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arXiv:1408.4566 · npj Quantum Information

Complete elimination of information leakage in continuous-variable quantum communication channels

Christian S. Jacobsen, Lars S. Madsen, Vladyslav C. Usenko, Radim Filip, Ulrik L. Andersen

Published Jul 18, 2018• 33 citations
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Abstract

Abstract In all lossy communication channels realized to date, information is inevitably leaked to a potential eavesdropper. Here we present a communication protocol that does not allow for any information leakage to a potential eavesdropper in a purely lossy channel. By encoding information into a restricted Gaussian alphabet of squeezed states we show, both theoretically and experimentally, that the Holevo information between the eavesdropper and the intended recipient can be exactly zero in a purely lossy channel while minimized in a noisy channel. This result is of fundamental interest, but might also have practical implications in extending the distance of secure quantum key distribution.

DOI
10.1038/s41534-018-0084-0

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•Jan 1, 2010•0 citations
Abstract In all lossy communication channels realized to date, information is inevitably leaked to a potential eavesdropper. Here we present a communication protocol that does not allow for any information leakage to a potential eavesdropper in a purely lossy channel. By encoding information into a restricted Gaussian alphabet of squeezed states we show, both theoretically and experimentally, that the Holevo information between the eavesdropper and the intended recipient can be exactly zero in a purely lossy channel while minimized in a noisy channel. This result is of fundamental interest, but might also have practical implications in extending the distance of secure quantum key distribution.
In all lossy communication channels realized to date, information is inevitably leaked to a potential eavesdropper. Here we present a communication protocol that does not allow for any information leakage to a potential eavesdropper in a purely lossy channel. By encoding information into a restricted Gaussian alphabet of squeezed states we show, both theoretically and experimentally, that the Holevo information between the eavesdropper and the intended recipient can be exactly zero in a purely lossy channel while minimized in a noisy channel. This result is of fundamental interest, but might also have practical implications in extending the distance of secure quantum key distribution.
We address the security of continuous-variable quantum key distribution with squeezed states upon the 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 the behaviour of the Holevo quantity, which describes the information leakage and is effectively minimized by the squeezed states.
The role of the side channels in the continuous-variable quantum key distribution is studied. It is shown how the information leakage through a side channel from the trusted sender station increases the vulnerability of the protocols to the eavesdropping in the main quantum communication channel. Moreover, the untrusted noise infusion by an eavesdropper on the trusted receiving side breaks the security even for a purely attenuating main quantum channel. As a method to compensate for the effect of the side-channel leakage on the sender side, we suggest several types of manipulations on the side-channel input. It is shown that by applying the modulated coherent light on the input of the side channel that is optimally correlated to the modulation on the main signal and optionally introducing additional squeezing in the case of the squeezed-state protocol, the negative influence of the lossy side channel on the sender side can be completely removed. For the trusted receiving side, the method of optimal monitoring of the residual noise from the side-channel noise infusion is suggested and shown to be able to completely eliminate the presence of the noisy side channel. We therefore prove that the side-channel effects can be completely removed using feasible operations if the trusted parties access the respective parts of the side channels.
Continuous variable quantum key distribution enables two parties to extract provably secure keys for cryptography by exploiting aspects of quantum mechanics. A central challenge in achieving QKD over long distances is overcoming optical loss, which limits the secret key rates and achievable transmission distances. Recent work has illustrated how to perform continuous variable quantum key distribution while eliminating information leakage to an eavesdropper in a pure-loss channel and minimizing information leakage in a noisy channel. In this work, we analyse this protocol under conditions where the quantum channel linking the sender and receiver is a fading channel, which can be used to model free-space links. We find that the protocol maintains strong performance over fading channels and outperforms comparable protocols.
The aim of this thesis is to study the security of two particular quantum communication protocols. We want to investigate what is the maximum amount of channel noise for which the protocols can still be secure. We do this by using well known bounds for limiting the information that an eavesdropper can obtain. The first protocol that we study is a direct communication protocol using two-qubit states. We find the security threshold by analyzing the protocol in an enanglement based setting. The Holevo bound was used to put an upper bound on the information of an eavesdropper. To arrive at a manageable optimisation probem, we restrict the eavesdropper's attack strategy such that the noise introduced will be unbiased. Furthermore, we also impose some additional constraints on the eavesdropper that arises from the symmetry of the protocol. After doing this we then optimise the remaining parameters to arrive at the eavesdropper's optimal strategy and find out what is the maximum amount of information she can obtain. Once the eavesdropper's maximum information is known, the security threshold for secure communication was obtained by comparing that information with the information between the legitimate communicating parties. The second protocol studied is a continuous variable quantum key distribution protocol using post-selection. For this protocol, we investigate the maximum amount of information the eavesdropper can get under individual and collective attacks in the presence of Gaussian excess noise in the channel. By providing the eavesdropper with additional information, we can use known results on the accessible information for pure input states to bound the eavesdropper's information. For individual attacks, Levitin's result on the optimal measurement was used while for collective attacks, Holevo's bound was used to arrive at an upper bound for the eavesdropper's information. From this we can then arrive at the post-selection region where the legitimate communicating parties have more information than the eavesdropper. We can then find the maximum amount of noise that the protocol can tolerate before the eavesdropper knows too much and the protocol fails.