Using time reversal to detect entanglement and spreading of quantum information

Nicole Yunger Halpern

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 enables fluctuation relations to provide insights into holography, condensed matter, and quantum information and vice versa.

Miłosz R. Michalski

Zeyang Li, Simone Colombo, Chi Shu +7 more

Quantum scrambling describes the spreading of information into many degrees of freedom in quantum systems, such that the information is no longer accessible locally but becomes distributed throughout the system. This idea can explain how quantum systems become classical and acquire a finite temperature, or how in black holes the information about the matter falling in is seemingly erased. We probe the exponential scrambling of a multiparticle system near a bistable point in phase space and utilize it for entanglement-enhanced metrology. A time-reversal protocol is used to observe a simultaneous exponential growth of both the metrological gain and the out-of-time-order correlator, thereby experimentally verifying the relation between quantum metrology and quantum information scrambling. Our results show that rapid scrambling dynamics capable of exponentially fast entanglement generation are useful for practical metrology, resulting in a 6.8(4)-decibel gain beyond the standard quantum limit.

Andrew G. White, Daniel F. V. James, William J. Munro +1 more

Maitri Ganguli

We study the behavior of spread complexity in the context of non-Hermitian many-body localization Transition (MBLT). Our analysis has shown that the singular value spread complexity is capable of distinguishing the ergodic and many-body localization (MBL) phase from the presaturation peak height for the non-hermitian models having time-reversal symmetry (TRS) and without TRS. On the other hand, the saturation value of the thermofield double (TFD) state complexity can detect the real-complex transition of the eigenvalues on increasing disorder strength. From the saturation value, we also distinguish the model with TRS and without TRS. The charge density wave complexity shows lower saturation values in the MBL phase for the model with TRS. However, the model without TRS shows a completely different behavior, which is also captivated by our analysis. So, our investigation unravels the real-complex transition in the eigenvalues, the difference between the model having TRS and without TRS, and the effect of boundary conditions for the non-hermitian models having MBL transitions, from the Krylov spread complexity perspective.