# Structure of the sets of mutually unbiased bases for N qubits

## Abstract

For a system of N qubits, living in a Hilbert space of dimension d=2{sup N}, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases with different properties as far as separability is concerned. Here we derive four sets of nine bases for three qubits, and show how they are unitarily related. We also briefly discuss the four-qubit case, give the entanglement structure of 16 sets of bases, and show some of them and their interrelations, as examples. The extension of the method to the general case of N qubits is outlined.

- Authors:

- School of Information and Communication Technology, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista (Sweden)
- Departamento de Fisica, Universidad de Guadalajara, 44420 Guadalajara, Jalisco (Mexico)
- Departamento de Optica, Facultad de Fisica, Universidad Complutense, 28040 Madrid (Spain)

- Publication Date:

- OSTI Identifier:
- 20786273

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.062310; (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; ALGORITHMS; HILBERT SPACE; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUBITS

### Citation Formats

```
Romero, J. L., Bjoerk, G., Klimov, A. B., and Sanchez-Soto, L. L.
```*Structure of the sets of mutually unbiased bases for N qubits*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Romero, J. L., Bjoerk, G., Klimov, A. B., & Sanchez-Soto, L. L.
```*Structure of the sets of mutually unbiased bases for N qubits*. United States. doi:10.1103/PHYSREVA.72.0.

```
Romero, J. L., Bjoerk, G., Klimov, A. B., and Sanchez-Soto, L. L. Thu .
"Structure of the sets of mutually unbiased bases for N qubits". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786273,
```

title = {Structure of the sets of mutually unbiased bases for N qubits},

author = {Romero, J. L. and Bjoerk, G. and Klimov, A. B. and Sanchez-Soto, L. L.},

abstractNote = {For a system of N qubits, living in a Hilbert space of dimension d=2{sup N}, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases with different properties as far as separability is concerned. Here we derive four sets of nine bases for three qubits, and show how they are unitarily related. We also briefly discuss the four-qubit case, give the entanglement structure of 16 sets of bases, and show some of them and their interrelations, as examples. The extension of the method to the general case of N qubits is outlined.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 6,

volume = 72,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.