16,393 research outputs found
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
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
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
Efficient Multi-Party Quantum Secret Sharing Schemes
In this work, we generalize the quantum secret sharing scheme of Hillary,
Bu\v{z}ek and Berthiaume[Phys. Rev. A59, 1829(1999)] into arbitrary
multi-parties. Explicit expressions for the shared secret bit is given. It is
shown that in the Hillery-Bu\v{z}ek-Berthiaume quantum secret sharing scheme
the secret information is shared in the parity of binary strings formed by the
measured outcomes of the participants. In addition, we have increased the
efficiency of the quantum secret sharing scheme by generalizing two techniques
from quantum key distribution. The favored-measuring-basis Quantum secret
sharing scheme is developed from the Lo-Chau-Ardehali technique[H. K. Lo, H. F.
Chau and M. Ardehali, quant-ph/0011056] where all the participants choose their
measuring-basis asymmetrically, and the measuring-basis-encrypted Quantum
secret sharing scheme is developed from the Hwang-Koh-Han technique [W. Y.
Hwang, I. G. Koh and Y. D. Han, Phys. Lett. A244, 489 (1998)] where all
participants choose their measuring-basis according to a control key. Both
schemes are asymptotically 100% in efficiency, hence nearly all the GHZ-states
in a quantum secret sharing process are used to generate shared secret
information.Comment: 7 page
Efficient sharing of a continuous-variable quantum secret
We propose an efficient scheme for sharing a continuous variable quantum
secret using passive optical interferometry and squeezers: this efficiency is
achieved by showing that a maximum of two squeezers is required to replicate
the secret state, and we obtain the cheapest configuration in terms of total
squeezing cost. Squeezing is a cost for the dealer of the secret as well as for
the receivers, and we quantify limitations to the fidelity of the replicated
secret state in terms of the squeezing employed by the dealer.Comment: 7 pages, 3 figure
Universal Communication Efficient Quantum Threshold Secret Sharing Schemes
Quantum secret sharing (QSS) is a cryptographic protocol in which a quantum
secret is distributed among a number of parties where some subsets of the
parties are able to recover the secret while some subsets are unable to recover
the secret. In the standard quantum threshold secret sharing scheme,
any subset of or more parties out of the total parties can recover the
secret while other subsets have no information about the secret. But recovery
of the secret incurs a communication cost of at least qudits for every
qudit in the secret. Recently, a class of communication efficient QSS schemes
were proposed which can improve this communication cost to by
contacting parties where is fixed prior to the distribution of
shares. In this paper, we propose a more general class of quantum
secret sharing schemes with low communication complexity. Our schemes are
universal in the sense that the combiner can contact any number of parties to
recover the secret with communication efficiency i.e. any in the range
can be chosen by the combiner. This is the first such class of
universal communication efficient quantum threshold schemes
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