Simply speaking quantum Zeno effect for an unstable quantum system represents total decay probability decrease by frequent decay detection. Analogously simply speaking quantum anti-Zeno effect for an unstable quantum system represents total no-decay probability decrease by frequent decay detection. Also, some authors considered optical, i.e. polarization detection analogy of quantum Zeno and anti-Zeno effects. In this work we consider basic standard quantum mechanical concepts in quantum Zeno and anti-Zeno effect. We use simplest (Malus law) form of mentioned ideas on the photon polarization detection analogy of quantum Zeno and anti-Zeno effects and we suggest some new situations (non-equivalent time duration of the quantum dynamical evolution between different frequent detection). Correspondingly we define new quantum effects, quantum Hamlet effect (when, by frequent detection, final total polarization angle and state converge but total probability for appearance of this state diverges) and quantum anti-Hamlet effect (when, by frequent detection, final total polarization angle and state diverge but total probability for appearance of this state converges). Also, we consider a rough classical mechanical analogy of Zeno effect. Finally we consider frequent interference of single photon at beam splitters and obtain for different values of reflection and transmission coefficients analogies of quantum Zeno and anti-Zeno effect as well as analogy of usual exponentially decreasing decay law.
We propose and analyze a nonunitary variant of the continuous time Grover search algorithm based on frequent Zeno-type measurements. We show that the algorithm scales similarly to the pure quantum version by deriving tight analytical lower bounds on its efficiency for arbitrary database sizes and measurement parameters. We also study the behavior of the algorithm subject to noise, and find that under certain oracle and operational errors our measurement-based algorithm outperforms the standard algorithm, showing robustness against these noises. Our analysis is based on deriving a non-hermitian…
We investigate stochastic entropy production in a two-level quantum system that performs Rabi oscillations while undergoing quantum measurement brought about by continuous random disturbance by an external measuring device or environment. The dynamics produce quantum Zeno and anti-Zeno effects for certain measurement regimes, and the stochastic entropy production is a measure of the irreversibility of the behaviour. When the strength of the measurement disturbance is time-dependent, the stochastic entropy production separates into three components. Two represent relaxational behaviour, one bei…
The quantum Zeno effect is well-known for fixing a system to an eigenstate by frequent measurements. It is also known that applying frequent unitary pulses induces a Zeno subspace that can also pin the system to an eigenspace. Both approaches have been studied as means to maintain a system in a certain subspace. Extending the two concepts, we consider making the measurements/pulses dynamical so that the state can move with the motion of the measurement axis/pulse basis. We show that the system stays in the dynamical eigenbasis when the measurements/pulses are slowly changing. Explicit bounds f…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are observed. We explore the effects of the measurements on the spreading of the packet on a one dimensional line, showing that except for the Zeno limit, the system converges to Gaussian statistics similarly to a classical random walk. A large deviation analysis and an Edgeworth expansion yield quantum corrections to this normal behavior. We then explore the first …
