# Groverian measure of entanglement for mixed states

## Abstract

The Groverian entanglement measure, introduced earlier for pure quantum states of multiple qubits [O. Biham, M.A. Nielsen, and T. Osborne, Phys. Rev. A 65, 062312 (2002)], is generalized to the case of mixed states. The Groverian measure of a mixed state of n qubits is obtained by a purification procedure into a pure state of 2n qubits, followed by an optimization process, before the resulting state is fed into Grover's search algorithm. It is expressed in terms of the maximal success probability of the algorithm and in this sense provides an operational measure of entanglement.

- Authors:

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

- Publication Date:

- OSTI Identifier:
- 20787169

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.73.044301; (c) 2006 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; ALGORITHMS; ENERGY LEVELS; MIXED STATE; PROBABILITY; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUBITS

### Citation Formats

```
Shapira, Daniel, Shimoni, Yishai, and Biham, Ofer.
```*Groverian measure of entanglement for mixed states*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Shapira, Daniel, Shimoni, Yishai, & Biham, Ofer.
```*Groverian measure of entanglement for mixed states*. United States. doi:10.1103/PHYSREVA.73.0.

```
Shapira, Daniel, Shimoni, Yishai, and Biham, Ofer. Sat .
"Groverian measure of entanglement for mixed states". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20787169,
```

title = {Groverian measure of entanglement for mixed states},

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

abstractNote = {The Groverian entanglement measure, introduced earlier for pure quantum states of multiple qubits [O. Biham, M.A. Nielsen, and T. Osborne, Phys. Rev. A 65, 062312 (2002)], is generalized to the case of mixed states. The Groverian measure of a mixed state of n qubits is obtained by a purification procedure into a pure state of 2n qubits, followed by an optimization process, before the resulting state is fed into Grover's search algorithm. It is expressed in terms of the maximal success probability of the algorithm and in this sense provides an operational measure of entanglement.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 4,

volume = 73,

place = {United States},

year = {Sat Apr 15 00:00:00 EDT 2006},

month = {Sat Apr 15 00:00:00 EDT 2006}

}

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