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Quantum state discrimination: a geometric approach
D. Markham, J. A. Miszczak, Z. Puchala +1
We analyse the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view this problem is equivalent to that of embedding…
Random Bistochastic Matrices
V. Cappellini, H. -J. Sommers, W. Bruzda +1
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bi…
Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
Stanislaw J. Szarek, Elisabeth Werner, Karol Zyczkowski
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable,…
Composition of quantum states and dynamical subadditivity
Wojciech Roga, Mark Fannes, Karol Zyczkowski
We introduce a composition of quantum states of a bipartite system which is based on the reshuffling of density matrices. This non-Abelian product is associative and stems from the…
Defect of a unitary matrix
Wojciech Tadej, Karol Zyczkowski
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, deter…
From a toy model to the double square root voting system
Wojciech Slomczynski, Karol Zyczkowski
We investigate systems of indirect voting based on the law of Penrose, in which each representative in the voting body receives the number of votes (voting weight) proportional to…