# Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous

## Abstract

Monogamy of quantum correlation measures puts restrictions on the sharability of quantum correlations in multiparty quantum states. Multiparty quantum states can satisfy or violate monogamy relations with respect to given quantum correlations. We show that all multiparty quantum states can be made monogamous with respect to all measures. More precisely, given any quantum correlation measure that is non-monogamic for a multiparty quantum state, it is always possible to find a monotonically increasing function of the measure that is monogamous for the same state. The statement holds for all quantum states, whether pure or mixed, in all finite dimensions and for an arbitrary number of parties. The monotonically increasing function of the quantum correlation measure satisfies all the properties that are expected for quantum correlations to follow. We illustrate the concepts by considering a thermodynamic measure of quantum correlation, called the quantum work deficit.

- Authors:

- School of Physics, IISER TVM, CET Campus, Thiruvananthapuram, Kerala 695 016 (India)
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019 (India)

- Publication Date:

- OSTI Identifier:
- 22403393

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 348; Other Information: Copyright (c) 2014 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; AUGMENTATION; CORRELATIONS; FUNCTIONS; QUANTUM STATES

### Citation Formats

```
Salini, K., Prabhu, R., Sen, Aditi, and Sen, Ujjwal, E-mail: ujjwal@hri.res.in.
```*Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous*. United States: N. p., 2014.
Web. doi:10.1016/J.AOP.2014.06.001.

```
Salini, K., Prabhu, R., Sen, Aditi, & Sen, Ujjwal, E-mail: ujjwal@hri.res.in.
```*Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous*. United States. doi:10.1016/J.AOP.2014.06.001.

```
Salini, K., Prabhu, R., Sen, Aditi, and Sen, Ujjwal, E-mail: ujjwal@hri.res.in. Mon .
"Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous". United States. doi:10.1016/J.AOP.2014.06.001.
```

```
@article{osti_22403393,
```

title = {Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous},

author = {Salini, K. and Prabhu, R. and Sen, Aditi and Sen, Ujjwal, E-mail: ujjwal@hri.res.in},

abstractNote = {Monogamy of quantum correlation measures puts restrictions on the sharability of quantum correlations in multiparty quantum states. Multiparty quantum states can satisfy or violate monogamy relations with respect to given quantum correlations. We show that all multiparty quantum states can be made monogamous with respect to all measures. More precisely, given any quantum correlation measure that is non-monogamic for a multiparty quantum state, it is always possible to find a monotonically increasing function of the measure that is monogamous for the same state. The statement holds for all quantum states, whether pure or mixed, in all finite dimensions and for an arbitrary number of parties. The monotonically increasing function of the quantum correlation measure satisfies all the properties that are expected for quantum correlations to follow. We illustrate the concepts by considering a thermodynamic measure of quantum correlation, called the quantum work deficit.},

doi = {10.1016/J.AOP.2014.06.001},

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

issn = {0003-4916},

number = ,

volume = 348,

place = {United States},

year = {2014},

month = {9}

}