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• W4381854199 abstract "We propose a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice $mathbb{Z}^d$, which we call specific quantum $W_1$ distance. The proposal is based on the $W_1$ distance for qudits of [De Palma et al., IEEE Trans. Inf. Theory 67, 6627 (2021)] and recovers Ornstein's $bar{d}$-distance for the quantum states whose marginal states on any finite number of spins are diagonal in the canonical basis. We also propose a generalization of the Lipschitz constant to quantum interactions on $mathbb{Z}^d$ and prove that such quantum Lipschitz constant and the specific quantum $W_1$ distance are mutually dual. We prove a new continuity bound for the von Neumann entropy for a finite set of quantum spins in terms of the quantum $W_1$ distance, and we apply it to prove a continuity bound for the specific von Neumann entropy in terms of the specific quantum $W_1$ distance for quantum spin systems on $mathbb{Z}^d$. Finally, we prove that local quantum commuting interactions above a critical temperature satisfy a transportation-cost inequality, which implies the uniqueness of their Gibbs states." @default.
• W4381854199 created "2023-06-25" @default.
• W4381854199 creator A5055460463 @default.
• W4381854199 creator A5060889284 @default.
• W4381854199 date "2023-06-24" @default.
• W4381854199 modified "2023-10-07" @default.
• W4381854199 title "The Wasserstein Distance of Order 1 for Quantum Spin Systems on Infinite Lattices" @default.
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• W4381854199 doi "https://doi.org/10.1007/s00023-023-01340-y" @default.
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