Bipartite fluctuations as a probe of many-body entanglement

By Francis Song, S. Rachel, C. Flindt, Israel Klich, N. Laflorencie, Karyn Le Hur. 2011

223 citations recorded by the source corpus.

We investigate in detail the behavior of the bipartite fluctuations of particle number $\hat{N}$ and spin $\hat{S}^z$ in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the R\'{e}nyi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the R\'{e}nyi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/80786aec46cbb0c753bf20e806da1e9c82457b4a

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Symmetry resolved entanglement in free fermionic systems (2019, background): “This quantity has been already studied in the literature [33–37] also because of its relation with the entanglement entropy itself.”
Many-body localization: An introduction and selected topics (2017, unknown): “Let us finally mention that bipartite fluctuations, which are believed to capture entanglement properties for several correlated ground-states [35], also provides a quantitative tool to track area versus volume law behaviors [4, 36].”
Quantum-enhanced measurements without entanglement (2017, background): “…Hines et al., 2003; Kraus et al., 2009; Lewenstein et al., 2007; Li et al., 2001; Micheli et al., 2003; Modi et al., 2012; Paskauskas and You, 2001; Schliemann et al., 2001; Schuch et al., 2004; Song et al., 2012; Tichy et al., 2013; Wiseman and Vaccaro, 2003; Y.Shi, 2004) and references therein.”
Simulating quantum many-body dynamics on a current digital quantum computer (2019, methodology): “For non-interacting models (as is the case for the Hamiltonian of (case (i))), there is a direct relationship between the bipartite von Neumann entanglement entropy and the magnetization ﬂuctuations [68–70].”