Exponential clustering of bipartite quantum entanglement at arbitrary temperatures

• URL: http://arxiv.org/abs/2108.12209v4
• Date: Thu, 28 Apr 2022 15:22:43 GMT
• Title: Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Authors: Tomotaka Kuwahara and Keiji Saito
• Abstract summary: We show that bi-partite long-range entanglement is unstable at arbitrary temperatures and exponentially decays with distance. Our work reveals novel general aspects of low-temperature quantum physics and sheds light on the characterization of long-range entanglement.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Macroscopic quantum effects play central roles in the appearance of inexplicable phenomena in low-temperature quantum many-body physics. Such macroscopic quantumness is often evaluated using long-range entanglement, i.e., entanglement in the macroscopic length scale. The long-range entanglement not only characterizes the novel quantum phases but also serves as a critical resource for quantum computation. Thus, the problem that arises is under which conditions can the long-range entanglement be stable even at room temperatures. Here, we show that bi-partite long-range entanglement is unstable at arbitrary temperatures and exponentially decays with distance. Our theorem provides a no-go theorem on the existence of the long-range entanglement. The obtained results are consistent with the existing observations that long-range entanglement at non-zero temperatures can exist in topologically ordered phases, where tripartite correlations are dominant. In the derivation of our result, we introduce a quantum correlation defined by the convex roof of the standard correlation function. We establish an exponential clustering theorem for generic quantum many-body systems for such a quantum correlation at arbitrary temperatures, which yields our main result by relating quantum correlation to quantum entanglement. As a simple application of our analytical techniques, we derived a general limit on the Wigner-Yanase-Dyson skew information and the quantum Fisher information, which will attract significant attention in the field of quantum metrology. Our work reveals novel general aspects of low-temperature quantum physics and sheds light on the characterization of long-range entanglement.

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