Quantum control by von Neumann measurements

Abstract

A general scheme is presented for controlling quantum systems using evolution driven by nonselective von Neumann measurements, with or without an additional tailored electromagnetic field.As an example, a 2-level quantum system controlled by non-selective quantum measurements is considered. The control goal is to find optimal system observables such that consecutive nonselective measurement of these observables transforms the system from a given initial state into a state which maximizes the expected value of a target operator (the objective). A complete analytical solution is found including explicit expressions for the optimal measured observables and for the maximal objective value given any target operator, any initial system density matrix, and any number of measurements. As an illustration, upper bounds on measurement-induced population transfer between the ground and the excited states for any number of measurements are found. The anti-Zeno effect is recovered in the limit of an infinite number of measurements. In this limit the system becomes completely controllable. The results establish the degree of control attainable by a finite number of measurements.

Optimal quantum measurement of finite-dimensional systems and coherent anti-Stokes Raman spectroscopy

“…It is interesting to note that, the maximum of M-dimensional system is just the same as that of a simple two-level system spanned by the initial state |α and the final state |β , which has been extensively studied [10,11].…”

“…For two-level quantum systems, analytical solutions for population transfer by optimized instantaneous projective measurements is obtained [10,11]. In these cases, we can associate each measurement with two projectors, and find the optimal transfer population between the initial and final mixed states, ρ i and ρ f .…”

“…(1), since it is easy to include it via a picture transformation [10,11]. For two-level quantum systems, analytical solutions for population transfer by optimized instantaneous projective measurements is obtained [10,11].…”

“…the quantum Zeno and anti-Zeno effects. In the absence of an active coherent control, instantaneous projective measurements were shown to be capable of driving population transfer in a two-level system, and a scheme for maximal population transfer was found under an arbitrary finite number of measurements [10,11]. Numerical simulations have been carried out to investigate the ability of measurements in quantum control [12].…”

“…Significant research efforts have been put forth to make progress in this field. We have previously studied the optimal projective measurements [10,11] in a simple two-level quantum system, and shown that quantum measurements can cooperate with lasers to control the system more effectively [12].…”