39,032 research outputs found
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
Which graph states are useful for quantum information processing?
Graph states are an elegant and powerful quantum resource for measurement
based quantum computation (MBQC). They are also used for many quantum protocols
(error correction, secret sharing, etc.). The main focus of this paper is to
provide a structural characterisation of the graph states that can be used for
quantum information processing. The existence of a gflow (generalized flow) is
known to be a requirement for open graphs (graph, input set and output set) to
perform uniformly and strongly deterministic computations. We weaken the gflow
conditions to define two new more general kinds of MBQC: uniform
equiprobability and constant probability. These classes can be useful from a
cryptographic and information point of view because even though we cannot do a
deterministic computation in general we can preserve the information and
transfer it perfectly from the inputs to the outputs. We derive simple graph
characterisations for these classes and prove that the deterministic and
uniform equiprobability classes collapse when the cardinalities of inputs and
outputs are the same. We also prove the reversibility of gflow in that case.
The new graphical characterisations allow us to go from open graphs to graphs
in general and to consider this question: given a graph with no inputs or
outputs fixed, which vertices can be chosen as input and output for quantum
information processing? We present a characterisation of the sets of possible
inputs and ouputs for the equiprobability class, which is also valid for
deterministic computations with inputs and ouputs of the same cardinality.Comment: 13 pages, 2 figure
New Protocols and Lower Bound for Quantum Secret Sharing with Graph States
We introduce a new family of quantum secret sharing protocols with limited
quantum resources which extends the protocols proposed by Markham and Sanders
and by Broadbent, Chouha, and Tapp. Parametrized by a graph G and a subset of
its vertices A, the protocol consists in: (i) encoding the quantum secret into
the corresponding graph state by acting on the qubits in A; (ii) use a
classical encoding to ensure the existence of a threshold. These new protocols
realize ((k,n)) quantum secret sharing i.e., any set of at least k players
among n can reconstruct the quantum secret, whereas any set of less than k
players has no information about the secret. In the particular case where the
secret is encoded on all the qubits, we explore the values of k for which there
exists a graph such that the corresponding protocol realizes a ((k,n)) secret
sharing. We show that for any threshold k> n-n^{0.68} there exists a graph
allowing a ((k,n)) protocol. On the other hand, we prove that for any k<
79n/156 there is no graph G allowing a ((k,n)) protocol. As a consequence there
exists n_0 such that the protocols introduced by Markham and Sanders admit no
threshold k when the secret is encoded on all the qubits and n>n_0
On Secure Workflow Decentralisation on the Internet
Decentralised workflow management systems are a new research area, where most
work to-date has focused on the system's overall architecture. As little
attention has been given to the security aspects in such systems, we follow a
security driven approach, and consider, from the perspective of available
security building blocks, how security can be implemented and what new
opportunities are presented when empowering the decentralised environment with
modern distributed security protocols. Our research is motivated by a more
general question of how to combine the positive enablers that email exchange
enjoys, with the general benefits of workflow systems, and more specifically
with the benefits that can be introduced in a decentralised environment. This
aims to equip email users with a set of tools to manage the semantics of a
message exchange, contents, participants and their roles in the exchange in an
environment that provides inherent assurances of security and privacy. This
work is based on a survey of contemporary distributed security protocols, and
considers how these protocols could be used in implementing a distributed
workflow management system with decentralised control . We review a set of
these protocols, focusing on the required message sequences in reviewing the
protocols, and discuss how these security protocols provide the foundations for
implementing core control-flow, data, and resource patterns in a distributed
workflow environment
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
Quantum network communication -- the butterfly and beyond
We study the k-pair communication problem for quantum information in networks
of quantum channels. We consider the asymptotic rates of high fidelity quantum
communication between specific sender-receiver pairs. Four scenarios of
classical communication assistance (none, forward, backward, and two-way) are
considered. (i) We obtain outer and inner bounds of the achievable rate regions
in the most general directed networks. (ii) For two particular networks
(including the butterfly network) routing is proved optimal, and the free
assisting classical communication can at best be used to modify the directions
of quantum channels in the network. Consequently, the achievable rate regions
are given by counting edge avoiding paths, and precise achievable rate regions
in all four assisting scenarios can be obtained. (iii) Optimality of routing
can also be proved in classes of networks. The first class consists of directed
unassisted networks in which (1) the receivers are information sinks, (2) the
maximum distance from senders to receivers is small, and (3) a certain type of
4-cycles are absent, but without further constraints (such as on the number of
communicating and intermediate parties). The second class consists of arbitrary
backward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair
communication problem, observations are made on quantum multicasting and a
static version of network communication related to the entanglement of
assistance.Comment: 15 pages, 17 figures. Final versio
Non-Threshold Quantum Secret Sharing Schemes in the Graph State Formalism
In a recent work, Markham and Sanders have proposed a framework to study
quantum secret sharing (QSS) schemes using graph states. This framework unified
three classes of QSS protocols, namely, sharing classical secrets over private
and public channels, and sharing quantum secrets. However, most work on secret
sharing based on graph states focused on threshold schemes. In this paper, we
focus on general access structures. We show how to realize a large class of
arbitrary access structures using the graph state formalism. We show an
equivalence between binary quantum codes and graph state secret
sharing schemes sharing one bit. We also establish a similar (but restricted)
equivalence between a class of Calderbank-Shor-Steane (CSS) codes and
graph state QSS schemes sharing one qubit. With these results we are able to
construct a large class of quantum secret sharing schemes with arbitrary access
structures.Comment: LaTeX, 6 page
Scather: programming with multi-party computation and MapReduce
We present a prototype of a distributed computational infrastructure, an associated high level programming language, and an underlying formal framework that allow multiple parties to leverage their own cloud-based computational resources (capable of supporting MapReduce [27] operations) in concert with multi-party computation (MPC) to execute statistical analysis algorithms that have privacy-preserving properties. Our architecture allows a data analyst unfamiliar with MPC to: (1) author an analysis algorithm that is agnostic with regard to data privacy policies, (2) to use an automated process to derive algorithm implementation variants that have different privacy and performance properties, and (3) to compile those implementation variants so that they can be deployed on an infrastructures that allows computations to take place locally within each participant’s MapReduce cluster as well as across all the participants’ clusters using an MPC protocol. We describe implementation details of the architecture, discuss and demonstrate how the formal framework enables the exploration of tradeoffs between the efficiency and privacy properties of an analysis algorithm, and present two example applications that illustrate how such an infrastructure can be utilized in practice.This work was supported in part by NSF Grants: #1430145, #1414119, #1347522, and #1012798
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