Karol Życzkowski

TL;DR: In this paper, the question of how many entangled or separable states there are in the set of all quantum states is considered, and a natural measure in the space of density matrices is proposed to describe $N$-dimensional quantum systems.

TL;DR: In this article, the space of isospectral 0Hermitian matrices is shown to be the space in which the number 6) and 7) occur twice in the figure, and the discussion between eqs.(5.14) and (5.15) is incorrect.

TL;DR: In this paper, the authors present a unified approach in which the basis states are labeled by numbers 0, 1, 2, …, N - 1 that are both elements of a Galois field and ordinary integers, and show how to use the thus constructed mutually unbiased bases in quantum-informatics applications, including dense coding, teleportation, entanglement swapping, covariant cloning, and state tomography.

TL;DR: It is shown that, in order to preserve the equivalence principle until late times in unitarily evaporating black holes, the thermodynamic entropy of a black hole must be primarily entropy of entanglement across the event horizon.

TL;DR: While the scalability of the stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), the method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device.