# A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature

@inproceedings{Feliciangeli2021ANE, title={A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature}, author={Dario Feliciangeli and Augusto Gerolin and Lorenzo Portinale}, year={2021} }

This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical…

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