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Physics of Atomic Nuclei

Group-theoretical approach to the construction of bases in 2 n -dimensional Hilbert space

Andrés García, José Luis Romero, A. B. Klimov

Published Jun 1, 2011• 1 citation
Publisher

Abstract

We propose a systematic procedure to construct all the possible bases with definite factorization structure in 2 n -dimensional Hilbert space and discuss an algorithm for the determination of basis separability. The results are applied for classification of bases for an n-qubit system.
DOI
10.1134/s1063778811060093

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We propose a systematic procedure to construct all the possible bases with a definite factorization structure (eigenstates of n commuting monomials constructed as products of Pauli operators) for an n -qubit system, as well as the possibility of collecting them into mutually unbiased sets. We also discuss an algorithm for the determination of basis separability and propose a criteria for complementarity between such bases. The results are applied to generate non-isomorphic complete sets of mutually unbiased bases.
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