# Relation between phase-space coverage and entanglement for spin-1/2 systems

## Abstract

For systems of two and three spins 1/2 it is known that the second moment of the Husimi function can be related to entanglement properties of the corresponding states. Here, we generalize this relation to an arbitrary number of spins in a pure state. It is shown that the second moment of the Husimi function can be expressed in terms of the lengths of the concurrence vectors for all possible partitions of the N-spin system in two subsystems. This relation implies that the phase space distribution of an entangled state is less localized than that of a nonentangled state. As an example, the second moment of the Husimi function is analyzed for an Ising chain subject to a magnetic field perpendicular to the chain axis.

- Authors:

- Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany)

- Publication Date:

- OSTI Identifier:
- 20982095

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022328; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISTRIBUTION; FUNCTIONS; ISING MODEL; MAGNETIC FIELDS; PHASE SPACE; QUANTUM ENTANGLEMENT; SPIN

### Citation Formats

```
Schenk, Stefan, and Ingold, Gert-Ludwig.
```*Relation between phase-space coverage and entanglement for spin-1/2 systems*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.022328.

```
Schenk, Stefan, & Ingold, Gert-Ludwig.
```*Relation between phase-space coverage and entanglement for spin-1/2 systems*. United States. doi:10.1103/PHYSREVA.75.022328.

```
Schenk, Stefan, and Ingold, Gert-Ludwig. Thu .
"Relation between phase-space coverage and entanglement for spin-1/2 systems". United States.
doi:10.1103/PHYSREVA.75.022328.
```

```
@article{osti_20982095,
```

title = {Relation between phase-space coverage and entanglement for spin-1/2 systems},

author = {Schenk, Stefan and Ingold, Gert-Ludwig},

abstractNote = {For systems of two and three spins 1/2 it is known that the second moment of the Husimi function can be related to entanglement properties of the corresponding states. Here, we generalize this relation to an arbitrary number of spins in a pure state. It is shown that the second moment of the Husimi function can be expressed in terms of the lengths of the concurrence vectors for all possible partitions of the N-spin system in two subsystems. This relation implies that the phase space distribution of an entangled state is less localized than that of a nonentangled state. As an example, the second moment of the Husimi function is analyzed for an Ising chain subject to a magnetic field perpendicular to the chain axis.},

doi = {10.1103/PHYSREVA.75.022328},

journal = {Physical Review. A},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}

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