# Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement

## Abstract

The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant ({Dirac_h}/2{pi})/2 as demonstrated by Heisenberg's thought experiment using a {gamma}-ray microscope. Here it is shown that this common assumption is not universally true: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck's constant when the intervention is dependent. A model of measuring interaction with dependent intervention shows that Heisenberg's lower bound for the noise-disturbance product is violated even by a nearly nondisturbing precise position measurement. An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices.

- Authors:

- Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, 980-8579 (Japan)

- Publication Date:

- OSTI Identifier:
- 20633935

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 67; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.67.042105; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; BASIC INTERACTIONS; CORRELATIONS; DISTURBANCES; GAMMA RADIATION; IMPLEMENTATION; NOISE; QUADRATURES; QUANTUM MECHANICS; UNCERTAINTY PRINCIPLE

### Citation Formats

```
Ozawa, Masanao.
```*Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement*. United States: N. p., 2003.
Web. doi:10.1103/PhysRevA.67.042105.

```
Ozawa, Masanao.
```*Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement*. United States. doi:10.1103/PhysRevA.67.042105.

```
Ozawa, Masanao. Tue .
"Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement". United States. doi:10.1103/PhysRevA.67.042105.
```

```
@article{osti_20633935,
```

title = {Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement},

author = {Ozawa, Masanao},

abstractNote = {The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant ({Dirac_h}/2{pi})/2 as demonstrated by Heisenberg's thought experiment using a {gamma}-ray microscope. Here it is shown that this common assumption is not universally true: a universally valid trade-off relation between the noise and the disturbance has an additional correlation term, which is redundant when the intervention brought by the measurement is independent of the measured object, but which allows the noise-disturbance product much below Planck's constant when the intervention is dependent. A model of measuring interaction with dependent intervention shows that Heisenberg's lower bound for the noise-disturbance product is violated even by a nearly nondisturbing precise position measurement. An experimental implementation is also proposed to realize the above model in the context of optical quadrature measurement with currently available linear optical devices.},

doi = {10.1103/PhysRevA.67.042105},

journal = {Physical Review. A},

issn = {1050-2947},

number = 4,

volume = 67,

place = {United States},

year = {2003},

month = {4}

}