Abstract
Out-of-time-order correlation (OTOC) functions provide a powerful theoretical tool for diagnosing chaos and the scrambling of information in strongly-interacting, quantum systems. However, their direct and unambiguous experimental measurement remains an essential challenge. At its core, this challenge arises from the fact that the effects of both decoherence and experimental noise can mimic that of information scrambling, leading to decay of OTOCs. Here, we analyze a quantum teleportation protocol that explicitly enables one to differentiate between scrambling and decoherence. Moreover, we demonstrate that within this protocol, one can extract a precise "noise" parameter which quantitatively captures the non-scrambling induced decay of OTOCs. Using this parameter, we prove explicit bounds on the true value of the OTOC. Our results open the door to experimentally measuring quantum scrambling with built-in verifiability.
Highlights
The thermalization of strongly interacting systems causes information about the initial configuration to become “scrambled” at late times, wherein two initial states become indistinguishable without measuring a macroscopic number of observables [1,2,3,4]
While a precise definition of quantum scrambling remains elusive, a powerful proxy for characterizing its behavior is provided by out-of-time-order correlation (OTOC) functions, which take the general form hVð0ÞWðtÞVð0ÞWðtÞi, where V, W are operators that act on sufficiently small subsystems [8,10,12,32]
Having detailed a teleportation protocol that explicitly enables experiments to distinguish between decoherence and quantum information scrambling [64], we propose two specific examples of scrambling Clifford circuits [49] amenable to near-term experiments in small-scale quantum simulators [67,68]
Summary
The thermalization of strongly interacting systems causes information about the initial configuration to become “scrambled” at late times, wherein two initial states (with the same conserved quantities) become indistinguishable without measuring a macroscopic number of observables [1,2,3,4]. Requires the precise reversal of time evolution and poses a daunting challenge for any experiment Despite this challenge, a tremendous amount of interest has been devoted to the development of protocols [33,34,35] and platforms [36,37] for the direct measurement of OTOCs. The crucial difficulty in interpreting such measurements can be summarized as follows: For a generic interacting system without symmetries, the scrambling of quantum information will cause out-of-time-order correlation functions to decay to zero. The only way to distinguish between these two contributions— namely, true chaotic scrambling versus noise and decoherence—is to perform full quantum tomography on the many-body system, requiring exponentially many measurements in the number of qubits [38,39,40,41] To this end, the ability to distinguish between genuine quantum information scrambling and extrinsic decoherence remains an essential open question [42]. It turns out that such a successful “decoding” of the original quantum state serves as smoking-gun evidence for the existence of true scrambling dynamics
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