Defect of a unitary matrix (2007)
Tadej, Wojciech, Zyczkowski, Karol
We analyze properties of a map B = f(U) sending a unitary matrix U of size N into a doubly stochastic matrix defined by B_{i,j} = |U_{i,j}|^2. For any U we define its DEFECT, determined by the...
Mubs and Hadamards of Order Six (2006)
Bengtsson, Ingemar, Bruzda, Wojciech, Ericsson, Asa, Larsson, Jan-Ake, Tadej, Wojciech, Zyczkowski, Karol
We report on a search for mutually unbiased bases (MUBs) in 6 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...
A concise guide to complex Hadamard matrices (2005)
Tadej, Wojciech, Zyczkowski, Karol
Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices...
Permutation Equivalence Classes of Kronecker Products of Unitary Fourier Matrices (2005)
Kronecker products of unitary Fourier matrices play important role in solving multilevel circulant systems by a multidimensional Fast Fourier Transform. They are also special cases of complex...
Birkhoff's polytope and unistochastic matrices, N=3 and N=4 (2004)
Bengtsson, Ingemar, Ericsson, Asa, Kus, Marek, Tadej, Wojciech, Zyczkowski, Karol
The set of bistochastic or doubly stochastic N by N matrices form a convex set called Birkhoff's polytope, that we describe in some detail. Our problem is to characterize the set of unistochastic...