While bipartite quantum correlations have been extensively studied across various fields, the role of multipartite quantum correlations in many-body systems remains elusive due to their complex structure. A primary challenge lies in the fact that the calculation of multipartite quantum correlation measure often requires an exponential cost with respect to the system size. In this work, we address this problem by adopting a thermodynamic approach: We introduce a measure of multipartite quantum correlations based on the difference in extractable thermodynamic work between global operations and LOCC (local operations and classical communication). This can be regarded as a multipartite generalization of the bipartite work deficit, which has attracted attention as a thermodynamic measure of bipartite quantum correlation. Importantly, we develop an efficient method for computing the multipartite work deficit in a special class of quantum many-body systems described by matrix product states (MPS). The numerical cost of this method scales linearly with system size, significantly reducing the exponential overhead required for direct calculations. We apply this method to an MPS family and show that a quantum phase transition is well captured by the multipartite work deficit, which exhibits singular behavior at the transition point. Our work shows that the multipartite work deficit not only highlights the fundamental connection between multipartite quantum correlations and quantum thermodynamics, but also serves as an efficiently computable probe of the structures of quantum many-body systems.
While bipartite quantum correlations have been extensively studied across various fields, the role of multipartite quantum correlations in many-body systems remains elusive due to their complex structure. A primary challenge lies in the fact that the calculation of multipartite quantum correlation measure often requires an exponential cost with respect to the system size. In this work, we address this problem by adopting a thermodynamic approach: We introduce a measure of multipartite quantum correlations based on the difference in extractable thermodynamic work between global operations and LOCC (local operations and classical communication). This can be regarded as a multipartite generalization of the bipartite work deficit, which has attracted attention as a thermodynamic measure of bipartite quantum correlation. Importantly, we develop an efficient method for computing the multipartite work deficit in a special class of quantum many-body systems described by matrix product states (MPS). The numerical cost of this method scales linearly with system size, significantly reducing the exponential overhead required for direct calculations. We apply this method to an MPS family and show that a quantum phase transition is well captured by the multipartite work deficit, which exhibits singular behavior at the transition point. Our work shows that the multipartite work deficit not only highlights the fundamental connection between multipartite quantum correlations and quantum thermodynamics, but also serves as an efficiently computable probe of the structures of quantum many-body systems.
Understanding the thermal behavior of quantum many-body pure states is one of the most fundamental issues in quantum thermodynamics. It is widely known that typical pure states yield vanishing work, just as thermal states do, when one restricts to local operations that cannot access correlations among subsystems. However, it remains unclear whether this equivalence to thermal states persists under LOCC (local operations and classical communication), where classically accessible correlations can be exploited for work extraction. In this work, we establish criteria for determining whether many-body pure states remain equivalent to thermal states even under LOCC, and show that this thermal equivalence is governed by their multipartite quantum correlation structure. We show that states with asymptotically maximal multipartite entanglement, such as Haar-random states, cannot yield extensive work under LOCC, whereas some states with limited multipartite entanglement, such as constant-degree graph states, allow extensive work extraction despite being locally indistinguishable from thermal states. Thus, our work provides a refined operational notion of thermal equivalence beyond the traditional local regime, which is becoming increasingly important due to the recent expansion of experimentally accessible operations.
Multipartite entanglement determines the strength and range of interactions in many-body quantum systems. Yet, it is hard to evaluate it, due to the complex structures of quantum states. Here, we introduce a generic method to quantify the k <= N-partite entanglement of an N-particle system, by maximizing an arbitrary bipartite entanglement measure within subsystems of size up to k. The resulting classification of multipartite states captures their experimental cost: creating a k-partite entangled state requires at least k-1 two-particle entangling gates. Further, we analytically calculate the newly defined k-partite entanglement of formation, which generalizes an important bipartite entanglement measure, in several classes of states, including the W states of any dimension.
We review methods that allow one to detect and characterize quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without requiring a number of measurements or computational resources to analyze the data that scale exponentially with the system size. We begin with introducing the concepts of quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in the bipartite scenario, to then present their multipartite generalization. We review recent progress on characterizing these quantum correlations from partial information on the system state, such as through data-driven methods or witnesses based on low-order moments of collective observables. We then review state-of-the-art experiments that demonstrate the preparation, manipulation and detection of highly-entangled many-body systems. For each platform (e.g. atoms, ions, photons, superconducting circuits) we illustrate the available toolbox for state preparation and measurement, emphasizing the challenges that each system poses. To conclude, we present a list of timely open problems in the field.
How we identify heat and work is a fundamental question in modern quantum thermodynamics. Usually, heat and work are attributed to changes in the density matrix and the Hamiltonian, respectively, during time-evolution processes in quantum systems. Recently, it has been recognized that this identification is ambiguous. Furthermore, quantum thermodynamics involving quantum measurement is still under development. Motivated by these on-going works, we consider a quantum many-body system from which we extract energy by local operations and classical communication (LOCC) according to the quantum energy teleportation (QET) protocol. The central idea to define heat and work unambiguously is based on a sharp insight into the optimization condition of LOCC. When LOCC is optimized, the extractable energy by QET becomes a daemonic ergotropy; thus, it can be attributed as work. On the other hand, when LOCC is not optimized, we have not squeezed out all the energy with the unitary operation. It means there is uncontrollable energy left in the system. The uncontrollable energy can be attributed as heat after careful treatment of many-body interactions. The heat term consists of nonlocal correlation due to communication between remote participants, and the correlation cannot be directly observed for the participant in the subsystem. Thus, this feature is consistent with the traditional perspective of heat as an uncontrollable energy. To deeply understand the nature of heat, we derive two types of generalized Clausius inequality in our effective quantum thermodynamics, and discuss the direction of the inequality. To justify our perspective, we examine a one-dimensional Kitaev-like model and discuss the physical meaning of effective temperature in our thermodynamics.
It has recently been shown that the work extractable from correlated bipartite quantum systems under an appropriate protocol can be used to distinguish entanglement from classical correlation. A natural question is now whether it can be generalized to multipartite systems. In this paper, we devise a protocol to distinguish the GHZ, the W, and separable states in terms of the thermodynamically extractable work under local operations and classical communication, and compare the results with those obtained from Mermin's inequalities.
Quantum deficit originates in questions regarding work extraction from quantum systems coupled to a heat bath [Phys. Rev. Lett. 89, 180402 (2002)]. It is a kind of quantum correlations besides entanglement and quantum discord, and links quantum thermodynamics with quantum correlations. In this paper, we evaluate the one-way deficit of two adjacent spins in the bulk for the XY model. We find that the one-way deficit characterizes the quantum phase transition in the XX model and the transverse field Ising model that the XY model reduces to for specified parameters. This study may enlighten extensive studies of quantum phase transitions from the perspective of quantum information and quantum correlations, including finite-temperature phase transitions, phase transitions of other quantum many-body models or even topological phase transitions.