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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -