Region of fidelities for a 1 -> N universal qubit quantum cloner

We analyze a region of fidelities for qubit which is obtained after an application of a 1 -> N universal quantum cloner. We express the allowed region for fidelities in terms of overlaps of pure states with irreps of S(n) (n = N+1) showing that the pure states can be taken with real coefficients only. Subsequently, the case n = 4, corresponding to a 1 -> 3 cloner is studied in more detail as an illustrative example. To obtain the main result, we make a convex hull of possible ranges of fidelities related to a given irrep. The formalism allows to construct the state giving rise to a given N-tuple of fidelities.Comment: 13 pages, 3 figures, final version to appear in Physics Letters

Extremal generalized quantum measurements

A measurement on a section K of the set of states of a finite dimensional C*-algebra is defined as an affine map from K to a probability simplex. Special cases of such sections are used in description of quantum networks, in particular quantum channels. Measurements on a section correspond to equivalence classes of so-called generalized POVMs, which are called quantum testers in the case of networks. We find extremality conditions for measurements on K and characterize generalized POVMs such that the corresponding measurement is extremal. These results are applied to the set of channels. We find explicit extremality conditions for two outcome measurements on qubit channels and give an example of an extremal qubit 1-tester such that the corresponding measurement is not extremal.Comment: 13 pages. The paper was rewritten, reorganized and shortened, the title changed, references were added. Main results are the sam

Multiple integral representation for the trigonometric SOS model with domain wall boundaries

Using the dynamical Yang-Baxter algebra we derive a functional equation for the partition function of the trigonometric SOS model with domain wall boundary conditions. The solution of the equation is given in terms of a multiple contour integral.Comment: 28 pages, v2: comments and references added, typos fixed, to appear in NP

Spooky action at a distance in general probabilistic theories

We call a probabilistic theory "complete" if it cannot be further refined by no-signaling hidden-variable models, and name a theory "spooky" if every equivalent hidden-variable model violates Shimony's Outcome Independence. We prove that a complete theory is spooky if and only if it admits a pure steering state in the sense of Schr\"odinger. Finally we show that steering of complementary states leads to a Schr\"odinger's cat-like paradox.Comment: 7 pages, 1 figure, elsart, significantly revised versio

Quantum computation with programmable connections between gates

A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g. in achieving the programmability of permutations of N different unitary channels with 1 use instead of N uses per channel. For this task, a new elemental resource is needed, the "quantum switch", which can be programmed to switch the order of two channels with a single use of each one.Comment: 5 pages, PRL styl

The Dirac quantum automaton: a short review

We briefly review the derivation from first principles of the quantum cellular automata, from which the free quantum field theory (Weyl, Dirac and Maxwell) emerges in the relativistic limit. We illustrate the deviations from the relativistic dynamics occuring at the Planck scale in terms of the main vectors that rule the evolution of wave packets

Density cubes and higher-order interference theories

10.1088/1367-2630/16/2/023028New Journal of Physics16