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Quantum Reports, Volume 6, Issue 2

2024 June - 11 articles

Cover Story: We consider a toy model for studying monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation from continuous monitoring of a random operator drawn from the Gaussian Unitary Ensemble. Due to unitary invariance, the dynamics of the eigenvalues of the density matrix decouples from that of the eigenvectors. We consider two regimes: in the presence of an extra dephasing term, the density matrix has a stationary distribution, matching the inverse Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs, and we find an exact solution for the joint distribution of the eigenvalues at each time and arbitrary Hilbert space size, transitioning from a Coulomb gas to a universal regime. View this paper
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Quantum Rep. - ISSN 2624-960X
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