Genuine three-partite entangled states with a local hidden variable model

We present a family of three-qubit quantum states with a basic local hidden variable model. Any von Neumann measurement can be described by a local model for these states. We show that some of these states are genuine three-partite entangled and also distillable. The generalization for larger dimensions or higher number of parties is also discussed. As a byproduct, we present symmetric extensions of two-qubit Werner states.Comment: 5 pages including 2 figures + 1 page appendix, revtex4; published versio

Gaussian Operations and Privacy

We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in M. Navascues et al., Phys. Rev. Lett. 94, 010502 (2005). Then, we prove that a generalized version of this protocol does not allow to distill a secret key out of bound entangled Gaussian states

Security bounds for continuous variables quantum key distribution

Security bounds for key distribution protocols using coherent and squeezed states and homodyne measurements are presented. These bounds refer to (i) general attacks and (ii) collective attacks where Eve interacts individually with the sent states, but delays her measurement until the end of the reconciliation process. For the case of a lossy line and coherent states, it is first proven that a secure key distribution is possible up to 1.9 dB of losses. For the second scenario, the security bounds are the same as for the completely incoherent attack.Comment: See also F. Grosshans, quant-ph/040714

Quantifying the randomness of copies of noisy Popescu-Rohrlich correlations

In a no-signaling world, the outputs of a nonlocal box cannot be completely predetermined, a feature that is exploited in many quantum information protocols exploiting non-locality, such as device-independent randomness generation and quantum key distribution. This relation between non-locality and randomness can be formally quantified through the min-entropy, a measure of the unpredictability of the outputs that holds conditioned on the knowledge of any adversary that is limited only by the no-signaling principle. This quantity can easily be computed for the noisy Popescu-Rohrlich (PR) box, the paradigmatic example of non-locality. In this paper, we consider the min-entropy associated to several copies of noisy PR boxes. In the case where n noisy PR-boxes are implemented using n non-communicating pairs of devices, it is known that each PR-box behaves as an independent biased coin: the min-entropy per PR-box is constant with the number of copies. We show that this doesn't hold in more general scenarios where several noisy PR-boxes are implemented from a single pair of devices, either used sequentially n times or producing n outcome bits in a single run. In this case, the min-entropy per PR-box is smaller than the min-entropy of a single PR-box, and it decreases as the number of copies increases.Comment: 14 pages + 8 figures. Mathematica files attached. Comments welcom

Transfer of d-Level quantum states through spin chains by random swapping

We generalize an already proposed protocol for quantum state transfer to spin chains of arbitrary spin. An arbitrary unknown $d-$ level state is transferred through a chain with rather good fidelity by the natural dynamics of the chain. We compare the performance of this protocol for various values of $d$. A by-product of our study is a much simpler method for picking up the state at the destination as compared with the one proposed previously. We also discuss entanglement distribution through such chains and show that the quality of entanglement transition increases with the number of levels $d$.Comment: More discussion about the ground state has been added. Accepted in Physical Review

On multipartite invariant states II. Orthogonal symmetry

We construct a new class of multipartite states possessing orthogonal symmetry. This new class defines a convex hull of multipartite states which are invariant under the action of local unitary operations introduced in our previous paper "On multipartite invariant states I. Unitary symmetry". We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.Comment: 6 pages; slight corrections + new reference

Security bounds in Quantum Cryptography using d-level systems

We analyze the security of quantum cryptography schemes for $d$-level systems using 2 or $d+1$ maximally conjugated bases, under individual eavesdropping attacks based on cloning machines and measurement after the basis reconciliation. We consider classical advantage distillation protocols, that allow to extract a key even in situations where the mutual information between the honest parties is smaller than the eavesdropper's information. In this scenario, advantage distillation protocols are shown to be as powerful as quantum distillation: key distillation is possible using classical techniques if and only if the corresponding state in the entanglement based protocol is distillable.Comment: 18 pages, 1 figure. Published versio