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Densities of the Raney distributions
Wojciech Mlotkowski, Karol A. Penson, Karol Zyczkowski
We prove that if and then the sequence , , is positive definite, more precisely, is the moment sequence of a probab…
Collectibility for Mixed Quantum States
Łukasz Rudnicki, Zbigniew Puchała, Paweł Horodecki +1
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the…
Unitary quantum gates, perfect entanglers and unistochastic maps
Marcin Musz, Marek Kus, Karol Zyczkowski
Non-local properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix U e…
Constructive entanglement test from triangle inequality
Łukasz Rudnicki, Zbigniew Puchała, Paweł Horodecki +1
We derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented…
Multiaccess quantum communication and product higher rank numerical range
Maciej Demianowicz, Paweł Horodecki, Karol Życzkowski
In the present paper we initiate the study of the product higher rank numerical range. The latter, being a variant of the higher rank numerical range [M.--D. Choi {\it et al.}, Rep…
Joint numerical ranges, quantum maps, and joint numerical shadows
Eugene Gutkin, Karol Zyczkowski
We associate with k hermitian N\times N matrices a probability measure on R^k. It is supported on the joint numerical range of the k-tuple of matrices. We call this measure the joi…