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Absent a drug or vaccine, containing epidemic outbreaks is achieved by means of mobility restrictions and lock-downs. Here, the authors propose an alternating quarantine strategy, in which half of the population remains under lockdown while the other half continues to be active, resulting in a dramatic reduction in transmission.

We consider a quantum walk where a detector repeatedly probes the system with fixed rate 1/τ until the walker is detected. This is a quantum version of the first-passage problem. We focus on the total probability P_{det} that the particle is eventually detected in some target state, for example, on a node r_{d} on a graph, after an arbitrary number of detection attempts. Analyzing the dark and bright states for finite graphs and more generally for systems with a discrete spectrum, we provide an explicit formula for P_{det} in terms of the energy eigenstates which is generically τ independent. We find that disorder in the underlying Hamiltonian renders perfect detection, P_{det}=1, and then expose the role of symmetry with respect to suboptimal detection. Specifically, we give a simple upper bound for P_{det} that is controlled by the number of equivalent (with respect to the detection) states in the system. We also extend our results to infinite systems, for example, the detection probability of a quantum walk on a line, which is τ dependent and less than half, well below Polya's optimal detection for a classical random walk.

The problem of the detection statistics of a quantum walker has received increasing interest. We investigate the effect of employing a moving detector, using a projective measurement approach with fixed sampling time , with the detector moving right before every detection attempt. For a tight-binding quantum walk on the line, the moving detector allows one to target a specific range of group velocities of the walker, qualitatively modifying the behavior of the quantum first-detection probabilities. We map the problem to that of a stationary detector with a modified unitary evolution operator and use established methods for the solution of that problem to study the first-detection statistics for a moving detector on a finite ring and on an infinite 1D lattice. On the line, the system exhibits a dynamical phase transition at a critical value of , from a state where the probability of detection decreases exponentially in time and the total detection probability is very small, to a state with power-law decay and a significantly higher total probability to detect the particle. The exponent describing the power-law decay of the detection probability at this critical is 10/3, as opposed to 3 for every larger . In addition, the moving detector strongly modifies the Zeno effect. [ABSTRACT FROM AUTHOR]