Exponential Clustering of Bipartite Quantum Entanglement at Arbitrary Temperatures
Tomotaka Kuwahara, Keiji Saito
Abstract
Many inexplicable phenomena in low-temperature many-body physics are a result of macroscopic quantum effects. Such macroscopic quantumness is often evaluated via long-range entanglement, that is, entanglement in the macroscopic length scale. Long-range entanglement is employed to characterize novel quantum phases and serves as a critical resource for quantum computation. However, the conditions under which long-range entanglement is stable, even at room temperatures, remain unclear. In this regard, this study demonstrates the unstable nature of bipartite long-range entanglement at arbitrary temperatures, which exponentially decays with distance. The proposed theorem is a no-go theorem pertaining to the existence of long-range entanglement. The obtained results are consistent with existing observations, indicating that long-range entanglement at nonzero temperatures can exist in topologically ordered phases, where tripartite correlations are dominant. The derivation in this study introduces a quantum correlation defined by the convex roof of the standard correlation function. Further, an exponential clustering theorem for generic quantum many-body systems under such a quantum correlation at arbitrary temperatures is established, which yields the primary result by relating quantum correlation with quantum entanglement. Moreover, a simple application of analytical techniques is demonstrated by deriving a general limit on the Wigner-Yanase-Dyson skew and quantum Fisher information; this is expected to attract significant attention in the field of quantum metrology. Notably, this study reveals the novel, general aspects of lowtemperature quantum physics and clarifies the characterization of long-range entanglement.