Resource theory of quantum scrambling

Garcia, Roy J.; Bu, Kaifeng; Jaffe, Arthur

doi:10.1073/pnas.2217031120

Cited by 12 publications

(6 citation statements)

References 96 publications

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“…While the majority of our simulated data points fulfil the inequality derived in Ref. [31], it is not always the case. This observation is an interesting starting point for further investigation.…”

Section: Conclusion and Discussionmentioning

confidence: 46%

“…Also, the analytical relations here could be the starting point for the investigation of the relation between the stabilizer Renyi entropy and the introduced magic measure in Ref. [31].…”

Section: Conclusion and Discussionmentioning

confidence: 97%

“…Ref. [31] puts forward a statement that the fluctuations of OTOC are always smaller or equal to a specific type of magic monotone. In this work, we complement this statement by numerically showing the relation of OTOC fluctuations to the stabilizer Renyi entropy.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Moreover, it was recently experimentally demonstrated that OTOCs can be used as an indicator of the degree of non-stabilizerness of scrambled quantum circuits [30]. In parallel, recent work has shown an analytical relation between the non-stabilizerness and OTOC [19,31].…”

Section: Introductionmentioning

confidence: 98%

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Quantifying non-stabilizerness via information scrambling

Ahmadi,

Greplova

2024

SciPost Phys.

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The advent of quantum technologies brought forward much attention to the theoretical characterization of the computational resources they provide. A method to quantify quantum resources is to use a class of functions called magic monotones and stabilizer entropies, which are, however, notoriously hard and impractical to evaluate for large system sizes. In recent studies, a fundamental connection between information scrambling, the magic monotone mana and 2-Renyi stabilizer entropy was established. This connection simplified magic monotone calculation, but this class of methods still suffers from exponential scaling with respect to the number of qubits. In this work, we establish a way to sample an out-of-time-order correlator that approximates magic monotones and 2-Renyi stabilizer entropy. We numerically show the relation of these sampled correlators to different non-stabilizerness measures for both qubit and qutrit systems and provide an analytical relation to 2-Renyi stabilizer entropy. Furthermore, we put forward and simulate a protocol to measure the monotonic behaviour of magic for the time evolution of local Hamiltonians.

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Section: Conclusion and Discussionmentioning

confidence: 46%

“…Also, the analytical relations here could be the starting point for the investigation of the relation between the stabilizer Renyi entropy and the introduced magic measure in Ref. [31].…”

Section: Conclusion and Discussionmentioning

confidence: 97%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

Quantifying non-stabilizerness via information scrambling

Ahmadi,

Greplova

2024

SciPost Phys.

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“…“Quantum scrambling” refers to the tendency of an initially localized quantum state to lose information by spreading across the system ( 1 ). There has been much interest recently in quantifying the rate of quantum scrambling ( 2 – 4 ), specifically using out-of-time-ordered correlators (OTOCs) ( 5 – 9 ) which have the general form

…”

mentioning

confidence: 99%

Instantons and the quantum bound to chaos

Sadhasivam,

Meuser,

Reichman

et al. 2023

Proc. Natl. Acad. Sci. U.S.A.

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The rate at which information scrambles in a quantum system can be quantified using out-of-time-ordered correlators. A remarkable prediction is that the associated Lyapunov exponent λ that quantifies the scrambling rate in chaotic systems obeys a universal bound λ < 2 π k B T / ħ . Previous numerical and analytical studies have indicated that this bound has a quantum-statistical origin. Here, we use path-integral techniques to show that a minimal theory to reproduce this bound involves adding contributions from quantum thermal fluctuations (describing quantum tunneling and zero-point energy) to classical dynamics. By propagating a model quantum-Boltzmann-conserving classical dynamics for a system with a barrier, we show that the bound is controlled by the stability of thermal fluctuations around the barrier instanton (a delocalized structure which dominates the tunneling statistics). This stability requirement appears to be general, implying that there is a close relation between the formation of instantons, or related delocalized structures, and the imposition of the quantum-chaos bound.

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Entropies and reflected entropies in the Hayden-Preskill protocol

Czech,

Shuai,

Tang

2024

J. High Energ. Phys.

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We revisit information retrieval from evaporating black holes in the Hayden-Preskill protocol, treating the black hole dynamics as Haar-random. We compute, down to the first exponentially suppressed terms, all integer-indexed Rényi mutual informations between a black hole, its radiation, and a reference that catalogues Alice’s diaries. We find that dropping a diary into a young black hole effectively delays the Page time. We also compute the radiation: diary reflected Rényi entropies, and identify a technical reason why they cannot be continued to the reflected entropy by the replica trick.

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Resource theory of quantum scrambling

Cited by 12 publications

References 96 publications

Quantifying non-stabilizerness via information scrambling

Quantifying non-stabilizerness via information scrambling

Instantons and the quantum bound to chaos

Entropies and reflected entropies in the Hayden-Preskill protocol

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