Unidimensional continuous-variable quantum key distribution

We propose the continuous-variable quantum key distribution protocol based on the Gaussian modulation of a single quadrature of the coherent states of light, which is aimed to provide simplified implementation compared to the symmetrically modulated Gaussian coherent-state protocols. The protocol waives the necessity in phase quadrature modulation and the corresponding channel transmittance estimation. The security of the protocol against collective attacks in a generally phase-sensitive Gaussian channels is analyzed and is shown achievable upon certain conditions. Robustness of the protocol to channel imperfections is compared to that of the symmetrical coherent-state protocol. The simplified unidimensional protocol is shown possible at a reasonable quantitative cost in terms of key rate and of tolerable channel excess noise.Comment: 7 pages, 5 figures, close to the published versio

Feasibility of a quantum memory for continuous variables based on trapped ions

We propose to use a large cloud of cold trapped ions as a medium for quantum optics and quantum information experiments. Contrary to most recent realizations of qubit manipulation based on a small number of trapped and cooled ions, we study the case of traps containing a macroscopic number of ions. We consider in particular the implementation of a quantum memory for quantum information stored in continuous variables and study the impact of the relevant physical parameters on the expected performances of the system.Comment: v2, typos correcte

Factoring Safe Semiprimes with a Single Quantum Query

Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform efficiently. SFA thus consists of a \emph{quantum order finding algorithm} (QOFA), bookended by classical routines which, given the order, return the factors. But, with probability up to $1/2$, these classical routines fail, and QOFA must be rerun. We modify these routines using elementary results in number theory, improving the likelihood that they return the factors. The resulting quantum factoring algorithm is better than SFA at factoring safe semiprimes, an important class of numbers used in cryptography. With just one call to QOFA, our algorithm almost always factors safe semiprimes. As well as a speed-up, improving efficiency gives our algorithm other, practical advantages: unlike SFA, it does not need a randomly picked input, making it simpler to construct in the lab; and in the (unlikely) case of failure, the same circuit can be rerun, without modification. We consider generalizing this result to other cases, although we do not find a simple extension, and conclude that SFA is still the best algorithm for general numbers (non safe semiprimes, in other words). Even so, we present some simple number theoretic tricks for improving SFA in this case.Comment: v2 : Typo correction and rewriting for improved clarity v3 : Slight expansion, for improved clarit

Random coding for sharing bosonic quantum secrets

We consider a protocol for sharing quantum states using continuous variable systems. Specifically we introduce an encoding procedure where bosonic modes in arbitrary secret states are mixed with several ancillary squeezed modes through a passive interferometer. We derive simple conditions on the interferometer for this encoding to define a secret sharing protocol and we prove that they are satisfied by almost any interferometer. This implies that, if the interferometer is chosen uniformly at random, the probability that it may not be used to implement a quantum secret sharing protocol is zero. Furthermore, we show that the decoding operation can be obtained and implemented efficiently with a Gaussian unitary using a number of single-mode squeezers that is at most twice the number of modes of the secret, regardless of the number of players. We benchmark the quality of the reconstructed state by computing the fidelity with the secret state as a function of the input squeezing.Comment: Updated figure 1, added figure 2, closer to published versio

Optimality of Gaussian Attacks in Continuous Variable Quantum Cryptography

We analyze the asymptotic security of the family of Gaussian modulated Quantum Key Distribution protocols for Continuous Variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.Comment: See also R. Garcia-Patron and N. Cerf, quant-ph/060803

Robust and Efficient Sifting-Less Quantum Key Distribution Protocols

We show that replacing the usual sifting step of the standard quantum-key-distribution protocol BB84 by a one-way reverse reconciliation procedure increases its robustness against photon-number-splitting (PNS) attacks to the level of the SARG04 protocol while keeping the raw key-rate of BB84. This protocol, which uses the same state and detection than BB84, is the m=4 member of a protocol-family using m polarization states which we introduce here. We show that the robustness of these protocols against PNS attacks increases exponentially with m, and that the effective keyrate of optimized weak coherent pulses decreases with the transmission T like T^{1+1/(m-2)}