Measuring multipartite quantum correlations by thermodynamic work extraction

Abstract: Quantum correlations are at the core of quantum mechanics and play a crucial role in various fields. While bipartite quantum correlations have been extensively studied, multipartite quantum correlations in many-body systems remain elusive due to their complex structure. In particular, a primary challenge lies in the fact that the calculation of multipartite quantum correlation measure often requires exponential cost. In this work, we tackle this problem by adopting a thermodynamic approach; we introduce a measure of multipartite quantum correlations based on the difference in extractable thermodynamic work by global operations and local operations and classical communication (LOCC). This can be regarded as a multipartite generalization of the work deficit, which has attracted attention as a thermodynamic measure of bipartite quantum correlation. A distinguishing feature of the thermodynamic approach to multipartite quantum correlation is that we can compare the degree of quantum correlations with clear operational meaning. Importantly, we develop an efficient calculation method of the multipartite work deficit. This efficient method works for a special class of quantum many-body systems described by matrix product states (MPS), where the numerical cost is shown to be proportional to the system size, significantly reducing the exponential cost required for the direct calculations. We demonstrate this efficient method in the AKLT state and the cluster state, and analytically obtain the exact values of this measure. We further show that a quantum phase transition described by MPS is well captured by the multipartite work deficit. This shows that the multipartite work deficit does not only highlight 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.