In quantum mechanics, frequent measurements cause the quantum Zeno effect, a reduction in transitions away from the system's initial state, slowing a system's time evolution. Sometimes this effect is interpreted as "a system cannot change while you are watching it". One can "freeze" the evolution of the system by measuring it frequently enough in its known initial state. The meaning of the term has since expanded, leading to a more technical definition, in which time evolution can be suppressed not only by measurement: the quantum Zeno effect is the suppression of unitary time evolution in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, among other factors. As an outgrowth of study of the quantum Zeno effect, it has become clear that applying a series of sufficiently strong and fast pulses with appropriate symmetry can also decouple a system from its decohering environment. The name comes by analogy to Zeno's arrow paradox, which states that because an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all. In the quantum Zeno effect an unstable state seems frozen – to not 'move' – due to a constant series of observations. The comparison is due to a 1977 article by Baidyanath Misra and E. C. George Sudarshan. According to the reduction postulate, each measurement causes the wavefunction to collapse to an eigenstate of the measurement basis. In the context of this effect, an observation can simply be the absorption of a particle, without the need of an observer in any conventional sense. However, there is controversy over the interpretation of the effect, sometimes referred to as the "measurement problem" in traversing the interface between microscopic and macroscopic objects. Another crucial problem related to the effect is strictly connected to the time–energy indeterminacy relation (part of the indeterminacy principle). If one wants to make the measurement process more and more frequent, one has to correspondingly decrease the time duration of the measurement itself. But the request that the measurement last only a very short time implies that the energy spread of the state in which reduction occurs becomes increasingly large. However, the deviations from the exponential decay law for small times is crucially related to the inverse of the energy spread, so that the region in which the deviations are appreciable shrinks when one makes the measurement process duration shorter and shorter. An explicit evaluation of these two competing requests shows that it is inappropriate, without taking into account this basic fact, to deal with the actual occurrence and emergence of Zeno's effect. Closely related (and sometimes not distinguished from the quantum Zeno effect) is the watchdog effect, in which the time evolution of a system is affected by its continuous coupling to the environment.
Description Unstable quantum systems are predicted to exhibit a short-time deviation from the exponential decay law. This universal phenomenon has led to the prediction that frequent measurements during this nonexponential period could inhibit decay of the system, one form of the quantum Zeno effect. Subsequently, it was predicted that measurements applied more slowly could also enhance decay rates, a phenomenon known as the quantum anti-Zeno effect. In quantum mechanics the interaction mentioned is called "measurement" because its result can be interpreted in terms of classical mechanics. Frequent measurement prohibits the transition. It can be a transition of a particle from one half-space to another (which could be used for an atomic mirror in an atomic nanoscope) as in the time-of-arrival problem, a transition of a photon in a waveguide from one mode to another, and it can be a transition of an atom from one quantum state to another. It can be a transition from the subspace without decoherent loss of a qubit to a state with a qubit lost in a quantum computer. In this sense, for the qubit correction, it is sufficient to determine whether the decoherence has already occurred or not. All these can be considered as applications of the Zeno effect. By its nature, the effect appears only in systems with distinguishable quantum states, and hence is inapplicable to classical phenomena and macroscopic bodies. The idea is implicit in John von Neumann's early work Mathematical Foundations of Quantum Mechanics, and in particular the rule sometimes called the reduction postulate. It was later shown that the quantum Zeno effect of a single system is equivalent to the indetermination of the quantum state of a single system.
History The unusual nature of the short-time evolution of quantum systems and the consequences for measurement was noted by John von Neumann in his Mathematical Foundations of Quantum Mechanics, published in 1932. This aspect of quantum mechanics lay unexplored until 1967 when Beskow and Nilsson suggested that the mathematics indicated that an unstable particle in a bubble chamber would not decay. In 1977, Baidyanath Misra and E. C. George Sudarshan presented a mathematical analysis of this quantum effect and proposed its association with Zeno's arrow paradox. This paradox of Zeno of Elea imagines seeing an flying arrow at any fixed instant: it is immobile, frozen in the space it occupies. Despite continued theoretical work, experimental confirmation did not appear until 1990 when Itano et al. applied the idea proposed by Cook to study oscillating systems rather than unstable ones. Itano drove a transition between two levels in trapped 9Be+ ions while simultaneously measuring absorption of laser pulses proportional to population of the lower level.
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