Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This is generally understood in terms competition between scrambling effects unitary dynamics and disentangling measurements. We find that, surprisingly, EPTs are possible even absence dynamics, where they best arising from alone. motivates us in...

The problem of a correct quantum description of the phase difference is examined from the perspective of parameter estimation theory. It is shown that an optimum phase-shift measurement defines a phase difference operator which coincides with other approaches to the same problem. We also study the fundamental limit to the accuracy of a phase difference shift detection. We show that this limit c...