A New Proof for the Existence of Mutually Unbiased Bases

• DOI: 10.1007/s00453-002-0980-7
• Publication Date: 2002-11-07T00:42:05Z
• Authors: Not Available Not...; Not Available Not...; Not Available Not...; Not Available Not...
• Keywords: Quantum Physics; 0103 physical sciences; FOS: Physical sciences; Quantum Physics (quant-ph); 01 natural sciences

Revised version. To appear in the special issue of Algorithmica on Quantum Algorithms and Quantum Cryptography<br/>We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d the number of mutually unbiased bases is at most d+1. An explicit representation of mutually unbiased observables in terms of Pauli matrices are provided for d=2^m.<br/>