Measurement-induced purification in large- N hybrid Brownian circuits

Monitored Open Fermion Dynamics: Exploring the Interplay of Measurement, Decoherence and Free Hamiltonian Evolution

“…Under the suitably combined evolution of perfect (projective or continuous) measurements and unitary gates, it has been shown that any mixed initial state purifies. The purification speed is characteristic for the underlying measurement-induced phase [5,6,31,43], distinguishing between, e.g., fast purification for weakly entangled phases and slow purification for strongly entangled phases.…”

“…In order to approach the dynamics analytically, we express the model as a replicated Keldysh field theory [26,27,36], which readily allows us to include dephasing and provides access to the fermion correlation functions (see also, e.g., Refs. [10,15,23,24,31,45] for related replica approaches). The robustness of the critical phase can be rationalized in terms of an effective bosonic, non-Hermitian variant of the sine-Gordon model, where the critical phase corresponds to the gapless theory with vanishing interactions.…”

Tunable Geometries in Sparse Clifford Circuits

“…Using the teleportation time t c (s) as a diagnostic, one might expect to observe a phase transition from a fast scrambling phase to a slow scrambling phase as a function of the parameter s near the points |s| = 1. It would also be interesting to study similar questions in Brownian qubit or fermion models, where analytical results are often possible [65,66]. In particular, these Brownian models typically lead to a description of entanglement dynamics in terms of effective field theories.…”

Measurement-induced phase transitions in sparse nonlocal scramblers

“…Measurement-induced phase transitions (MIPT) [1][2][3][4] are transitions driven by a competition between scrambling dynamics, which tends to generate many-body entanglement across all degrees of freedom of a quantum many-body system, and local measurements, which tend to destroy this entanglement. Measurement-driven transitions of this type have garnered an extraordinary amount of theoretical interest recently [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], and have been studied in a wide range of physical systems, including in random quantum circuits, free fermions [21][22][23], and non-Hermitian Brownian models [24]. They have also been extended to systems with long-range interactions [25][26][27][28], including models with all-to-all coupling [29,30], and non-Hermitian Sachdev-Ye-Kitaev (SYK) models [31][32][33].…”