# Optimal entanglement witnesses for qubits and qutrits

## Abstract

We study the connection between the Hilbert-Schmidt measure of entanglement (that is the minimal distance of an entangled state to the set of separable states) and entanglement witness in terms of a generalized Bell inequality which distinguishes between entangled and separable states. A method for checking the nearest separable state to a given entangled one is presented. We illustrate the general results by considering isotropic states, in particular two-qubit and two-qutrit states--and their generalizations to arbitrary dimensions--where we calculate the optimal entanglement witnesses explicitly.

- Authors:

- Institute for Theoretical Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)

- Publication Date:

- OSTI Identifier:
- 20786483

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052331; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; BELL THEOREM; DISTANCE; ENERGY LEVELS; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUBITS

### Citation Formats

```
Bertlmann, Reinhold A., Durstberger, Katharina, Hiesmayr, Beatrix C., and Krammer, Philipp.
```*Optimal entanglement witnesses for qubits and qutrits*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Bertlmann, Reinhold A., Durstberger, Katharina, Hiesmayr, Beatrix C., & Krammer, Philipp.
```*Optimal entanglement witnesses for qubits and qutrits*. United States. doi:10.1103/PHYSREVA.72.0.

```
Bertlmann, Reinhold A., Durstberger, Katharina, Hiesmayr, Beatrix C., and Krammer, Philipp. Tue .
"Optimal entanglement witnesses for qubits and qutrits". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786483,
```

title = {Optimal entanglement witnesses for qubits and qutrits},

author = {Bertlmann, Reinhold A. and Durstberger, Katharina and Hiesmayr, Beatrix C. and Krammer, Philipp},

abstractNote = {We study the connection between the Hilbert-Schmidt measure of entanglement (that is the minimal distance of an entangled state to the set of separable states) and entanglement witness in terms of a generalized Bell inequality which distinguishes between entangled and separable states. A method for checking the nearest separable state to a given entangled one is presented. We illustrate the general results by considering isotropic states, in particular two-qubit and two-qutrit states--and their generalizations to arbitrary dimensions--where we calculate the optimal entanglement witnesses explicitly.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 5,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}

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