332 research outputs found
Bounds on entanglement distillation and secret key agreement for quantum broadcast channels
The squashed entanglement of a quantum channel is an additive function of
quantum channels, which finds application as an upper bound on the rate at
which secret key and entanglement can be generated when using a quantum channel
a large number of times in addition to unlimited classical communication. This
quantity has led to an upper bound of on the capacity
of a pure-loss bosonic channel for such a task, where is the average
fraction of photons that make it from the input to the output of the channel.
The purpose of the present paper is to extend these results beyond the
single-sender single-receiver setting to the more general case of a single
sender and multiple receivers (a quantum broadcast channel). We employ
multipartite generalizations of the squashed entanglement to constrain the
rates at which secret key and entanglement can be generated between any subset
of the users of such a channel, along the way developing several new properties
of these measures. We apply our results to the case of a pure-loss broadcast
channel with one sender and two receivers.Comment: 35 pages, 1 figure, accepted for publication in IEEE Transactions on
Information Theor
Secret Sharing Based on a Hard-on-Average Problem
The main goal of this work is to propose the design of secret sharing schemes
based on hard-on-average problems. It includes the description of a new
multiparty protocol whose main application is key management in networks. Its
unconditionally perfect security relies on a discrete mathematics problem
classiffied as DistNP-Complete under the average-case analysis, the so-called
Distributional Matrix Representability Problem. Thanks to the use of the search
version of the mentioned decision problem, the security of the proposed scheme
is guaranteed. Although several secret sharing schemes connected with
combinatorial structures may be found in the bibliography, the main
contribution of this work is the proposal of a new secret sharing scheme based
on a hard-on-average problem, which allows to enlarge the set of tools for
designing more secure cryptographic applications
Bipartite and Multipartite Entanglement of Gaussian States
In this chapter we review the characterization of entanglement in Gaussian
states of continuous variable systems. For two-mode Gaussian states, we discuss
how their bipartite entanglement can be accurately quantified in terms of the
global and local amounts of mixedness, and efficiently estimated by direct
measurements of the associated purities. For multimode Gaussian states endowed
with local symmetry with respect to a given bipartition, we show how the
multimode block entanglement can be completely and reversibly localized onto a
single pair of modes by local, unitary operations. We then analyze the
distribution of entanglement among multiple parties in multimode Gaussian
states. We introduce the continuous-variable tangle to quantify entanglement
sharing in Gaussian states and we prove that it satisfies the
Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure,
symmetric three-mode Gaussian states, at variance with their discrete-variable
counterparts, allow a promiscuous sharing of quantum correlations, exhibiting
both maximum tripartite residual entanglement and maximum couplewise
entanglement between any pair of modes. Finally, we investigate the connection
between multipartite entanglement and the optimal fidelity in a
continuous-variable quantum teleportation network. We show how the fidelity can
be maximized in terms of the best preparation of the shared entangled resources
and, viceversa, that this optimal fidelity provides a clearcut operational
interpretation of several measures of bipartite and multipartite entanglement,
including the entanglement of formation, the localizable entanglement, and the
continuous-variable tangle.Comment: 21 pages, 4 figures, WS style. Published as Chapter 1 in the book
"Quantum Information with Continuous Variables of Atoms and Light" (Imperial
College Press, 2007), edited by N. Cerf, G. Leuchs, and E. Polzik. Details of
the book available at http://www.icpress.co.uk/physics/p489.html . For recent
follow-ups see quant-ph/070122
Entanglement Verification in Quantum Networks with Tampered Nodes
In this paper, we consider the problem of entanglement verification across
the quantum memories of any two nodes of a quantum network. Its solution can be
a means for detecting (albeit not preventing) the presence of intruders that
have taken full control of a node, either to make a denial-of-service attack or
to reprogram the node. Looking for strategies that only require local
operations and classical communication (LOCC), we propose two entanglement
verification protocols characterized by increasing robustness and efficiency.Comment: 14 pages, 7 figure
Unconditional security of entanglement-based continuous-variable quantum secret sharing
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes still remains unproven almost two decades after their original conception. Here we establish an unconditional security proof for entanglement-based continuous-variable quantum secret sharing schemes, in the limit of asymptotic keys and for an arbitrary number of players. We tackle the problem by resorting to the recently developed one-sided device-independent approach to quantum key distribution. We demonstrate theoretically the feasibility of our scheme, which can be implemented by Gaussian states and homodyne measurements, with no need for ideal single-photon sources or quantum memories. Our results contribute to validating quantum secret sharing as a viable primitive for quantum technologies
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