Towards a classification of 6 × 6 complex hadamard matrices

Matolcsi, Máté and Szöllősi, Ferenc (2008) Towards a classification of 6 × 6 complex hadamard matrices. OPEN SYSTEMS & INFORMATION DYNAMICS, 15 (2). pp. 93-108. ISSN 1230-1612

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Abstract

Complex Hadamard matrices have received considerable attention in the past few years due to their application in quantum information theory. While a complete characterization currently available [5] is only up to order 5, several new constructions of higher order matrices have appeared recently [4, 12, 2, 7, 11]. In particular, the classification of self-adjoint complex Hadamard matrices of order 6 was completed by Beuachamp and Nicoara in [2], providing a previously unknown non-affine one-parameter orbit. In this paper we classify all dephased, symmetric complex Hadamard matrices with real diagonal of order 6. Furthermore, relaxing the condition on the diagonal entries we obtain a new non-affine one-parameter orbit connecting the Fourier matrix F(6) and Dita's matrix D(6). This answers a recent question of Bengtsson et al. [3].

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