Jarzynski-like equality for the out-of-time-ordered correlator

TL;DR

This paper derives a Jarzynski-like equality for the out-of-time-ordered correlator (OTOC), linking quantum chaos diagnostics with fluctuation relations, and proposes a universal measurement protocol.

Contribution

It introduces a novel Jarzynski-like equality for the OTOC, connecting quantum chaos measures with nonequilibrium fluctuation relations and enabling indirect measurement protocols.

Findings

The equality relates the OTOC to a measurable quantity.

The protocol does not require reversing time evolution.

It is applicable across various quantum platforms.

Abstract

The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the scrambling of quantum information via the spread of entanglement. The OTOC encodes forward and reverse evolutions and has deep connections with the flow of time. So do fluctuation relations such as Jarzynski's Equality, derived in nonequilibrium statistical mechanics. I unite these two powerful, seemingly disparate tools by deriving a Jarzynski-like equality for the OTOC. The equality's left-hand side equals the OTOC. The right-hand side suggests a protocol for measuring the OTOC indirectly. The protocol is platform-nonspecific and can be performed with weak measurement or with interference. Time evolution need not be reversed in any interference trial. The equality opens holography, condensed matter, and quantum information to new insights from fluctuation relations and vice versa.