Quantifying multipartite entanglement in quantum many-body systems and hybrid quantum computing architectures is a fundamental yet challenging task. In recent years, thermodynamic quantities such as the maximum extractable work from an isolated system (the ergotropy) have allowed for entanglement measures that are operationally more accessible. However, these measures can be restrictive when applied to systems governed by Hamiltonians with strong collective or interparticle interactions. Motivated by advances in quantum simulators, we propose a framework that circumvents these restrictions by evaluating global and local ergotropy either through controlled quenching of interactions or by measuring suitable local observables only. We show that this formalism allows us to correctly estimate genuine multipartite entanglement in both stationary and time-evolved states of systems with strong interactions, including parametrized quantum states simulated on a quantum circuit with varying circuit depth and noise. We demonstrate its applicability to realistic physical models, namely, the Tavis-Cummings model, the three-level Dicke model, and the transverse-field Ising model, highlighting its potential as a versatile tool for characterizing entanglement in near-term quantum simulators.
Quantifying multipartite entanglement in quantum many-body systems and hybrid quantum computing architectures is a fundamental yet challenging task. In recent years, thermodynamic quantities such as the maximum extractable work from an isolated system (the ergotropy) have allowed for entanglement measures that are operationally more accessible. However, these measures can be restrictive when applied to systems governed by Hamiltonians with strong collective or interparticle interactions. Motivated by advances in quantum simulators, we propose a framework that circumvents these restrictions by evaluating global and local ergotropy either through controlled quenching of interactions or by measuring suitable local observables only. We show that this formalism allows us to correctly estimate genuine multipartite entanglement in both stationary and time-evolved states of systems with strong interactions, including parametrized quantum states simulated on a quantum circuit with varying circuit depth and noise. We demonstrate its applicability to realistic physical models, namely, the Tavis-Cummings model, the three-level Dicke model, and the transverse-field Ising model, highlighting its potential as a versatile tool for characterizing entanglement in near-term quantum simulators.
The theory of bipartite entanglement shares profound similarities with thermodynamics. In this Letter we extend this connection to multipartite quantum systems where entanglement appears in different forms with genuine entanglement being the most exotic one. We propose thermodynamic quantities that capture a signature of genuineness in multipartite entangled states. Instead of entropy, these quantities are defined in terms of energy-particularly the difference between global and local extractable works (ergotropies) that can be stored in quantum batteries. Some of these quantities suffice as faithful measures of genuineness and to some extent distinguish different classes of genuinely entangled states. Along with scrutinizing properties of these measures we compare them with the other existing genuine measures, and argue that they can serve the purpose in a better sense. Furthermore, the generality of our approach allows us to define suitable functions of ergotropies capturing the signature of k nonseparability that characterizes qualitatively different manifestations of entanglement in multipartite systems.
Entanglement microscopy reveals the true quantum correlations among the microscopic building blocks of many-body systems [Nat. Commun. 16, 96 (2025)]. Using this approach, we study the multipartite entanglement of the quantum Ising model in 1D, 2D, and 3D. We first obtain the full reduced density matrix (tomography) of subregions that have at most four sites via quantum Monte Carlo, exact diagonalization, and the exact solution in 1D. We then analyze both bipartite and genuine multipartite entanglement (GME) among the sites in the subregion. To do so, we use a variety of measures including the negativity, as well as a true measure of GME: the genuinely multipartite concurrence (or GME concurrence), and its computationally cheaper lower bound I2. We provide a complete proof that I2 bounds the GME concurrence, and show how the symmetries of the state simplify its evaluation. For adjacent sites, we find three- and four-spin GME present across large portions of the phase diagram, reaching a maximum near the quantum critical point. In 1D, we identify the singular scaling of the derivative dI2/dh approaching the critical point. We observe a sharp decrease in GME with increasing dimensionality, consistent with the monogamous nature of entanglement. Furthermore, we find that GME vanishes for subregions consisting of nonadjacent sites in both 2D and 3D, offering a stark illustration of the short-ranged nature of entanglement in equilibrium quantum matter [arXiv:2402.06677]. Finally, we analyze the most collective form of entanglement by evaluating the GME concurrence among all spins in the lattice, which can be obtained from a simple observable: the single-site transverse magnetization. This global concurrence is larger in 1D compared to 2D and 3D, but it is relatively less robust against perturbations such as local measurements.
Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.
Abstract Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology and life sciences. For arbitrary multiparticle systems, entanglement quantification typically involves nontrivial optimisation problems, and it may require demanding tomographical techniques. Here, we develop an experimentally feasible approach to the evaluation of geometric measures of multiparticle entanglement. Our framework provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, or genuine multiparticle entanglement of any general state. For global and partial entanglement, useful bounds are obtained with minimum effort, requiring local measurements in just three settings for any N. For genuine entanglement, a number of measurements scaling linearly with N are required. We demonstrate the power of our approach to estimate and quantify different types of multiparticle entanglement in a variety of N-qubit states useful for quantum information processing and recently engineered in laboratories with quantum optics and trapped ion setups.
The design and benchmarking of quantum computer architectures traditionally rely on practical hardware restrictions, such as gate fidelities, control, and cooling. At the theoretical and software levels, numerous approaches have been proposed for benchmarking quantum devices, ranging from, , quantum volume to randomized benchmarking. In this work, we utilize the quantum information-theoretic properties of multipartite maximally entangled quantum states, in addition to their correspondence with quantum error-correction codes, permitting us to quantify the entanglement generated on near-term bilinear spin-qubit architectures. For this aim, we introduce four metrics that ascertain the quality of genuine multipartite quantum entanglement, along with circuit-level fidelity measures. As part of the task of executing a quantum circuit on a device, we devise simulations, which combine expected hardware characteristics of spin-qubit devices with appropriate compilation techniques; we then analyze three different architectural choices of varying lattice sizes for bilinear arrays, under three increasingly realistic noise models. We find that if the use of a compiler is assumed, sparsely connected spin-qubit lattices can approach comparable values of our metrics to those of the most highly connected device architecture. Even more surprisingly, by incorporating crosstalk into our last noise model, we find that, as error rates for crosstalk approach realistic values, the benefits of utilizing a bilinear array with advanced connectivity vanish. Our results highlight the limitations of adding local connectivity to near-term spin-qubit devices, and can be readily adapted to other qubit technologies. The framework developed here can be used for analyzing quantum entanglement on a device before fabrication, informing experimentalists on concomitant realistic expectations.
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.