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Entanglement of Gaussian states and the applicability to quantum key distribution over fading channels T h e o p e n -a c c e s s j o u r n a l f o r p h y s i c s New Journal of PhysicsEntanglement of Gaussian states and the applicability to quantum key distribution over fading channels Abstract. Entanglement properties of Gaussian states of light as well as the security of continuous variable quantum key distribution with Gaussian states in free-space fading channels are studied. These qualities are shown to be sensitive to the statistical properties of the transmittance distribution in the cases when entanglement is strong or when channel excess noise is present. Fading, i.e. transmission fluctuations, caused by beam wandering due to atmospheric turbulence, is a frequent challenge in free-space communication.We introduce a method of fading discrimination and subsequent post-selection of the corresponding sub-states and show that it can improve the entanglement 6 Authors to whom any correspondence should be addressed.Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercialShareAlike 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New Journal of Physics 14 (2012) 0930481367-2630/12/093048+20$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2 resource and restore the security of the key distribution over a realistic fading link. Furthermore, the optimal post-selection strategy in combination with an optimized entangled resource is shown to drastically increase the protocol's robustness to excess noise, which is confirmed for experimentally measured fading channel characteristics. The stability of the result against finite data ensemble size and imperfect channel estimation is also addressed. Contents

Quantum key distribution enables two remote parties to grow a shared key, which they can use for unconditionally secure communication over a certain distance. The maximal distance depends on the loss and the excess noise of the connecting quantum channel. several quantum key distribution schemes based on coherent states and continuous variable measurements are resilient to high loss in the channel, but are strongly affected by small amounts of channel excess noise. Here we propose and experimentally address a continuous variable quantum key distribution protocol that uses modulated fragile entangled states of light to greatly enhance the robustness to channel noise. We experimentally demonstrate that the resulting quantum key distribution protocol can tolerate more noise than the benchmark set by the ideal continuous variable coherent state protocol. our scheme represents a very promising avenue for extending the distance for which secure communication is possible.

Abstract:We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and noisy channels. The influence of such a noise on the security of Gaussian quantum cryptography can be crucial, even despite the fact that a noise is trusted, due to a strongly nonlinear behavior of the quantum entropies involved in the security analysis. We recapitulate the known effect of the preparation noise in both direct and reverse-reconciliation protocols, as well as the detection noise in the reverse-reconciliation scenario. As a new result, we show the negative role of the trusted detection noise in the direct-reconciliation scheme. We also describe the role of the trusted preparation or detection noise added at the reference side of the protocols in improving the robustness of the protocols to the channel noise, confirming the positive effect for the coherent-state reverse-reconciliation protocol. Finally, we address the combined effect of trusted noise added both in the source and the detector.

We address security of the quantum key distribution scheme based on the noisy modulation of coherent states and investigate how it is robust against noise in the modulation regardless of the particular technical implementation. As the trusted preparation noise is shown to be security breaking even for purely lossy channels, we reveal the essential difference between two types of trusted noise, namely sender-side preparation noise and receiver-side detection noise, the latter being security preserving. We consider the method of sender-side state purification to compensate the preparation noise and show its applicability in the realistic conditions of channel loss, untrusted channel excess noise, and trusted detection noise. We show that purification makes the scheme robust to the preparation noise (i.e., even the arbitrary noisy coherent states can in principle be used for the purpose of quantum key distribution). We also take into account the effect of realistic reconciliation and show that the purification method is still efficient in this case up to a limited value of preparation noise.

We investigate the main limitations which prevent the continuous-variable quantum key distribution protocols from achieving long distances in the finite-size setting. We propose a double-modulation protocol which allows using each state for both channel estimation and key distribution. As opposed to the standard method, we optimize the parameters of the protocol and consider squeezed as well as coherent states as a signal. By optimally combining the resources the key rate can approach the theoretical limit for long distances, and one can obtain about ten times higher key rate using ten times shorter block size than in the current state-of-the-art implementation.

We address the security of continuous-variable quantum key distribution with squeezed states upon realistic conditions of noisy and lossy environment and limited reconciliation efficiency. Considering the generalized preparation scheme and clearly distinguishing between classical and quantum resources, we investigate the effect of finite squeezing on the tolerance of the protocol to untrusted channel noise. For a long-distance strongly attenuating channel and the consequent low reconciliation efficiency, we show that feasible limited squeezing is surprisingly sufficient to provide the security of Gaussian quantum key distribution in the presence of untrusted noise. We explain the effect by behaviour of the Holevo quantity, which describes the information leakage, and is effectively minimized by the squeezed states.

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 one of quadrature modulations 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.