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Three-fold way of entanglement dynamics in monitored quantum circuits

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Three-fold way of entanglement dynamics in monitored quantum circuits. / Kalsi, Tara; Romito, Alessandro; Schomerus, Henning.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 55, No. 26, 264009, 01.07.2022.

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Kalsi, Tara ; Romito, Alessandro ; Schomerus, Henning. / Three-fold way of entanglement dynamics in monitored quantum circuits. In: Journal of Physics A: Mathematical and Theoretical. 2022 ; Vol. 55, No. 26.

Bibtex

@article{0ef33179e7a7451c94412ad19f4fe6ec,
title = "Three-fold way of entanglement dynamics in monitored quantum circuits",
abstract = "We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles (circular unitary, orthogonal, and symplectic ensembles; CUE, COE and CSE). We utilise the established model of a one-dimensional circuit evolving under alternating local random unitary gates and projective measurements performed with tunable rate, which for gates drawn from the CUE is known to display a transition from extensive to intensive entanglement scaling as the measurement rate is increased. By contrasting this case to the COE and CSE, we obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements. For this, we combine exact analytical random-matrix results for the entanglement generated by the individual gates in the different ensembles, and numerical results for the complete quantum circuit. These considerations include an efficient rephrasing of the statistical entangling power in terms of a characteristic entanglement matrix capturing the essence of Cartan's KAK decomposition, and a general result for the eigenvalue statistics of antisymmetric matrices associated with the CSE.",
keywords = "entanglement, random matrix theory, phase transitions, quantum circuits",
author = "Tara Kalsi and Alessandro Romito and Henning Schomerus",
year = "2022",
month = jul,
day = "1",
doi = "10.1088/1751-8121/ac71e8",
language = "English",
volume = "55",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "26",

}

RIS

TY - JOUR

T1 - Three-fold way of entanglement dynamics in monitored quantum circuits

AU - Kalsi, Tara

AU - Romito, Alessandro

AU - Schomerus, Henning

PY - 2022/7/1

Y1 - 2022/7/1

N2 - We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles (circular unitary, orthogonal, and symplectic ensembles; CUE, COE and CSE). We utilise the established model of a one-dimensional circuit evolving under alternating local random unitary gates and projective measurements performed with tunable rate, which for gates drawn from the CUE is known to display a transition from extensive to intensive entanglement scaling as the measurement rate is increased. By contrasting this case to the COE and CSE, we obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements. For this, we combine exact analytical random-matrix results for the entanglement generated by the individual gates in the different ensembles, and numerical results for the complete quantum circuit. These considerations include an efficient rephrasing of the statistical entangling power in terms of a characteristic entanglement matrix capturing the essence of Cartan's KAK decomposition, and a general result for the eigenvalue statistics of antisymmetric matrices associated with the CSE.

AB - We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles (circular unitary, orthogonal, and symplectic ensembles; CUE, COE and CSE). We utilise the established model of a one-dimensional circuit evolving under alternating local random unitary gates and projective measurements performed with tunable rate, which for gates drawn from the CUE is known to display a transition from extensive to intensive entanglement scaling as the measurement rate is increased. By contrasting this case to the COE and CSE, we obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements. For this, we combine exact analytical random-matrix results for the entanglement generated by the individual gates in the different ensembles, and numerical results for the complete quantum circuit. These considerations include an efficient rephrasing of the statistical entangling power in terms of a characteristic entanglement matrix capturing the essence of Cartan's KAK decomposition, and a general result for the eigenvalue statistics of antisymmetric matrices associated with the CSE.

KW - entanglement

KW - random matrix theory

KW - phase transitions

KW - quantum circuits

U2 - 10.1088/1751-8121/ac71e8

DO - 10.1088/1751-8121/ac71e8

M3 - Journal article

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 26

M1 - 264009

ER -