Quantum information spreading in random spin chains

Ruggiero, Paola; Turkeshi, Xhek

doi:10.48550/arxiv.2206.02934

Cited by 1 publication

(1 citation statement)

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“…The Page curve (1.3) is extended to the multipartite case [16,17] and random mixed states [18]. Besides black hole, it is also applied to many different fields such as fermion systems [19,20], random spin chain [21], bosonic [22] and fermion [23,24] Gaussian states, quantum thermalization [25][26][27][28], and quantum chaos [26,[29][30][31][32][33]. It is also applied to the quantum information theories like random quantum circuits [34][35][36] and random quantum channels [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Average Rényi Entropy of a Subsystem in Random Pure State

Kim¹,

Hwang²,

Jung³

et al. 2023

Preprint

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In this paper we examine the average Rényi entropy S α of a subsystem A when the whole composite system AB is a random pure state. We assume that the Hilbert space dimensions of A and AB are m and mn respectively. First, we compute the average Rényi entropy analytically for m = α = 2. We compare this analytical result with the approximate average Rényi entropy, which is shown to be very close. For general case we compute the average of the approximate Rényi entropy, which is in agreement with the asymptotic expression of the average von Neumann entropy. Based on the analytic result of S α (m, n) we plot the ln m-dependence of the quantum information derived from S α (m, n). It is remarkable to note that the nearly vanishing region of the information becomes shorten with increasing α, and eventually disappears in the limit of α → ∞. The physical implication of the result is briefly discussed.

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