Experimental lower bounds on entanglement entropy without twin copy

• URL: http://arxiv.org/abs/2404.09935v4
• Date: Mon, 28 Oct 2024 21:54:32 GMT
• Title: Experimental lower bounds on entanglement entropy without twin copy
• Authors: Yannick Meurice,
• Abstract summary: We calculate the Shannon entropy $S_ABX$ associated with the experimental measurements of adiabatically prepared ground states. We show several examples for which, in good approximation, $S_AvNpropto (2S_AX-S_ABX)$ with a constant of proportionality slightly larger than one.
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• Abstract: We discuss the possibility of estimating experimentally the von Neumann entanglement entropy $S_{A}^{vN}$ of a symmetric bi-partite quantum system $AB$ by using the basic measurement counts for a it $single$ copy of a prepared state. Using exact diagonalization and analog simulations performed with the publicly available QuEra facilities for chains and ladders of Rydberg atoms, we calculate the Shannon entropy $S_{AB}^X$ associated with the experimental measurements of adiabatically prepared ground states and the reduced entropy $S_A^X$ obtained by tracing the experimental probabilities over the $B$ half of the system. We show several examples for which, in good approximation, $S_{A}^{vN}\propto (2S_A^X-S_{AB}^X)$ with a constant of proportionality slightly larger than one. Our data and specific examples of states suggest that one should have the inequality $S_{A}^{vN}\geq(2S_A^X-S_{AB}^X)$ holding in more general circumstances. This is actually a consequence of Holevo's bound. $2S_A^X-S_{AB}^X$ can be calculated easily for many qubit platforms and appears to be generically robust under measurement errors. Similar results are found for the second order R\'enyi entanglement entropy.

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