We discuss a simple and analytically solvable measurement model which describes the famous Quantum Zeno Effect (QZE) and Inverse Zeno Effect (IZE), that correspond to the slow down and to the increase of the decay rate caused by measurements (or, more in general, by the interaction of an unstable state with the detector and the environment). Within this model one can understand quite general features of the QZE and IZE: by considering an unstable quantum state, such as an unstable particle, whose decay width as function of energy is $Γ(ω)=g^{2}ω^α,$ then -- under quite general assumptions -- the QZE occurs for $α\in(0,1)$ , while the IZE for $α\in(-\infty,0)\cup(1,\infty).$ This result is valid also for more realistic measurement models than the one described in this work. We then apply these considerations to the decay of the neutron, for which $α=5.$ Hence, the realization of the IZE for the neutron decay (and for the majority of weak decays) is in principle possible. Indeed, trap experiments find a lifetime that is $8.7\pm2.1$ s shorter than beam experiments, suggesting that the IZE could have taken place.We discuss a simple and analytically solvable measurement model which describes the famous Quantum Zeno Effect (QZE) and Inverse Zeno Effect (IZE), that correspond to the slow down and to the increase of the decay rate caused by measurements (or, more in general, by the interaction of an unstable state with the detector and the environment). Within this model one can understand quite general features of the QZE and IZE: by considering an unstable quantum state, such as an unstable particle, whose decay width as function of energy is $Γ(ω)=g^{2}ω^α,$ then -- under quite general assumptions -- the QZE occurs for $α\in(0,1)$, while the IZE for $α\in(-\infty,0)\cup(1,\infty).$ This result is valid also for more realistic measurement models than the one described in this work. We then apply these considerations to the decay of the neutron, for which $α=5.$ Hence, the realization of the IZE for the neutron decay (and for the majority of weak decays) is in principle possible. Indeed, trap experiments find a lifetime that is $8.7\pm2.1$ s shorter than beam experiments, suggesting that the IZE could have taken place.

arXiv:2004.07772Acta Physica Polonica BJan 1, 20201 citation

Quantum Zeno effect by incomplete measurements

Manchao Zhang, Chun-Wang Wu, Yi Xie +2 more

Quantum Information ProcessingFeb 18, 20196 citations

5 Quantum Zeno effect by general measurements

Kazuki Koshino, Akira Shimizu

It was predicted that frequently repeated measurements on an unstable state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. The results are based on the quantum measurement theory, which is also reviewed briefly. As a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. This measurement is an indirect negative-result one, for which the curiosity of the QZE and AZE is emphasized. It is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. In a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. However, drastic differences emerge in general cases where the detector responds only to limited photon modes. For example, against predictions of the conventional theories, the QZE or AZE may take place even for states that exactly follow the exponential decay law. We also discuss relation to the cavity quantum electrodynamics.It was predicted that frequently repeated measurements on an unstable state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. The results are based on the quantum measurement theory, which is also reviewed briefly. As a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. This measurement is an indirect negative-result one, for which the curiosity of the QZE and AZE is emphasized. It is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. In a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. However, drastic differences emerge in general cases where the detector responds only to limited photon modes. For example, against predictions of the conventional theories, the QZE or AZE may take place even for states that exactly follow the exponential decay law. We also discuss relation to the cavity quantum electrodynamics.

Nov 19, 2004136 citations

Some Mathematical Aspects of Quantum Zeno Effect

Asao Arai, Toru Fuda

Letters in Mathematical PhysicsDec 2, 20112 citations

Understanding the quantum Zeno effect

Hiromichi Nakazato, Mikio Namiki, Saverio Pascazio +1 more

arXiv:quant-ph/9605008Physics Letters AJul 1, 199656 citations

On the Quantum Zeno Effect and Time Series Related to Quantum Measurements

Karl‐Heinz Fichtner, Kei Inoue

Our main aim is to prove a more general version of the quantum Zeno effect. Then we discuss some examples of the quantum Zeno effect. Furthermore, we discuss a possibility that based on the quantum Zeno effect and certain experiments one could check whether, from the statistical point of view, a concrete system behaves like a quantum system. The more general version of quantum Zeno effect can be helpful to prove that the brain acts like in a quantum system. The proof of our main result is based on certain formulas describing probability distributions of time series related to quantum measurements.Our main aim is to prove a more general version of the quantum Zeno effect. Then we discuss some examples of the quantum Zeno effect. Furthermore, we discuss a possibility that based on the quantum Zeno effect and certain experiments one could check whether, from the statistical point of view, a concrete system behaves like a quantum system. The more general version of quantum Zeno effect can be helpful to prove that the brain acts like in a quantum system. The proof of our main result is based on certain formulas describing probability distributions of time series related to quantum measurements.

Applied MathematicsJan 1, 20131 citation

Γ(ω)=g^{2}ω^α,

then -- under quite general assumptions -- the QZE occurs for

α\in(0,1)

, while the IZE for

α\in(-\infty,0)\cup(1,\infty).

This result is valid also for more realistic measurement models than the one described in this work. We then apply these considerations to the decay of the neutron, for which

α=5.

Hence, the realization of the IZE for the neutron decay (and for the majority of weak decays) is in principle possible. Indeed, trap experiments find a lifetime that is

8.7\pm2.1

s shorter than beam experiments, suggesting that the IZE could have taken place.