A purely dynamical explanation for the quantum Zeno effect is proposed. It is argued that a quantum system undergoes a quantum-Zeno-type dynamics as a consequence of a particular type of evolution involving a series of frequent spectral decompositions. The role of quantum measurements and of the ``collapse of the wave function'' is investigated and it is clarified that, provided a final observation is performed, the dynamical quantum Zeno effect can be obtained without making use of von Neumann's projection postulate. The meaning of infinitely frequent measurements is critically discussed and it is argued that it should be regarded as a mathematical idealization, impossible to realize from a physical point of view.
A purely dynamical explanation for the quantum Zeno effect is proposed. It is argued that a quantum system undergoes a quantum-Zeno-type dynamics as a consequence of a particular type of evolution involving a series of frequent spectral decompositions. The role of quantum measurements and of the ``collapse of the wave function'' is investigated and it is clarified that, provided a final observation is performed, the dynamical quantum Zeno effect can be obtained without making use of von Neumann's projection postulate. The meaning of infinitely frequent measurements is critically discussed and it is argued that it should be regarded as a mathematical idealization, impossible to realize from a physical point of view.
The change of dynamics in a quantum system under frequent or continuous observation, known as the quantum Zeno effect, is generally derived from the projection or reduction of the wave-packet hypothesis that is the central postulate in the theory of quantum measurements. The only experiment in which the Zeno effect has yet been clearly demonstrated, though, allows no conclusion on the necessity or validity of the projection postulate. This is shown by calculating, in detail, the outcome of the experiment on the basis of the standard three-level Bloch equations. These equations follow from the quantum theory of irreversible processes with no additional assumptions necessary, such as which part of the system serves as measuring apparatus or how efficient the measurement would be.
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.
The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test, that make use of an oscillating system. PACS: 03.65.Bz, 42.50.-p 1 The seminal formulation of the quantum Zeno effect, due to Misra and Sudarshan [1], deals with the probability of observing an unstable system in its initial state throughout a time interval ∆ = [0, t]. The purpose of this note is to point out that the quantum Zeno effect has not been experimentally observed, yet, in its original formulation. Indeed, we shall argue that the interesting proposal by Cook [2], that makes use of a two-level system undergoing Rabi oscillations, as well as the beautiful experiment performed by Itano et al. [3], investigate the probability of finding the
Abstract. 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 provide a general dynamical approach for the quantum Zeno and anti-Zeno effects in an open quantum system under repeated non-demolition measurements. In our approach the repeated measurements are described by a general dynamical model without the wave function collapse postulation. Based on that model, we further study both the short-time and long-time evolutions of the open quantum system under repeated non-demolition measurements, and derive the measurement-modified decay rates of the excited state. In the cases with frequent ideal measurements at zero-temperature, we re-obtain the same decay rate as that from the wave function collapse postulation (Nature {\bf 405}, 546 (2000)). The correction to the ideal decay rate is also obtained under the non-ideal measurements. Especially, we find that the quantum Zeno and anti-Zeno effects are possibly {\it enhanced} by the non-ideal natures of measurements. For the open system under measurements with arbitrary period, we generally derive the rate equation for the long-time evolution for the cases with {\it arbitrary} temperature and noise spectrum, and show that in the long-time evolution the noise spectrum is effectively tuned by the repeated measurements. Our approach is also able to describe the quantum Zeno and anti-Zeno effects given by the phase modulation pulses, as well as the relevant quantum control schemes.
Itano and co-workers [Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A 41, 2295 (1990)] have recently reported the experimental verification of the quantum Zeno effect, which is the inhibition of a quantum transition by frequent measurements. In this article, we offer an alternative interpretation of the quantum Zeno effect. We show that an analysis of the dynamics of the full three-level system gives the same result. There is no need to assume explicitly that the wave function has collapsed, nor even to assume that an ideal measurement has been made. In addition, we differentiate between what has been referred to as the quantum Zeno effect and what has been termed the quantum Zeno paradox. The former is the inhibition of induced transitions, and the latter is the, as yet experimentally unobserved, inhibition of spontaneous decay. Our interpretation, which emphasizes the ``measurement''-induced interruption of atomic-state coherences as the cause of inhibited quantum transitions, suggests a resolution to the quantum Zeno paradox. The theoretical limit of continuous observation is discussed.