24,768 research outputs found
Optimal accessing and non-accessing structures for graph protocols
An accessing set in a graph is a subset B of vertices such that there exists
D subset of B, such that each vertex of V\B has an even number of neighbors in
D. In this paper, we introduce new bounds on the minimal size kappa'(G) of an
accessing set, and on the maximal size kappa(G) of a non-accessing set of a
graph G. We show strong connections with perfect codes and give explicitly
kappa(G) and kappa'(G) for several families of graphs. Finally, we show that
the corresponding decision problems are NP-Complete
On Weak Odd Domination and Graph-based Quantum Secret Sharing
A weak odd dominated (WOD) set in a graph is a subset B of vertices for which
there exists a distinct set of vertices C such that every vertex in B has an
odd number of neighbors in C. We point out the connections of weak odd
domination with odd domination, [sigma,rho]-domination, and perfect codes. We
introduce bounds on \kappa(G), the maximum size of WOD sets of a graph G, and
on \kappa'(G), the minimum size of non WOD sets of G. Moreover, we prove that
the corresponding decision problems are NP-complete. The study of weak odd
domination is mainly motivated by the design of graph-based quantum secret
sharing protocols: a graph G of order n corresponds to a secret sharing
protocol which threshold is \kappa_Q(G) = max(\kappa(G), n-\kappa'(G)). These
graph-based protocols are very promising in terms of physical implementation,
however all such graph-based protocols studied in the literature have
quasi-unanimity thresholds (i.e. \kappa_Q(G)=n-o(n) where n is the order of the
graph G underlying the protocol). In this paper, we show using probabilistic
methods, the existence of graphs with smaller \kappa_Q (i.e. \kappa_Q(G)<
0.811n where n is the order of G). We also prove that deciding for a given
graph G whether \kappa_Q(G)< k is NP-complete, which means that one cannot
efficiently double check that a graph randomly generated has actually a
\kappa_Q smaller than 0.811n.Comment: Subsumes arXiv:1109.6181: Optimal accessing and non-accessing
structures for graph protocol
Information Flow in Secret Sharing Protocols
The entangled graph states have emerged as an elegant and powerful quantum
resource, indeed almost all multiparty protocols can be written in terms of
graph states including measurement based quantum computation (MBQC), error
correction and secret sharing amongst others. In addition they are at the
forefront in terms of implementations. As such they represent an excellent
opportunity to move towards integrated protocols involving many of these
elements. In this paper we look at expressing and extending graph state secret
sharing and MBQC in a common framework and graphical language related to flow.
We do so with two main contributions.
First we express in entirely graphical terms which set of players can access
which information in graph state secret sharing protocols. These succinct
graphical descriptions of access allow us to take known results from graph
theory to make statements on the generalisation of the previous schemes to
present new secret sharing protocols.
Second, we give a set of necessary conditions as to when a graph with flow,
i.e. capable of performing a class of unitary operations, can be extended to
include vertices which can be ignored, pointless measurements, and hence
considered as unauthorised players in terms of secret sharing, or error qubits
in terms of fault tolerance. This offers a way to extend existing MBQC patterns
to secret sharing protocols. Our characterisation of pointless measurements is
believed also to be a useful tool for further integrated measurement based
schemes, for example in constructing fault tolerant MBQC schemes
Practical sharing of quantum secrets over untrusted channels
In this work we address the issue of sharing a quantum secret over untrusted
channels between the dealer and players. Existing methods require entanglement
over a number of systems which scales with the security parameter, quickly
becoming impractical. We present protocols (interactive and a non-interactive)
where single copy encodings are sufficient. Our protocols work for all quantum
secret sharing schemes and access structures, and are implementable with
current experimental set ups. For a single authorised player, our protocols act
as quantum authentication protocols
SWI-Prolog and the Web
Where Prolog is commonly seen as a component in a Web application that is
either embedded or communicates using a proprietary protocol, we propose an
architecture where Prolog communicates to other components in a Web application
using the standard HTTP protocol. By avoiding embedding in external Web servers
development and deployment become much easier. To support this architecture, in
addition to the transfer protocol, we must also support parsing, representing
and generating the key Web document types such as HTML, XML and RDF.
This paper motivates the design decisions in the libraries and extensions to
Prolog for handling Web documents and protocols. The design has been guided by
the requirement to handle large documents efficiently. The described libraries
support a wide range of Web applications ranging from HTML and XML documents to
Semantic Web RDF processing.
To appear in Theory and Practice of Logic Programming (TPLP)Comment: 31 pages, 24 figures and 2 tables. To appear in Theory and Practice
of Logic Programming (TPLP
Photonic multipartite entanglement conversion using nonlocal operations
We propose a simple setup for the conversion of multipartite entangled states
in a quantum network with restricted access. The scheme uses nonlocal
operations to enable the preparation of states that are inequivalent under
local operations and classical communication, but most importantly does not
require full access to the states. It is based on a flexible linear optical
conversion gate that uses photons, which are ideally suited for distributed
quantum computation and quantum communication in extended networks. In order to
show the basic working principles of the gate, we focus on converting a
four-qubit entangled cluster state to other locally inequivalent four-qubit
states, such as the GHZ and symmetric Dicke state. We also show how the gate
can be incorporated into extended graph state networks, and can be used to
generate variable entanglement and quantum correlations without entanglement
but nonvanishing quantum discord.Comment: 10 pages, 6 figures, correction of reference list, add Journal ref.
and DO
Security in Locally Repairable Storage
In this paper we extend the notion of {\em locally repairable} codes to {\em
secret sharing} schemes. The main problem that we consider is to find optimal
ways to distribute shares of a secret among a set of storage-nodes
(participants) such that the content of each node (share) can be recovered by
using contents of only few other nodes, and at the same time the secret can be
reconstructed by only some allowable subsets of nodes. As a special case, an
eavesdropper observing some set of specific nodes (such as less than certain
number of nodes) does not get any information. In other words, we propose to
study a locally repairable distributed storage system that is secure against a
{\em passive eavesdropper} that can observe some subsets of nodes.
We provide a number of results related to such systems including upper-bounds
and achievability results on the number of bits that can be securely stored
with these constraints.Comment: This paper has been accepted for publication in IEEE Transactions of
Information Theor
Graph States, Pivot Minor, and Universality of (X,Z)-measurements
The graph state formalism offers strong connections between quantum
information processing and graph theory. Exploring these connections, first we
show that any graph is a pivot-minor of a planar graph, and even a pivot minor
of a triangular grid. Then, we prove that the application of measurements in
the (X,Z)-plane over graph states represented by triangular grids is a
universal measurement-based model of quantum computation. These two results are
in fact two sides of the same coin, the proof of which is a combination of
graph theoretical and quantum information techniques
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