The quantum Zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus. A few significant examples are proposed and their practical relevance discussed. We also focus on decoherence-free subspaces.PACS numbers: 03.65. Xp, 03.67.Lx If very frequent measurements are performed on a quantum system, in order to ascertain whether it is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place [1,2]. This phenomenon stems from general features of the Schrödinger equation that yield quadratic behavior of the survival probability at short times [3,4]. The first realistic test of the quantum Zeno effect (QZE) for oscillating (two-level) systems was proposed about 15 years ago [5]. This led to experiments, discussions and new proposals [6]. A few years ago, the presence of a short-time quadratic region was experimentally confirmed also for a bona fide unstable system [7]. The same experimental setup has been used very recently [8] in order to prove the existence of the Zeno effect (as well as its inverse [9,10]) for an unstable quantum mechanical system, leading to new ideas [11,12].It is important to stress that the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multi-dimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. This continuing time evolution within the projected subspace ("quantum Zeno dynamics") has been recently investigated [13]. It has peculiar physical and mathematical features and sheds light on some subtle mathematical issues [2,14,15].All the above-mentioned investigations deal with what can be called "pulsed" measurements, according to von Neumann's projection postulate [16]. However, from a physical point of view, a "measurement" is nothing but an interaction with an external system (another quantum object, or a field, or simply another degree of freedom of the very system investigated), playing the role of apparatus. In this respect, if one is not too demanding in philosophical terms, von Neumann's postulate can be regarded as a useful shorthand notation, summarizing the final effect of the quantum measurement. This simple observation enables one to reformulate the QZE in terms of a (strong) coupling to an external agent. We emphasize that in such a case the QZE is a consequence of the dynamical features (i.e. the form factors) of the coupling between the system investigated and the external system, and no use is made of projection operators (and non-unitary dynamics). The idea of "continuous" measurement in a QZE context has been proposed several times during the last two decades [18,19], although the first quantitative comparison with the "pulsed" situation is rather recent [20].The purpose of the present article is to cast the quantum Zeno evolution in terms of an adiabatic theorem and stud...

If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.

We unify the quantum Zeno effect (QZE) and the "bang-bang" (BB) decoupling method for suppressing decoherence in open quantum systems: in both cases strong coupling to an external system or apparatus induces a dynamical superselection rule that partitions the open system's Hilbert space into quantum Zeno subspaces. Our unification makes use of von Neumann's ergodic theorem and avoids making any of the symmetry assumptions usually made in discussions of BB. Thus we are able to generalize BB to arbitrary fast and strong pulse sequences, requiring no symmetry, and to show the existence of two alternatives to pulsed BB: continuous decoupling, and pulsed measurements. Our unified treatment enables us to derive limits on the efficacy of the BB method: we explicitly show that the inverse QZE implies that BB can in some cases accelerate, rather than inhibit, decoherence.

The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno effect) or slowed down (quantum Zeno effect), depending on the features of the interaction Hamiltonian. A geometric criterion is proposed for a transition to occur between these two regimes.

2 Temporal behavior of quantum mechanical systemsThe temporal behavior of quantum mechanical systems is reviewed. We mainly focus our attention on the time development of the so-called "survival" probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by assuming that the latter has a continuous spectrum.The exponential decay of the survival probability, familiar, for example, in radioactive decay phenomena, is representative of a purely probabilistic character of the system under consideration and is naturally expected to lead to a master equation. This behavior, however, can be found only at intermediate times, for deviations from it exist both at short and long times and can have significant consequences.After a short introduction to the long history of the research on the temporal behavior of such quantum mechanical systems, the short-time behavior and its controversial consequences when it is combined with von Neumann's projection postulate in quantum measurement theory are critically overviewed from a dynamical point of view. We also discuss the so-called quantum Zeno effect from this standpoint.The behavior of the survival amplitude is then scrutinized by investigating the analytic properties of its Fourier and Laplace transforms. The analytic property that there is no singularity except a branch cut running along the real energy axis in the first Riemannian sheet is an important reflection of the time-reversal invariance of the dynamics governing the whole process. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter.In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system, since the exponential behavior is regarded as a manifestation of a complete loss of coherence of the quantum subsystem under consideration. In this respect, a few attempts at extracting the exponential decay form on the basis of quantum theory, aiming at the master equation, are briefly reviewed, including van Hove's pioneering work and his well-known "λ 2 T " limit.In the attempt to further clarify the mechanism of the appearance of a purely probabilistic behavior without resort to any approximation, a solvable dynamical model is presented and extensively studied. The model describes an ultrarelativistic particle interacting with N two-level systems (called "spins") and is shown to exhibit an exponential behavior at all times in the weak-coupling, macroscopic limit. Furthermore, it is shown that the model can even reproduce the short-time Gaussian behavior followed by the exponential law when an appropriate initial state is chosen. The analysis is ...

We introduce the notion of maximally multipartite entangled states of n qubits as a generalization of the bipartite case. These pure states have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. They are solutions of a minimization problem. Examples for small n are investigated, both analytically and numerically.

We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions ͑"bang-bang" pulses and their generalization, quantum dynamical decoupling͒, and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency N of the measurements or pulses is large enough or if the coupling K is sufficiently strong. Otherwise, if N or K is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.

We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.