7,438 research outputs found
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
Quantum secret sharing with qudit graph states
We present a unified formalism for threshold quantum secret sharing using
graph states of systems with prime dimension. We construct protocols for three
varieties of secret sharing: with classical and quantum secrets shared between
parties over both classical and quantum channels.Comment: 13 pages, 12 figures. v2: Corrected to reflect imperfections of (n,n)
QQ protocol. Also changed notation from to , corrected typos,
updated references, shortened introduction. v3: Updated acknowledgement
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
Quantum Secret Sharing with Graph States
Revised Selected Papers - http://www.memics.cz/2012/International audienceWe study the graph-state-based quantum secret sharing protocols [24,17] which are not only very promising in terms of physical implementation, but also resource efficient since every player's share is composed of a single qubit. The threshold of a graph-state-based protocol admits a lower bound: for any graph of order n, the threshold of the corresponding n-player protocol is at least 0.506n. Regarding the upper bound, lexicographic product of the C 5 graph (cycle of size 5) are known to provide n-player protocols which threshold is n − n 0.68. Using Paley graphs we improve this bound to n − n 0.71. Moreover, using probabilistic methods, we prove the existence of graphs which associated threshold is at most 0.811n. Albeit non-constructive, probabilistic methods permit to prove that a random graph G of order n has a threshold at most 0.811n with high probability. However, verifying that the threshold of a given graph is acually smaller than 0.811n is hard since we prove that the corresponding decision problem is NP-Complete. These results are mainly based on the graphical characterization of the graph-state-based secret sharing properties, in particular we point out strong connections with domination with parity constraints
Experimental demonstration of graph-state quantum secret sharing
Distributed quantum communication and quantum computing offer many new
opportunities for quantum information processing. Here networks based on highly
nonlocal quantum resources with complex entanglement structures have been
proposed for distributing, sharing and processing quantum information. Graph
states in particular have emerged as powerful resources for such tasks using
measurement-based techniques. We report an experimental demonstration of
graph-state quantum secret sharing, an important primitive for a quantum
network. We use an all-optical setup to encode quantum information into photons
representing a five-qubit graph state. We are able to reliably encode,
distribute and share quantum information between four parties. In our
experiment we demonstrate the integration of three distinct secret sharing
protocols, which allow for security and protocol parameters not possible with
any single protocol alone. Our results show that graph states are a promising
approach for sophisticated multi-layered protocols in quantum networks
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
Classical Knowledge for Quantum Security
We propose a decision procedure for analysing security of quantum
cryptographic protocols, combining a classical algebraic rewrite system for
knowledge with an operational semantics for quantum distributed computing. As a
test case, we use our procedure to reason about security properties of a
recently developed quantum secret sharing protocol that uses graph states. We
analyze three different scenarios based on the safety assumptions of the
classical and quantum channels and discover the path of an attack in the
presence of an adversary. The epistemic analysis that leads to this and similar
types of attacks is purely based on our classical notion of knowledge.Comment: extended abstract, 13 page
Generalized parity measurements
Measurements play an important role in quantum computing (QC), by either
providing the nonlinearity required for two-qubit gates (linear optics QC), or
by implementing a quantum algorithm using single-qubit measurements on a highly
entangled initial state (cluster state QC). Parity measurements can be used as
building blocks for preparing arbitrary stabilizer states, and, together with
1-qubit gates are universal for quantum computing. Here we generalize parity
gates by using a higher dimensional (qudit) ancilla. This enables us to go
beyond the stabilizer/graph state formalism and prepare other types of
multi-particle entangled states. The generalized parity module introduced here
can prepare in one-shot, heralded by the outcome of the ancilla, a large class
of entangled states, including GHZ_n, W_n, Dicke states D_{n,k}, and, more
generally, certain sums of Dicke states, like G_n states used in secret
sharing. For W_n states it provides an exponential gain compared to linear
optics based methods.Comment: 7 pages, 1 fig; updated to the published versio
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
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