Divergence-free approach for obtaining decompositions of quantum-optical processes

Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for continuous-variable systems, such schemes contain natural divergences since the maximally entangled state is ill-defined. We introduce a method that avoids such divergences by utilizing finitely entangled (squeezed) states and then taking the limit of arbitrary large squeezing. Using this method we derive an operator-sum representation for all single-mode bosonic Gaussian channels where a unique feature is that both quantum-limited and noisy channels are treated on an equal footing. This technique facilitates a proof that the rank-one Kraus decomposition for Gaussian channels at its respective entanglement-breaking thresholds, obtained in the overcomplete coherent state basis, is unique. The methods could have applications to simulation of continuous-variable channels.Comment: 18 pages (8 + appendices), 4 figs. V2: close to published version, dropped Sec.VI of v1 to be expanded elsewher

Heisenberg-limited eavesdropping on the continuous-variable quantum cryptographic protocol with no basis switching is impossible

The Gaussian quantum key distribution protocol based on coherent states and heterodyne detection [Phys. Rev. Lett. 93, 170504 (2004)] has the advantage that no active random basis switching is needed on the receiver's side. Its security is, however, not very satisfyingly understood today because the bounds on the secret key rate that have been derived from Heisenberg relations are not attained by any known scheme. Here, we address the problem of the optimal Gaussian individual attack against this protocol, and derive tight upper bounds on the information accessible to an eavesdropper. The optical scheme achieving this bound is also exhibited, which concludes the security analysis of this protocol.Comment: 10 pages, 6 figure

Experimental Proof of Quantum Nonlocality without Squeezing

It is shown that the ensemble $\{p (\alpha),|\alpha>|\alpha^*>\}$ where $p (\alpha)$ is a Gaussian distribution of finite variance and $| \alpha>$ is a coherent state can be better discriminated with an entangled measurement than with any local strategy supplemented by classical communication. Although this ensemble consists of products of quasi-classical states, it exhibits some quantum nonlocality. This remarkable effect is demonstrated experimentally by implementing the optimal local strategy together with a joint nonlocal strategy that yields a higher fidelity.Comment: 4 pages, 2 figure

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

Boson Sampling in Low-depth Optical Systems

Optical losses are the main obstacle to demonstrating a quantum advantage via boson sampling without leaving open the possibility of classical spoofing. We propose a method for generating low-depth optical circuits suitable for boson sampling with very high efficiencies. Our circuits require only a constant number of optical components (namely three) to implement an optical transformation suitable for demonstrating a quantum advantage. Consequently, our proposal has a constant optical loss regardless of the number of optical modes. We argue that sampling from our family of circuits is computationally hard by providing numerical evidence that our family of circuits converges to that of the original boson sampling proposal in the limit of large optical systems. Our work opens a new route to demonstrate an optical quantum advantage.Comment: 11 pages, 6 figure

Continuous variable quantum key distribution with two-mode squeezed states

Quantum key distribution (QKD) enables two remote parties to grow a shared key which they can use for unconditionally secure communication [1]. The applicable distance of a QKD protocol depends on the loss and the excess noise of the connecting quantum channel [2-10]. Several QKD schemes based on coherent states and continuous variable (CV) measurements are resilient to high loss in the channel, but strongly affected by small amounts of channel excess noise [2-6]. Here we propose and experimentally address a CV QKD protocol which uses fragile squeezed states combined with a large coherent modulation to greatly enhance the robustness to channel noise. As a proof of principle we experimentally demonstrate that the resulting QKD protocol can tolerate more noise than the benchmark set by the ideal CV coherent state protocol. Our scheme represents a very promising avenue for extending the distance for which secure communication is possible.Comment: 8 pages, 5 figure

Improvement of continuous-variable quantum key distribution systems by using optical preamplifiers

Continuous-variable quantum key distribution protocols, based on Gaussian modulation of the quadratures of coherent states, have been implemented in recent experiments. A present limitation of such systems is the finite efficiency of the detectors, which can in principle be compensated for by the use of classical optical preamplifiers. Here we study this possibility in detail, by deriving the modified secret key generation rates when an optical parametric amplifier is placed at the output of the quantum channel. After presenting a general set of security proofs, we show that the use of preamplifiers does compensate for all the imperfections of the detectors when the amplifier is optimal in terms of gain and noise. Imperfect amplifiers can also enhance the system performance, under conditions which are generally satisfied in practice.Comment: 11 pages, 7 figures, submitted to J. Phys. B (special issue on Few Atoms Optics

Effect of Intensity Modulator Extinction on Practical Quantum Key Distribution System

We study how the imperfection of intensity modulator effects on the security of a practical quantum key distribution system. The extinction ratio of the realistic intensity modulator is considered in our security analysis. We show that the secret key rate increases, under the practical assumption that the indeterminable noise introduced by the imperfect intensity modulator can not be controlled by the eavesdropper.Comment: 6 pages, 5 figures. EPJD accepte

Continuous Variable Quantum Cryptography using Two-Way Quantum Communication

Quantum cryptography has been recently extended to continuous variable systems, e.g., the bosonic modes of the electromagnetic field. In particular, several cryptographic protocols have been proposed and experimentally implemented using bosonic modes with Gaussian statistics. Such protocols have shown the possibility of reaching very high secret-key rates, even in the presence of strong losses in the quantum communication channel. Despite this robustness to loss, their security can be affected by more general attacks where extra Gaussian noise is introduced by the eavesdropper. In this general scenario we show a "hardware solution" for enhancing the security thresholds of these protocols. This is possible by extending them to a two-way quantum communication where subsequent uses of the quantum channel are suitably combined. In the resulting two-way schemes, one of the honest parties assists the secret encoding of the other with the chance of a non-trivial superadditive enhancement of the security thresholds. Such results enable the extension of quantum cryptography to more complex quantum communications.Comment: 12 pages, 7 figures, REVTe

An improved two-way continuous-variable quantum key distribution protocol with added noise in homodyne detection

We propose an improved two-way continuous-variable quantum key distribution (CV QKD) protocol by adding proper random noise on the receiver's homodyne detection, the security of which is analysed against general collective attacks. The simulation result under the collective entangling cloner attack indicates that despite the correlation between two-way channels decreasing the secret key rate relative to the uncorrelated channels slightly, the performance of the two-way protocol is still far beyond that of the one-way protocols. Importantly, the added noise in detection is beneficial for the secret key rate and the tolerable excess noise of this two-way protocol. With the reasonable reconciliation efficiency of 90%, the two-way CV QKD with added noise allows the distribution of secret keys over 60 km fibre distance.Comment: 12 pages, 6 figure