# Simultaneous amplitude and phase damping of x-p symmetric Gaussian states and their separability

## Abstract

We give the time evolution solution of simultaneous amplitude and phase damping for any continuous variable state. For the simultaneous amplitude and phase damping of two-mode x-p symmetric entangled Gaussian states, two analytical conditions of the separability are given. One is the sufficient condition of separability. The other is the condition of positive partial transpose (PPT) separability where the Peres-Horodecki criterion is applied. Between the two conditions there may exist bound entanglement. The simplest example is the simultaneous amplitude and phase damping of a two-mode squeezed vacuum state. The damped state is non-Gaussian.

- Authors:

- Laboratory of Quantum Information, China Institute of Metrology, Hangzhou, 310018 (China)

- Publication Date:

- OSTI Identifier:
- 20974523

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.022307; (c) 2006 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; AMPLITUDES; GAUSSIAN PROCESSES; MATHEMATICAL SOLUTIONS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; VACUUM STATES

### Citation Formats

```
Chen Xiaoyu.
```*Simultaneous amplitude and phase damping of x-p symmetric Gaussian states and their separability*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.022307.

```
Chen Xiaoyu.
```*Simultaneous amplitude and phase damping of x-p symmetric Gaussian states and their separability*. United States. doi:10.1103/PHYSREVA.73.022307.

```
Chen Xiaoyu. Wed .
"Simultaneous amplitude and phase damping of x-p symmetric Gaussian states and their separability". United States.
doi:10.1103/PHYSREVA.73.022307.
```

```
@article{osti_20974523,
```

title = {Simultaneous amplitude and phase damping of x-p symmetric Gaussian states and their separability},

author = {Chen Xiaoyu},

abstractNote = {We give the time evolution solution of simultaneous amplitude and phase damping for any continuous variable state. For the simultaneous amplitude and phase damping of two-mode x-p symmetric entangled Gaussian states, two analytical conditions of the separability are given. One is the sufficient condition of separability. The other is the condition of positive partial transpose (PPT) separability where the Peres-Horodecki criterion is applied. Between the two conditions there may exist bound entanglement. The simplest example is the simultaneous amplitude and phase damping of a two-mode squeezed vacuum state. The damped state is non-Gaussian.},

doi = {10.1103/PHYSREVA.73.022307},

journal = {Physical Review. A},

number = 2,

volume = 73,

place = {United States},

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

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

}

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