Measuring multipartite entanglement through dynamic susceptibilities

Abstract

Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterising quantum phases and quantum phase transitions. Developing protocols to detect and quantify entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, representing a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles via the dynamic susceptibility, i.e., with resources readily available in present cold atomic gas and condensed-matter experiments. This moreover establishes a fundamental connection between multipartite entanglement and many-body correlations contained in response functions, with profound implications close to quantum phase transitions. There, the quantum Fisher information becomes universal, allowing us to identify strongly entangled phase transitions with a divergent multipartiteness of entanglement. We illustrate our framework using paradigmatic quantum Ising models, and point out potential signatures in optical-lattice experiments.Entanglement is a central theoretical concept underlying the characterisation of quantum many-body states in condensed-matter and high-energy physics, as well as quantum information. For example, entanglement properties reveal exotic states of matter such as topological spin liquids [1] or many-body localization [2,3], the holographic entanglement entropy identifies confinement/deconfinement transitions in gauge theories [4,5], and entanglement is considered the central resource for quantum-enhanced metrology [6,7] as well as quantum computation [8][9][10][11]. In experiments, entanglement becomes measurable via a tomographic determination of the many-particle quantum state [12][13][14][15], and protocols have been developed [16] and implemented in remarkable experiments [17] to measure entanglement entropies in quench dynamics and quantum phase transitions. However, the resources required by these protocols scale exponentially with the system size, and these experimental efforts are thus limited a priori to few-particle systems.To address the problem of detecting and quantifying multipartite entanglement for large systems, we consider below the quantum Fisher information (QFI) as an entanglement witness [18][19][20]. Our key result is thatfor a many-body system at thermal equilibrium at any temperature-the QFI can be determined directly from a measurement of Kubo linear response functions, in particular the dynamic susceptibility (see Fig. 1). We emphasise that this measurement prescription is independent of microscopic details of the system of interest and that the measurement of linear response is a standard tool in experiments. Importantly, only modest measurement resources are required that do not scale with system size. The presented prescription therefore makes multipartite entanglement observable for a large variety of * philipp.hauke@uibk.ac.at χ (ω, T ) gives the quantum Fisher information (shaded areas). (c) This pro...

Achieving sub-shot-noise sensing at finite temperatures

“…That is, the SLD characterizes the most informative measurements about λ. Importantly enough, the QFI is also a witness of multipartite entanglement among the individual constituents of a many-body system [39][40][41][42].…”

“…For instance, if the parameter to be estimated is temperature, the specific heat is the relevant figure of merit and, as we will see below, what limits the sensitivity of a magnetometer is its magnetic susceptibility [26,33,36,39,[45][46][47][48].…”

Entanglement and entropy production in coupled single-mode Bose-Einstein condensates

“…In particular, it has been shown that the entanglement entropy shows a logarithmic divergence at the critical point of the quantum phase transition [31,32]. Similar divergence in the entanglement properties of the ground state at the critical point has also been observed in other systems, like the Dicke model or the transverse field Ising model [33,34]. Moreover, the dynamics of the von Neumann entropy of a single spin in the Lipkin-Meshkov-Glick model has also been investigated [35].…”

Edge insulating topological phases in a two-dimensional superconductor with long-range pairing

“…Notably, even there, β remains smaller than 2, implying that multipartite entanglement cannot be detected using local operators involving (linear combinations of) c i and c † i . This results enlarges the picture achieved for the LR Kitaev chain [47,53].…”