Experimentally Feasible Security Check for n-qubit Quantum Secret Sharing

In this article we present a general security strategy for quantum secret sharing (QSS) protocols based on the HBB scheme presented by Hillery, Bu\v{z}ek and Berthiaume [Phys. Rev A \textbf{59}, 1829 (1999)]. We focus on a generalization of the HBB protocol to $n$ communication parties thus including $n$-partite GHZ states. We show that the multipartite version of the HBB scheme is insecure in certain settings and impractical when going to large $n$. To provide security for such QSS schemes in general we use the framework presented by some of the authors [M. Huber, F. Minert, A. Gabriel, B. C. Hiesmayr, Phys. Rev. Lett. \textbf{104}, 210501 (2010)] to detect certain genuine $n$ partite entanglement between the communication parties. In particular, we present a simple inequality which tests the security.Comment: 5 pages, submitted to Phys. Rev.

Dihydrofolate reductase of Streptococcus faecium II. Purification and some properties of two dihydrofolate reductases from the Amethopterin-resistant mutant, Streptococcus Faecium Var. Durans Strain A

From a single amethopterin-resistant organism, Streptococcus faecium var. durans strain A, two different dihydrofolate reductases have been obtained as essentially homogeneous proteins in good yield. One of the reductases has a similar substrate specificity and turnover number (about 8000 moles per min per mole of enzyme) to the single reductase found in the amethopterin-sensitive strain of S. faecium var. durans, ATCC 8043, and has therefore been designated "wild type." The other enzyme, which is distinguished by its ability to catalyze the reduction of folate, in addition to dihydrofolate, and by its lower turnover number (about 900 with dihydrofolate), has been designated "mutant type." Since the wild type and mutant type reductases have sedimentation constants (s20,buffer) of 2.58 S and 2.04 S, respectively, they are probably significantly different in molecular weight. Each exhibits a single pH optimum at pH 5.8 and is inactivated by urea. Neither is affected by methylmercuric salts but the wild type reductase is inactivated by phenyl-mercuric acetate and p-mercuribenzoate. Monovalent cations increase the activity of the mutant type reductase but decrease that of the wild type reductase. It is suggested that the amethopterin resistance in vivo of strain A depends at least partly on the folate reductase activity of the mutant type reductase

Short-Term Effects of Shrew Predation Upon Invertebrate Prey Sets in Prairie Ecosystem

During August of 1971, the effects of different densities of shrews (Sorex cinereus) upon the density and species composition of invertebrate prey sets on two prairies in northwestern Iowa were studied. Invertebrates were sampled using pitfall traps set on areas containing known shrew densities. In general, different levels of shrew predation produced certain differences in the prey sets. Increased shrew density was associated with the following prey set characteristics: 1) decreased numerical densities, but not the total biomass of prey sets; 2) decreased species dominance of prey sets; and 3) increased species diversity of the largest prey size subsets of the total prey set. These observed effects of shrew predation are short-term effects which are typical of keystone predators

Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

Economical (k,m)-threshold controlled quantum teleportation

We study a (k,m)-threshold controlling scheme for controlled quantum teleportation. A standard polynomial coding over GF(p) with prime p > m-1 needs to distribute a d-dimensional qudit with d >= p to each controller for this purpose. We propose a scheme using m qubits (two-dimensional qudits) for the controllers' portion, following a discussion on the benefit of a quantum control in comparison to a classical control of a quantum teleportation.Comment: 11 pages, 2 figures, v2: minor revision, discussions improved, an equation corrected in procedure (A) of section 4.3, v3: major revision, protocols extended, citations added, v4: minor grammatical revision, v5: minor revision, discussions extende

Matroids and Quantum Secret Sharing Schemes

A secret sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum secret sharing schemes. In addition to providing a new perspective on quantum secret sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum secret sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum secret sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure state quantum secret sharing scheme with information rate one

Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement

We present a way for symmetric multiparty-controlled teleportation of an arbitrary two-particle entangled state based on Bell-basis measurements by using two Greenberger-Horne-Zeilinger states, i.e., a sender transmits an arbitrary two-particle entangled state to a distant receiver, an arbitrary one of the $n+1$ agents via the control of the others in a network. It will be shown that the outcomes in the cases that $n$ is odd or it is even are different in principle as the receiver has to perform a controlled-not operation on his particles for reconstructing the original arbitrary entangled state in addition to some local unitary operations in the former. Also we discuss the applications of this controlled teleporation for quantum secret sharing of classical and quantum information. As all the instances can be used to carry useful information, its efficiency for qubits approaches the maximal value.Comment: 9 pages, 3 figures; the revised version published in Physical Review A 72, 022338 (2005). The detail for setting up a GHZ-state quantum channel is adde