Stochastic quantum Zeno by large deviation theory

Abstract

Quantum measurements are crucial for observing the properties of a quantum system, which, however, unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system being subjected to a sequence of projective measurements applied at random times. In the case of independent and identically distributed intervals of time between consecutive measurements, we analytically demonstrate that the survival probability of the system to remain in the projected state assumes a large deviation (exponentially decaying) form in the limit of an infinite number of measurements. This allows us to estimate the typical value of the survival probability, which can therefore be tuned by controlling the probability distribution of the random time intervals. Our analytical results are numerically tested for Zeno-protected entangled states, which also demonstrate that the presence of disorder in the measurement sequence further enhances the survival probability when the Zeno limit is not reached (as it happens in experiments). Our studies provide a new tool for protecting and controlling the amount of quantum coherence in open complex quantum systems by means of tunable stochastic measurements.

Ergodicity in randomly perturbed quantum systems

“…Then, since the discrepancy between the statistical averages, here investigated, do strongly depend on the second and fourth statistical moments of the noise distribution m ( ) p outside the Zeno regime, one could effectively determine the influence of the stochastic noise source on the dynamics of a fully controlled quantum system, hence characterising the external environment. On top of that, although we have explicitly studied Hamiltonian dynamics and applied the projective measurement on an initial pure state, the method can be also generalised to arbitrary mixed input states with the dynamics being described by completely positive trace-preserving maps [30] and to the case of measurements projecting the system on higher dimensional Hilbert subspaces, hence leading to Stochastic Quantum Zeno Dynamics [25,26,32]. Finally, these results are expected to represent further steps towards controlled manipulations of quantum systems via dissipative interactions [33,34] where one can indeed control the noisy environment or part of it in order to perform desired challenging tasks like the ones necessary for future quantum technologies.…”

“…In [26], it has been proved that this most probable value is equivalent to the log-average of the quantity m ( ) q with respect to m ( ) p , namely to the geometric average  g of the survival probability weighted by m ( ) p :…”

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

“…An important observation is that the bounds on fluctuations of a counting observable and its FPTs are controlled by the average dynamical activity, in analogy to the role played by the entropy production in the case of currents [1,13]. We hope these results will add to the growing body of work applying large deviation ideas and methods to the study of dynamics in driven systems [29][30][31][32][33][34][35][36][37][38][39][40][41], glasses [25,[42][43][44][45][46][47], protein folding and signaling networks [48][49][50][51], open quantum systems [52][53][54][55][56][57][58][59][60][61][62][63][64], and many other problems in nonequilibrium [65][66][67][68][69][70][71][72].…”

Experimental proof of quantum Zeno-assisted noise sensing

“…Recently, sequences of Zeno measurements have been studied in the presence of additional stochastic contributions to analyze how the confinement probability of the system to remain in the measured subspace changes with the amount and type of stochasticity [36][37][38]. Such a regime is called weak quantum Zeno (WQZ) and it has been observed that, although projective measurements could constantly monitor a quantum system, its decay is boosted by the presence of disorder.…”