Purification through Zeno-Like Measurements

Abstract

A series of frequent measurements on a quantum system (Zeno-like measurements) is shown to result in the "purification" of another quantum system in interaction with the former. Even though the measurements are performed on the former system, their effect drives the latter into a pure state, irrespectively of its initial (mixed) state, provided certain conditions are satisfied.PACS numbers: 03.65.XpIt is well known that unstable particles or quantum states display a peculiar behavior at short and long times [1]. Phenomenologically, they are known to decay exponentially and this is well confirmed experimentally [2]. Short-time deviations were only observed very recently [3]. The deviations from the familiar exponential decay law are unavoidable consequences of the quantum dynamics both at short and long times, and the derivation of the exponential decay law itself is not a trivial matter in quantum mechanics. These deviations reflect the unitarity of the time evolution operator or the time reversal symmetry of the Schrödinger equation at short times and the lower boundedness of the Hamiltonian or the stability of the vacuum at long times. See, e.g., Ref.[1] for a review.The quantum behavior of unstable states at short times has been one of the central issues of investigation and discussion in recent years, since it is closely connected to the so-called quantum Zeno effect (QZE) [4,5], where the act of measurement [6] (usually represented by the von Neumann projection or the generalized spectral decomposition [7]) affects in an essential way the dynamics of the measured system and results in a hindrance of the decay process. The first attempt at the experimental observation of the QZE in an atomic transition process [8], following Cook's theoretical work [9], has triggered heated discussions on this subject. Furthermore, another exciting experiment has been reported very recently: the observation of the QZE (and also of the inverse QZE [10]) in an atomic tunneling process [11], which is the first experimental observation of the (inverse) QZE in a truly unstable quantum system, unlike in the previous experiment [8] performed on an oscillating system.In this Letter, we will shed new light on another (and so far not well explored) feature of the quantum dynamics with measurements, closely related to the QZE. Notice first that the system under consideration cannot be considered completely isolated and usually interacts with other systems. Therefore, it would be interesting and maybe more realistic to consider the case where the measurement, represented by a von Neumann projection for simplicity, is not performed on the total system, but only on the system of interest. Here, we consider such measurements and address the following point: How does a series of frequent measurements on a system affect the dynamics of another system in interaction with the former? Under frequent measurements performed only on the former system, the latter evolves away from its initial state. We shall show that such measurements can result i...

Resonant purification of mixed states for closed and open quantum systems

“…Several strategies have already been proposed, especially in the context of entanglement purification [2,3]. They rely on two mechanisms: measurement or cooling procedures (see [4,5,6,7,8] and references therein). From a general viewpoint, it is necessary to consider how it is possible to affect the dynamics of the system, and what states can be attained during its time evolution.…”

Thwarted dynamics by partial projective measurements

“…At this point, it is possible to predict the final state of the field mode F in the large N limit keeping τ finite. It is shown [4] that the spectrum ofV is discrete and its largest (in magnitude) eigenvalue is unique and nondegenerate [1], and the corresponding eigenstate is a squeezed state |ξ with…”

“…Under certain conditions, the non-measured system is driven toward a pure state (distilled) irrespectively of its initial (in general, mixed) state [1]. This procedure would be useful in the context of quantum information for initializing quantum systems and would be utilized to prepare entangled states [2,3].…”

Extraction of an entanglement by repetition of the resonant transmission of an ancilla qubit

“…Preparation of a quantum state (not necessarily an entangled state) from an arbitrary given state is also an important and nontrivial subject. A generic scheme has been proposed to prepare a pure quantum state from an arbitrary (mixed, in general) state by repeated measurements on an ancilla system interacting with the target [11]. Applying this idea to the present issue, schemes for the extraction of entanglement between separated qubits, from an arbitrary given state [4] or from a state belonging to a certain class of states [8], by repeated measurements on the mediator have been explored.…”