Finite Fields and Applications pp 137-144
Constructions of Mutually Unbiased Bases
- Cite this paper as:
- Klappenecker A., Rötteler M. (2004) Constructions of Mutually Unbiased Bases. In: Mullen G.L., Poli A., Stichtenoth H. (eds) Finite Fields and Applications. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg
Two orthonormal bases B and B′ of a d-dimensional complex inner-product space are called mutually unbiased if and only if |〈b|b′ 〉|2 = 1/d holds for all b ∈ B and b′ ∈ B′. The size of any set containing pairwise mutually unbiased bases of ℂd cannot exceed d + 1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to exist. We give a simplified proof of this fact based on the estimation of exponential sums. We discuss conjectures and open problems concerning the maximal number of mutually unbiased bases for arbitrary dimensions.
KeywordsQuantum cryptography quantum state estimation Weil sums finite fields Galois rings
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