Purification of Quantum State Through Zeno-Like Measurements

Abstract

We present a novel procedure to purify quantum states, i.e., purification through Zeno-like measurements. By simply repeating one and the same measurement on a quantum system, one can purify another system in interaction with the former. The conditions for the (efficient) purification are specified on a rather general setting, and the framework of the method possesses wide applicability. It is explicitly demonstrated on a specific setup that the purification becomes very efficient by tuning relevant parameters.KEYWORDS: purification of quantum states, quantum Zeno effect, repeated measurement One cannot observe a quantum system without any disturbance on the object, and the dynamics of the quantum system is affected by the measurement. An interesting manifestation of this effect is the "quantum Zeno effect" (QZE):1-3) if one repeats measurement very frequently in order to ascertain whether a system remains in the initial state, the evolution of the system is slowed down and totally hindered in the limit of infinite frequency. Or conversely, one can also accelerate the decay of an unstable state by repeating the measurement less frequently than a critical frequency (inverse QZE). 4)These are typical examples of the effects of measurement on quantum dynamics.In this article, we present another interesting effect of measurement on quantum dynamics when the measurement is repeated as in the case of the (inverse) QZE: purification of quantum state through Zeno-like measurements.5) We show in the following that a series of measurements on a quantum system indirectly affects the dynamics of another system in interaction with the former, and the latter (initially in any mixed state) is driven into a pure state, provided certain conditions are satisfied. The state of the latter system is purified through the repeated measurement on the former.In the ideas of quantum information and computation, quantum coherence plays crucial roles.6, 7) It is hence one of the important issues to be addressed how to maintain and/or recover quantum coherence, and various schemes have been proposed attacking this subject. 6-14)The work presented here contributes to this issue and provides a novel method to purify quantum states (i.e., to recover quantum coherence), which is simple compared to the standard purification techniques 6, 9, 10) and the framework is rather general.Let a total system A+B be described by a Hamiltonian of the formwhere H A(B) is a free Hamiltonian of system A(B) and H int is an interaction between A and B. We prepare system A in a pure state |φ at time t = 0, while the initial state of system B, denoted by ρ B , can be arbitrary * E-mail address: yuasa@hep.phys.waseda.ac.jp † E-mail address: hiromici@waseda.jp (a mixed state). The total system starts to evolve from the initial statewith the Hamiltonian (1), and we check the state of system A at time t = τ . If it is confirmed that system A remains in its initial state |φ , the state of the total system is projected by a projection operatorand restarts to evolve. We ...