Discrete phase-space structure of n-qubit mutually unbiased bases

Journal Article · Thu Jan 15 00:00:00 EST 2009 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2008.10.003· OSTI ID:21167698

Klimov, A B; Romero, J L ^[1]; Bjoerk, G ^[2]

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1. Departamento de Fisica, Universidad de Guadalajara, 44420 Guadalajara, Jalisco (Mexico)
2. School of Information and Communication Technology, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista (Sweden)

We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(2{sup n}) and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for n qubits.

• OSTI ID: 21167698
• Journal Information: Annals of Physics (New York), Vol. 324, Issue 1; Other Information: DOI: 10.1016/j.aop.2008.10.003; PII: S0003-4916(08)00154-1; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSIFICATION
INFORMATION THEORY
PHASE SPACE
QUANTUM MECHANICS
QUBITS
TRANSFORMATIONS