# Quantum perfect correlations

## Abstract

The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The transitivity of perfect correlations is proved to generally hold, and applied to a simple articulation for the failure of Hardy's nonlocality proof for maximally entangled states. The notion of perfect correlations between observables and POVMs is used for defining the notion of a precise measurement of a given observable in a given state. A longstanding misconception on the correlation made by the measuring interaction is resolved in the light of the new theory of quantum perfect correlations.

- Authors:

- Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579 (Japan). E-mail: ozawa@math.is.tohoku.ac.jp

- Publication Date:

- OSTI Identifier:
- 20766997

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 321; Journal Issue: 3; Other Information: DOI: 10.1016/j.aop.2005.08.007; PII: S0003-4916(05)00139-9; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; LOCALITY; QUANTUM FIELD THEORY; QUANTUM MECHANICS; STATISTICAL MECHANICS

### Citation Formats

```
Ozawa, Masanao.
```*Quantum perfect correlations*. United States: N. p., 2006.
Web. doi:10.1016/j.aop.2005.08.007.

```
Ozawa, Masanao.
```*Quantum perfect correlations*. United States. doi:10.1016/j.aop.2005.08.007.

```
Ozawa, Masanao. Wed .
"Quantum perfect correlations". United States.
doi:10.1016/j.aop.2005.08.007.
```

```
@article{osti_20766997,
```

title = {Quantum perfect correlations},

author = {Ozawa, Masanao},

abstractNote = {The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The transitivity of perfect correlations is proved to generally hold, and applied to a simple articulation for the failure of Hardy's nonlocality proof for maximally entangled states. The notion of perfect correlations between observables and POVMs is used for defining the notion of a precise measurement of a given observable in a given state. A longstanding misconception on the correlation made by the measuring interaction is resolved in the light of the new theory of quantum perfect correlations.},

doi = {10.1016/j.aop.2005.08.007},

journal = {Annals of Physics (New York)},

number = 3,

volume = 321,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}