Generalized Entanglement Entropies of Quantum Designs

We study how quantum states are scrambled via braiding in systems of non-Abelian anyons through the lens of entanglement spectrum statistics. In particular, we focus on the degree of scrambling, defined as the randomness produced by braiding, at the same amount of entanglement entropy. To quantify the degree of randomness, we define a distance between the entanglement spectrum level spacing distribution of a state evolved under random braids and that of a Haar-random state, using the Kullback-Leibler divergence DKL. We study DKL numerically for random braids of Majorana fermions (supplemented with random local four-body interactions) and Fibonacci anyons. For comparison, we also obtain DKL for the Sachdev-Ye-Kitaev model of Majorana fermions with all-to-all interactions, random unitary circuits built out of (a) Hadamard (H), π/8 (T), and CNOT gates, and (b) random unitary circuits built out of two-qubit Haar-random unitaries. To compare the degree of randomness that different systems produce beyond entanglement entropy, we look at DKL as a function of the Page limit-normalized entanglement entropy S/Smax. Our results reveal a hierarchy of scrambling among various models -even for the same amount of entanglement entropy -at intermediate times, whereas all models exhibit the same late-time behavior. In particular, we find that braiding of Fibonacci anyons randomizes initial product states more efficiently than the universal H+T+CNOT set.

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“…We thank Zi-Wen Liu for pointing out refs. [23,24] to us and helpful discussions. Z.-C. Y. and C. C. are supported by DOE Grant No.…”

Section: Acknowledgmentsmentioning

confidence: 96%

Scrambling via braiding of nonabelions

et al. 2019

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“…That is, it does rely on any particular device model [44, 50]. The entanglement properties of random quantum states and dynamics are important [51]. Quantum randomness is the result of context and quantization.…”

Section: Introductionmentioning

confidence: 99%

Generating randomness: making the most out of disordering a false order into a real one

Ilan

2019

J Transl Med

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Randomness is far from a disturbing disorder in nature. Rather, it underlies many processes and functions. Randomness can be used to improve the efficacy of development and of systems under certain conditions. Moreover, valid unpredictable random-number generators are needed for secure communication, rendering predictable pseudorandom strings unsuitable. This paper reviews methods of generating randomness in various fields. The potential use of these methods is also discussed. It is suggested that by disordering a “false order,” an effective disorder can be generated to improve the function of systems.

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“…This provided evidence for the existence of the quantum effect of entanglement between the mass eigenstates which make up a flavour state. The entropy of entanglement [22] is an entanglement measure for a manybody quantum state and the question arises if the results shown in Figure 2 may find an interpretation in terms of the evolution of an entanglement entropy over time.…”

Section: Introductionmentioning

confidence: 99%

A generalized entropy optimization and Maxwell–Boltzmann distribution

Mathai

Haubold

2018

Eur. Phys. J. B

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Abstract. Based on the results of the diffusion entropy analysis of Super-Kamiokande solar neutrino data, a generalized entropy, introduced earlier by the first author is optimized under various conditions and it is shown that Maxwell-Boltzmann distribution, Raleigh distribution and other distributions can be obtained through such optimization procedures. Some properties of the entropy measure are examined and then Maxwell-Boltzmann and Raleigh densities are extended to multivariate cases. Connections to geometrical probability problems, isotropic random points, and spherically symmetric and elliptically contoured statistical distributions are pointed out.

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Generalized Entanglement Entropies of Quantum Designs

Cited by 42 publications

References 51 publications

Scrambling via braiding of nonabelions

Scrambling via braiding of nonabelions

Generating randomness: making the most out of disordering a false order into a real one

A generalized entropy optimization and Maxwell–Boltzmann distribution

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