# On the measurability of quantum correlation functions

## Abstract

The concept of correlation function is widely used in classical statistical mechanics to characterize how two or more variables depend on each other. In quantum mechanics, on the other hand, there are observables that cannot be measured at the same time; the so-called incompatible observables. This prospect imposes a limitation on the definition of a quantum analog for the correlation function in terms of a sequence of measurements. Here, based on the notion of sequential weak measurements, we circumvent this limitation by introducing a framework to measure general quantum correlation functions, in principle, independently of the state of the system and the operators involved. To illustrate, we propose an experimental configuration to obtain explicitly the quantum correlation function between two Pauli operators, in which the input state is an arbitrary mixed qubit state encoded on the polarization of photons.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22451171

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics

- Additional Journal Information:
- Journal Volume: 356; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; PAULI SPIN OPERATORS; PHOTONS; POLARIZATION; QUANTUM MECHANICS; STATISTICAL MECHANICS

### Citation Formats

```
Lima Bernardo, Bertúlio de, E-mail: bertulio.fisica@gmail.com, Azevedo, Sérgio, and Rosas, Alexandre.
```*On the measurability of quantum correlation functions*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2015.03.012.

```
Lima Bernardo, Bertúlio de, E-mail: bertulio.fisica@gmail.com, Azevedo, Sérgio, & Rosas, Alexandre.
```*On the measurability of quantum correlation functions*. United States. doi:10.1016/J.AOP.2015.03.012.

```
Lima Bernardo, Bertúlio de, E-mail: bertulio.fisica@gmail.com, Azevedo, Sérgio, and Rosas, Alexandre. Fri .
"On the measurability of quantum correlation functions". United States. doi:10.1016/J.AOP.2015.03.012.
```

```
@article{osti_22451171,
```

title = {On the measurability of quantum correlation functions},

author = {Lima Bernardo, Bertúlio de, E-mail: bertulio.fisica@gmail.com and Azevedo, Sérgio and Rosas, Alexandre},

abstractNote = {The concept of correlation function is widely used in classical statistical mechanics to characterize how two or more variables depend on each other. In quantum mechanics, on the other hand, there are observables that cannot be measured at the same time; the so-called incompatible observables. This prospect imposes a limitation on the definition of a quantum analog for the correlation function in terms of a sequence of measurements. Here, based on the notion of sequential weak measurements, we circumvent this limitation by introducing a framework to measure general quantum correlation functions, in principle, independently of the state of the system and the operators involved. To illustrate, we propose an experimental configuration to obtain explicitly the quantum correlation function between two Pauli operators, in which the input state is an arbitrary mixed qubit state encoded on the polarization of photons.},

doi = {10.1016/J.AOP.2015.03.012},

journal = {Annals of Physics},

issn = {0003-4916},

number = ,

volume = 356,

place = {United States},

year = {2015},

month = {5}

}