993 research outputs found
Multiparty Quantum Secret Sharing
Based on a quantum secure direct communication (QSDC) protocol [Phys. Rev.
A69(04)052319], we propose a -threshold scheme of multiparty quantum
secret sharing of classical messages (QSSCM) using only single photons. We take
advantage of this multiparty QSSCM scheme to establish a scheme of multiparty
secret sharing of quantum information (SSQI), in which only all quantum
information receivers collaborate can the original qubit be reconstructed. A
general idea is also proposed for constructing multiparty SSQI schemes from any
QSSCM scheme
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
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
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
The GHZ state in secret sharing and entanglement simulation
In this note, we study some properties of the GHZ state. First, we present a
quantum secret sharing scheme in which the participants require only classical
channels in order to reconstruct the secret; our protocol is significantly more
efficient than the trivial usage of teleportation. Second, we show that the
classical simulation of an n-party GHZ state requires at least n log n - 2n
bits of communication. Finally, we present a problem simpler than the complete
simulation of the multi-party GHZ state, that could lead to a no-go theorem for
GHZ state simulation.Comment: 5 page
How to share a quantum secret
We investigate the concept of quantum secret sharing. In a ((k,n)) threshold
scheme, a secret quantum state is divided into n shares such that any k of
those shares can be used to reconstruct the secret, but any set of k-1 or fewer
shares contains absolutely no information about the secret. We show that the
only constraint on the existence of threshold schemes comes from the quantum
"no-cloning theorem", which requires that n < 2k, and, in all such cases, we
give an efficient construction of a ((k,n)) threshold scheme. We also explore
similarities and differences between quantum secret sharing schemes and quantum
error-correcting codes. One remarkable difference is that, while most existing
quantum codes encode pure states as pure states, quantum secret sharing schemes
must use mixed states in some cases. For example, if k <= n < 2k-1 then any
((k,n)) threshold scheme must distribute information that is globally in a
mixed state.Comment: 5 pages, REVTeX, submitted to PR
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