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A new proof for the existence of mutually unbiased bases. (English) Zbl 1012.68069

Summary: 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 that are powers of primes 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 \(d=2^m\).

MSC:

68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
81P68 Quantum computation
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