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Numerical shadows: measures and densities on the numerical range
Charles F. Dunkl, Piotr Gawron, John A. Holbrook +2
For any operator acting on an -dimensional Hilbert space we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numeri…
How often is a random quantum state k-entangled?
Stanislaw J. Szarek, Elisabeth Werner, Karol Zyczkowski
The set of trace preserving, positive maps acting on density matrices of size d forms a convex body. We investigate its nested subsets consisting of k-positive maps, where k=2,...,…
Generating random density matrices
Karol Zyczkowski, Karol A. Penson, Ion Nechita +1
We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of…
Product numerical range in a space with tensor product structure
Zbigniew Puchała, Piotr Gawron, Jarosław Adam Miszczak +3
We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds f…
Truncations of Random Orthogonal Matrices
Boris A. Khoruzhenko, Hans-Juergen Sommers, Karol Zyczkowski
Statistical properties of non--symmetric real random matrices of size , obtained as truncations of random orthogonal matrices are investigated. We derive an exact fo…
Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence
Wojciech Roga, Mark Fannes, Karol Zyczkowski
The Holevo quantity provides an upper bound for the mutual information between the sender of a classical message encoded in quantum carriers and the receiver. Applying the strong s…