# Quantum Anti-Zeno Paradox

## Abstract

We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator E(t)=U(t)EU{sup {dagger}}( t) is measured continuously from t=0 to T , where E is a projector leaving the initial state unchanged and U(t) a unitary operator obeying U(0)=1 . We prove that the probability of always finding E(t)=1 from t=0 to T is unity. If U(t){ne}1 , the watched kettle is sure to ''boil.'' (c) 2000 The American Physical Society.

- Authors:

- Department of Physics, Syracuse University, Syracuse, New York 13244 (United States)
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, (India)

- Publication Date:

- OSTI Identifier:
- 20216328

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 18; Other Information: PBD: 1 May 2000; Journal ID: ISSN 0031-9007

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; PROJECTION OPERATORS; PROBABILITY; PROPAGATOR; SCHROEDINGER PICTURE; DENSITY MATRIX; THEORETICAL DATA

### Citation Formats

```
Balachandran, A. P., and Roy, S. M.
```*Quantum Anti-Zeno Paradox*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevLett.84.4019.

```
Balachandran, A. P., & Roy, S. M.
```*Quantum Anti-Zeno Paradox*. United States. doi:10.1103/PhysRevLett.84.4019.

```
Balachandran, A. P., and Roy, S. M. Mon .
"Quantum Anti-Zeno Paradox". United States. doi:10.1103/PhysRevLett.84.4019.
```

```
@article{osti_20216328,
```

title = {Quantum Anti-Zeno Paradox},

author = {Balachandran, A. P. and Roy, S. M.},

abstractNote = {We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator E(t)=U(t)EU{sup {dagger}}( t) is measured continuously from t=0 to T , where E is a projector leaving the initial state unchanged and U(t) a unitary operator obeying U(0)=1 . We prove that the probability of always finding E(t)=1 from t=0 to T is unity. If U(t){ne}1 , the watched kettle is sure to ''boil.'' (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevLett.84.4019},

journal = {Physical Review Letters},

issn = {0031-9007},

number = 18,

volume = 84,

place = {United States},

year = {2000},

month = {5}

}

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