We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock st...

We consider explicitly two examples of d-dimensional quantum channels with correlated noise and show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of the output mutual information than product states. We obtain a strong dependence of this effect on the nature of the noise correlations as well a...

We prove the following theorem: Let F be an algebraic closure of a finite field of characteristic p. If ρ is a continuous homomorphism from the absolute Galois group of Q to GLn(F) which is isomorphic to a direct sum of one-dimensional representations, and if p > n+1 and the conductors of the one-dimensional representations are pairwise relatively prime, and if a certain parity condition holds,...

in this paper, we mainly investigate the uniqueness of the entire function sharing a small entire function with its high difference operators. we obtain one results, which can give a negative answer to an uniqueness question relate to the bruck conjecture dealt by liu and yang. meanwhile, we also establish a difference analogue of the bruck conjecture for entire functions of order less than 2, ...

We present 3 open challenges in the field of Costas arrays. They are: a) the determination of the number of dots on the main diagonal of a Welch array, and especially the maximal such number for a Welch array of a given order; b) the conjecture that the fraction of Welch arrays without dots on the main diagonal behaves asymptotically as the fraction of permutations without fixed points and henc...

We introduce a protocol for authentication between a human and a computer, where the human is able to use no special hardware other than a dumb terminal. Authentication is based on a shared secret which can be reused polynomially often with no danger of exposure, assuming the conjectured uniform hardness of learning parity functions in the presence of noise. Under this conjecture, the protocol ...

We present previously unpublished elementary proofs by Dekker and Ottens (1991) and Boyce (private communication) of a special case of the Dinitz conjecture. We prove a special case of a related basis conjecture by Rota, and give a reformulation of Rota's conjecture using the Nullstellensatz. Finally we give an asymptotic result on a related Latin square conjecture.

Arrow’s impossibility theorem [1] shows that the set of acyclic tournaments is not closed to non dictatorial Boolean aggregation. In this paper we extend the notion of aggregation to general tournaments and we show that for tournaments with four vertices or more any proper symmetric (closed to vertex permutations) subset cannot be closed to non dictatorial monotone aggregation and to non neutra...

We discuss the existence of vertex disjoint path coverings with prescribed ends for the n-dimensional hypercube with or without deleted vertices. Depending on the type of the set of deleted vertices and desired properties of the path coverings we establish the minimal integer m such that for every n ≥ m such path coverings exist. Using some of these results, for k ≤ 4, we prove Locke’s conjectu...

Here we perform a Kaluza–Klein dimensional reduction of Vasiliev’s first-order description massless spin-s particles from D=3+1 to D=2+1 and derive self-dual models describing with helicities ±s for the cases s=1,2,3. In first two recover known (parity singlets) models. spin-3 case new order model local Weyl symmetry which lifts traceless restriction on rank-3 tensor. A gauge fixed version this...