport can be interpreted as a physical operation on the system. Our main result is the proof of a modified triangle inequality for our transport distance. We also prove that the distance between a quantum state and itself is intimately connected with the Wigner-Yanase metric on the manifold of quantum states. We then specialize to quantum Gaussian systems, which provide the mathematical model for the electromagnetic radiation in the quantum regime. We prove that the noiseless quantum Gaussian attenuators and amplifiers are the optimal transport plans between thermal quantum Gaussian states, and that our distance recovers the classical Wasserstein distance in the semiclassical limit.
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Optimal transport yields a generalized Wasserstein distance on field space, obtained from a WKB expansion of a Schrödinger equation and extended to dynamical gravity via the Wheeler-DeWitt equation in the ADM formalism.
Within quadratic costs from ≤ d^{2}-1 observables, Wasserstein isometries are precisely the Wigner symmetries iff the cost is isotropic (a positive multiple of the identity on the traceless subspace).
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Notes on Wasserstein distance and wormholes
Defines Boltzmann-Wasserstein distance on quantum theories via optimal W2 transport of Boltzmann-weighted spectra, equates it to thermal correlators, and constructs a Schwinger-Keldysh wormhole saddle that reproduces the spectral optimum.
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Optimal paths across potentials on scalar field space
Optimal transport yields a generalized Wasserstein distance on field space, obtained from a WKB expansion of a Schrödinger equation and extended to dynamical gravity via the Wheeler-DeWitt equation in the ADM formalism.
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Wigner symmetries single out symmetric Wasserstein distances in all finite dimensions
Within quadratic costs from ≤ d^{2}-1 observables, Wasserstein isometries are precisely the Wigner symmetries iff the cost is isotropic (a positive multiple of the identity on the traceless subspace).