Mutually unbiased bases and Hadamard matrices of order six

Bengtsson, Ingemar (author): Stockholms universitet,Fysikum,Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden

Bruzda, Wojciech (author): Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, Kraków, Poland

Ericsson, Åsa (author): Stockholms universitet,Fysikum,Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden

Larsson, Jan-Åke, 1969- (author): Linköpings universitet,Tekniska högskolan,Tillämpad matematik

Tadej, Wojciech (author): Wydział Matematyczno-Przyrodniczy, Szkoła Nauk Ścisłych, Universytet Kardynała Stefana Wyszyńskiego, Warszawa, Poland

Zyczkowski, Karol (author): Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, Kraków, Poland and Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Warszawa, Poland

(creator_code:org_t)

American Institute of Physics (AIP), 2007
2007
English.
In: Journal of Mathematical Physics. - : American Institute of Physics (AIP). - 0022-2488 .- 1089-7658. ; 48:5, s. 052106-1-052106-21

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Abstract Subject headings

We report on a search for mutually unbiased bases (MUBs) in six dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a detailed map of where in the landscape the MUB triplets are situated. We use available tools, such as the theory of the discrete Fourier transform, to organize our results. Finally, we present some evidence for the conjecture that there exists a four dimensional family of complex Hadamard matrices of order 6. If this conjecture is true the landscape in which one may search for MUBs is much larger than previously thought.

By the author/editor: Bengtsson, Ingem ...; Bruzda, Wojciech; Ericsson, Åsa; Larsson, Jan-Åke ...; Tadej, Wojciech; Zyczkowski, Karo ...

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