# Groverian entanglement measure of pure quantum states with arbitrary partitions

## Abstract

The Groverian entanglement measure of pure quantum states of n qubits is generalized to the case in which the qubits are divided into any p{<=}n parties. The entanglement between these parties is evaluated numerically using an efficient parametrization. To demonstrate this measure we apply it to symmetric states such as the Greenberg-Horne-Zeiliner state and the W state. Interestingly, this measure is equivalent to an entanglement measure introduced earlier [H. Barnum and N. Linden, J. Phys. A 34, 6787 (2001)], using different considerations.

- Authors:

- Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)

- Publication Date:

- OSTI Identifier:
- 20982075

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022308; (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; ENERGY LEVELS; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM INFORMATION; QUANTUM MECHANICS; QUBITS

### Citation Formats

```
Shimoni, Yishai, and Biham, Ofer.
```*Groverian entanglement measure of pure quantum states with arbitrary partitions*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.022308.

```
Shimoni, Yishai, & Biham, Ofer.
```*Groverian entanglement measure of pure quantum states with arbitrary partitions*. United States. doi:10.1103/PHYSREVA.75.022308.

```
Shimoni, Yishai, and Biham, Ofer. Thu .
"Groverian entanglement measure of pure quantum states with arbitrary partitions". United States.
doi:10.1103/PHYSREVA.75.022308.
```

```
@article{osti_20982075,
```

title = {Groverian entanglement measure of pure quantum states with arbitrary partitions},

author = {Shimoni, Yishai and Biham, Ofer},

abstractNote = {The Groverian entanglement measure of pure quantum states of n qubits is generalized to the case in which the qubits are divided into any p{<=}n parties. The entanglement between these parties is evaluated numerically using an efficient parametrization. To demonstrate this measure we apply it to symmetric states such as the Greenberg-Horne-Zeiliner state and the W state. Interestingly, this measure is equivalent to an entanglement measure introduced earlier [H. Barnum and N. Linden, J. Phys. A 34, 6787 (2001)], using different considerations.},

doi = {10.1103/PHYSREVA.75.022308},

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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