Separation of Out-Of-Time-Ordered Correlation and Entanglement

Harrow, Aram W.; Kong, Linghang; Liu, Ziwen; Mehraban, Saeed

doi:10.1103/prxquantum.2.020339

Cited by 27 publications

(21 citation statements)

References 26 publications

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“…It was recently shown that the OTOC and the entanglement between parts of the system are in general characterized by different time scales [1,7]. Nevertheless, we show in section 3 that our model is a fast scrambler [8] in the sense that it takes time that scales logarithmically in the system size to establish large entanglement between two unentangled…”

Section: Introductionmentioning

confidence: 66%

“…In section 4 we review Shor's cell model description of black hole dynamics and the consequent puzzle raised by it. Shor's work distinguishes two notions of information scrambling, which was later justified more rigorously in a random quantum circuit model defined on graphs with a bottleneck [7]. Strong scrambling, defined as reaching a nearly maximally entangled state starting from two weakly-entangled macroscopic parts of a system, is seemingly constrained by the causal structure of the black hole spacetime to occur too slowly relative to expectations from quantum black hole physics.…”

Section: Jhep01(2022)083mentioning

confidence: 99%

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Chaos-protected locality

Jian

Swingle

2022

J. High Energ. Phys.

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Microscopic speed limits that constrain the motion of matter, energy, and information abound in physics, from the “ultimate” speed limit set by light to Lieb-Robinson speed limits in quantum spin systems. In addition to these state-independent speed limits, systems can also be governed by emergent state-dependent speed limits indicating slow dynamics arising, for example, from slow low-energy quasiparticles. Here we describe a different kind of speed limit: a situation where complex information/entanglement spreads rapidly, in a fashion inconsistent with any speed limit, but where simple signals continue to obey an approximate speed limit. If we take the point of view that the motion of simple signals defines the local spacetime geometry of the universe, then the effects we describe show that spacetime locality can be compatible with a high degree of non-local interactions provided these are sufficiently chaotic. With this perspective, we sharpen a puzzle about black holes recently raised by Shor and propose a schematic resolution.

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Section: Introductionmentioning

confidence: 66%

Section: Jhep01(2022)083mentioning

confidence: 99%

Chaos-protected locality

Jian

Swingle

2022

J. High Energ. Phys.

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“…This work shows that entanglement complexity arises from the interplay of magic and entanglement. It has been shown [37] that this interplay is also at the root of the onset of complex behavior as revealed by OTOCs [10,61]. We believe that the same mechanism is responsible for a more general transition to complex quantum behavior, for instance in the retrieval of information (or lack thereof) from a black hole [62].…”

Section: Discussionmentioning

confidence: 88%

Transitions in Entanglement Complexity in Random Circuits

True¹,

Hamma²

2022

Preprint

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“…Moving away from all-to-all connected models, one should expect the scrambling time to increase as one reduces the connectivity since it will take longer for a local perturbation to spread over the system. One approach to reduce the connectivity is to require that J rr decreases as a function of the distance |r − r | (Also see discussion about scrambling on sparse graphs [33][34][35]). As a result, C(r, t) generally develops a space-time profile, from which one can define an information lightcone by considering the contours of constant C(r, t),…”

Section: B Scrambling Dynamics In Geometrically Local Systemsmentioning

confidence: 99%

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Xu¹,

Swingle²

2022

Preprint

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This tutorial article introduces the physics of quantum information scrambling in quantum manybody systems. The goals are to understand how to quantify the spreading of quantum information precisely and how causality emerges in complex quantum systems. We introduce the general framework to study the dynamics of quantum information, including detection and decoding. We show that the dynamics of quantum information is closely related to operator dynamics in the Heisenberg picture, and, in certain circumstances, can be precisely quantified by the so-called out-the-time ordered correlator (OTOC). The general behavior of OTOC is discussed based on several toy models, including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian models, in which OTOC is analytically tractable. We introduce numerical methods, both exact diagonalization and tensor network methods, to calculate OTOC for generic quantum many-body systems. We also survey current experiment schemes to measure OTOC in various quantum simulators.

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Separation of Out-Of-Time-Ordered Correlation and Entanglement

Cited by 27 publications

References 26 publications

Chaos-protected locality

Chaos-protected locality

Transitions in Entanglement Complexity in Random Circuits

Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

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