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.

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

Circular quantum secret sharing

A circular quantum secret sharing protocol is proposed, which is useful and efficient when one of the parties of secret sharing is remote to the others who are in adjacent, especially the parties are more than three. We describe the process of this protocol and discuss its security when the quantum information carrying is polarized single photons running circularly. It will be shown that entanglement is not necessary for quantum secret sharing. Moreover, the theoretic efficiency is improved to approach 100% as almost all the instances can be used for generating the private key, and each photon can carry one bit of information without quantum storage. It is straightforwardly to utilize this topological structure to complete quantum secret sharing with multi-level two-particle entanglement in high capacity securely.Comment: 7 pages, 2 figure

Efficient symmetric multiparty quantum state sharing of an arbitrary m-qubit state

We present a scheme for symmetric multiparty quantum state sharing of an arbitrary $m$-qubit state with $m$ Greenberger-Horne-Zeilinger states following some ideas from the controlled teleportation [Phys. Rev. A \textbf{72}, 02338 (2005)]. The sender Alice performs $m$ Bell-state measurements on her $2m$ particles and the controllers need only to take some single-photon product measurements on their photons independently, not Bell-state measurements, which makes this scheme more convenient than the latter. Also it does not require the parties to perform a controlled-NOT gate on the photons for reconstructing the unknown $m$-qubit state and it is an optimal one as its efficiency for qubits approaches the maximal value.Comment: 6 pages, no figures; It simplifies the process for sharing an arbitrary m-qubit state in Phys. Rev. A 72, 022338 (2005) (quant-ph/0501129

A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance

Cancer risks from arsenic in drinking water.

Ingestion of arsenic, both from water supplies and medicinal preparations, is known to cause skin cancer. The evidence assessed here indicates that arsenic can also cause liver, lung, kidney, and bladder cancer and that the population cancer risks due to arsenic in U.S. water supplies may be comparable to those from environmental tobacco smoke and radon in homes. Large population studies in an area of Taiwan with high arsenic levels in well water (170-800 micrograms/L) were used to establish dose-response relationships between cancer risks and the concentration of inorganic arsenic naturally present in water supplies. It was estimated that at the current EPA standard of 50 micrograms/L, the lifetime risk of dying from cancer of the liver, lung, kidney, or bladder from drinking 1 L/day of water could be as high as 13 per 1000 persons. It has been estimated that more than 350,000 people in the United States may be supplied with water containing more than 50 micrograms/L arsenic, and more than 2.5 million people may be supplied with water with levels above 25 micrograms/L. For average arsenic levels and water consumption patterns in the United States, the risk estimate was around 1/1000. Although further research is needed to validate these findings, measures to reduce arsenic levels in water supplies should be considered

Emergent global patterns of ecosystem structure and function from a mechanistic general ecosystem model

Anthropogenic activities are causing widespread degradation of ecosystems worldwide, threatening the ecosystem services upon which all human life depends. Improved understanding of this degradation is urgently needed to improve avoidance and mitigation measures. One tool to assist these efforts is predictive models of ecosystem structure and function that are mechanistic: based on fundamental ecological principles. Here we present the first mechanistic General Ecosystem Model (GEM) of ecosystem structure and function that is both global and applies in all terrestrial and marine environments. Functional forms and parameter values were derived from the theoretical and empirical literature where possible. Simulations of the fate of all organisms with body masses between 10 µg and 150,000 kg (a range of 14 orders of magnitude) across the globe led to emergent properties at individual (e.g., growth rate), community (e.g., biomass turnover rates), ecosystem (e.g., trophic pyramids), and macroecological scales (e.g., global patterns of trophic structure) that are in general agreement with current data and theory. These properties emerged from our encoding of the biology of, and interactions among, individual organisms without any direct constraints on the properties themselves. Our results indicate that ecologists have gathered sufficient information to begin to build realistic, global, and mechanistic models of ecosystems, capable of predicting a diverse range of ecosystem properties and their response to human pressures

Loop Interactions during Catalysis by Dihydrofolate Reductase fromMoritella profunda

Dihydrofolate reductase (DHFR) is often used as a model system to study the relation between protein dynamics and catalysis. We have studied a number of variants of the cold-adapted DHFR from Moritella profunda (MpDHFR), in which the catalytically important M20 and FG loops have been altered, and present a comparison with the corresponding variants of the wellstudied DHFR from Escherichia coli (EcDHFR). Mutations in the M20 loop do not affect the actual chemical step of transfer of hydride from reduced nicotinamide adenine dinucleotide phosphate to the substrate 7,8-dihydrofolate in the catalytic cycle in either enzyme; they affect the steady state turnover rate in EcDHFR but not in MpDHFR. Mutations in the FG loop also have different effects on catalysis by the two DHFRs. Despite the two enzymes most likely sharing a common catalytic cycle at pH 7, motions of these loops, known to be important for progression through the catalytic cycle in EcDHFR, appear not to play a significant role in MpDHFR