Exponential clustering of bipartite quantum entanglement at arbitrary temperatures

TL;DR

This paper proves that bipartite long-range entanglement in quantum many-body systems cannot be stable at arbitrary temperatures, decaying exponentially with distance, and introduces a new exponential clustering theorem related to quantum correlations.

Contribution

The authors establish a no-go theorem for long-range entanglement at finite temperatures and develop an exponential clustering theorem for a new quantum correlation measure, linking it to entanglement.

Findings

Long-range bipartite entanglement decays exponentially at any temperature.

A new exponential clustering theorem for quantum correlations is proven.

Derived limits on quantum Fisher information relevant to quantum metrology.

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.