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Synopsis

Systems made up of many interacting quantum particles can exhibit a remarkable variety of phenomena, from superconductivity to exotic phases of matter. Over the past two decades, physicists have discovered that many of these phenomena can be understood in terms of quantum entanglement — the strange connections that can exist between different parts of a quantum system. This perspective has not only transformed our understanding of quantum matter, but has also revealed fundamental connections between entanglement and the difficulty of simulating quantum systems on a computer.

In this talk, I will discuss recent theoretical work aimed at extending these ideas beyond the idealized setting of absolute zero, to quantum systems at finite temperatures. In this regime, the role of entanglement is much less well understood, and even determining whether a system is entangled can be surprisingly difficult. To make progress, we draw on ideas from an apparently unrelated field: quantum cryptography, which uses the laws of quantum mechanics to enable secure communication. I will explain how these ideas provide new ways to identify entanglement in thermal systems, revealing that it can persist in unexpected circumstances. We will then see how these results can be used to establish fundamental limits on how efficiently quantum computers can simulate such systems.