2003/12/26 by Claude archer, archer, Claude
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0312204
17 pages
arxiv created 2003/12/26 · arxiv updated 2009/12/01
In a quantum system having a finite number N of orthogonal states, two orthonormal bases \ai\ and \bj\ are called mutually unbiased if all inner products <ai|bj> have the same modulus 1/√(N). This concept appears in several quantum information problems. The number of pairwise mutually unbiased bases is at most N+1 and various constructions of N+1 such bases have been found when N is a power of a prime number. We study families of formulas that generalize these constructions to arbitrary dimensions using finite rings.We then prove that there exists a set of N+1 mutually unbiased bases described by such formulas, if and only if N is a power of a prime number.