Quantum Physics
[Submitted on 15 Apr 2024 (v1), last revised 3 May 2024 (this version, v2)]
Title:Experimental lower bounds on entanglement entropy without twin copy
View PDFAbstract: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. We argue that one should have the inequality $S_{A}^{vN}\geq(2S_A^X-S_{AB}^X)$ holding in more general circumstances. $2S_A^X-S_{AB}^X$ 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 Rényi entanglement entropy.
Submission history
From: Yannick Meurice [view email][v1] Mon, 15 Apr 2024 17:02:17 UTC (731 KB)
[v2] Fri, 3 May 2024 17:09:28 UTC (1,542 KB)
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