90 citations · 760 across the 38 of their papers we have counts for
8 papers · 1 filter
Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach
Giacomo De Palma, Davide Pastorello
We prove new concentration inequalities for quantum spin systems which apply to any local observable measured on any product state or on any state with exponentially decaying corre…
Quantum Optimal Transport: Quantum Channels and Qubits
Giacomo De Palma, Dario Trevisan
These notes are based on the lectures given by the second author at the School on Optimal Transport on Quantum Structures at Erdös Center in September 2022. The focus of the exposi…
The Wasserstein distance of order 1 for quantum spin systems on infinite lattices
Giacomo De Palma, Dario Trevisan
We propose a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice , which we call specific quantum distance. The proposa…
Quantum optimal transport with quantum channels
Giacomo De Palma, Dario Trevisan
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 tran…
The conditional Entropy Power Inequality for bosonic quantum systems
Giacomo De Palma, Dario Trevisan
We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the ou…
Multimode Gaussian optimizers for the Wehrl entropy and quantum Gaussian channels
Giacomo De Palma, Dario Trevisan, Vittorio Giovannetti
We prove in the multimode scenario a fundamental relation between the Wehrl and the von Neumann entropy, stating that the minimum Wehrl entropy among all the quantum states with a…
The Wehrl entropy has Gaussian optimizers
Giacomo De Palma
We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy, and prove that it is achieved by thermal Gaussian states. This result determines t…
The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers
Giacomo De Palma, Dario Trevisan, Vittorio Giovannetti
We determine the p->q norms of the Gaussian one-mode quantum-limited attenuator and amplifier and prove that they are achieved by Gaussian states, extending to noncommutative proba…