The arrow of time exhibits nonanalytic behavior at the critical point of measurement-induced phase transitions, with an identified critical exponent, in an exactly solved model of random quantum circuits with non-projective measurements.
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The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.
Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.
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Arrow of Time as an indicator of Measurement-Induced Phase Transitions
The arrow of time exhibits nonanalytic behavior at the critical point of measurement-induced phase transitions, with an identified critical exponent, in an exactly solved model of random quantum circuits with non-projective measurements.