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arXiv:1603.06620 · Physical Review A

Sufficiency of quantum non-Gaussianity for discrete-variable quantum key distribution over noisy channels

Mikołaj Lasota, Radim Filip, Vladyslav C. Usenko

Published Jul 5, 2017• 12 citations
arXivHTMLPDF

Abstract

Quantum key distribution can be enhanced and extended if nonclassical single-photon states of light are used. We study a connection between the security of quantum key distribution and quantum non-Gaussianity of light arriving at the receiver's detection system after the propagation through a noisy quantum channel, being under full control of an eavesdropper performing general collective attacks. We show that while quantum nonclassicality exhibited by the light arriving at the receiver's station is a necessary indication of the security of the discrete-variable protocols, quantum non-Gaussianity can be a sufficient indication of their security. Therefore, checking for non-Gaussianity of this light by performing standard autocorrelation function measurement can be used for prior verification of the usability of prepare-and-measure schemes. It can play a similar role to the prior verification of the quantum correlations sufficient to violate Bell inequalities for entanglement-based protocols.

DOI
10.1103/physreva.96.012301

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Quantum key distribution can be enhanced and extended if nonclassical single-photon states of light are used. We study a connection between the security of quantum key distribution and quantum non-Gaussianity of light arriving at the receiver's detection system after the propagation through a noisy quantum channel, being under full control of an eavesdropper performing general collective attacks. We show that while quantum nonclassicality exhibited by the light arriving at the receiver's station is a necessary indication of the security of the discrete-variable protocols, quantum non-Gaussianity can be a sufficient indication of their security. Therefore, checking for non-Gaussianity of this light by performing standard autocorrelation function measurement can be used for prior verification of the usability of prepare-and-measure schemes. It can play a similar role to the prior verification of the quantum correlations sufficient to violate Bell inequalities for entanglement-based protocols.
We address the robustness of quantum key distribution protocols to imperfections of a quantum channel. Starting from the Gaussian continuous-variable protocols we recapitulate the role of quadrature squeezing in providing security of the key in the noisy channels taking into account the limited efficiency of data processing. We then develop a model of channel noise that allows an equivalent quantification as for the continuous-variable protocols and apply it to the discrete-variable protocols. This allows us to perform the comparison of robustness of the protocols to the channel noise when either continuous- or discrete-variable coding is used. We show that while continuous-variable protocols enforced by arbitrarily strong nonclassicality demonstrate some quantitative advantage in the channels with relatively low losses, the discrete-variable protocols can achieve better tolerance to the channel noise even when using the limited nonclassical resource. The result is promising for planning of integrated secure communication systems.
We theoretically analyse the relation between non-Gaussianity and security of entanglement-based quantum key distribution (QKD) protocols, namely device-independent (DI) and entanglement-based BB848484. A similar analysis has already been made for prepare-and-measure (P\&M) protocols \cite{Lasota2017}. In addition, we consider imperfect detection with dark counts and limited efficiency. We assume a perfect source of entangled Bell states as produced by quantum-dot type sources, depolarisation in the channel and different noise statistics, namely thermal and Poissonian. We consider single-photon avalanche photodiodes (SPAD) and photon number resolving detectors (PNRD) and use their respective criteria for non-Gaussianity. The results show cross-regions for both security and non-Gaussianity, hence, the possibility to conclude about the suitability of a given channel for secret key distribution. Our results can be useful as a pre-check for the implementation of QKD protocols.
Quantum key distribution (QKD) protocols allow two trusted parties to distribute a cryptographic key which they can further use for the unconditionally secure classical communication. During the last decades the field has grown mature with the commercial prototypes being available. They mostly rely on the faint laser pulses implementing the protocols on the basis of single qubits and qubit pairs. Alternatively, the continuous-variable (CV) protocols based on the multi-photon states of light were developed recently. They are typically built using the quadrature modulation of the coherent or squeezed states and subsequent homodyne detection. In the case of Gaussian modulation the security of the protocols is based on the extremality of Gaussian states, which allows estimating bounds on the leaked information. The Gaussian CV QKD protocols were shown secure for any degree of channel attenuation, but are restricted by the channel noise. Moreover, the applicability of Gaussian CV QKD protocols is limited by the effectiveness of classical post-processing algorithms, used by the trusted parties to process the measured data and distill the cryptographic key. On the other hand, the squeezedstate CV QKD protocols were previously considered ineffective under limited degrees of squeezing, while strong squeezing remains experimentally challenging. In the present work we distinguish between the classical and quantum resources in the Gaussian CV QKD and address the role of nonclassicality in the Gaussian protocols. We demonstrate, that by properly combining squeezed resource and coherent modulation, trusted parties are able to decouple eavesdropper from the channel, thus being able to establish the secure key from any amount of the classical mutual information. Our result shows a very promising path towards the long-distance CV QKD.
In this paper we investigate the security of continuous variable BB84 quantum key distribution protocol using single photon added then subtracted squeezed coherent state SPASSCS. It's found that the SPASSCS is a non-Gaussian and nonclassical state. Its non-Gaussianity and non-classicality are exhibited via the Wigner function. It's shown that the proposed state is generally robust against the eavesdropping strategies, such as intercept-resend attack and superior channel attack. Further, a comparative study has proved the strong efficiency of the proposed state over coherent state, squeezed coherent state and photon added then subtracted coherent state. Our analysis employs bit error rate, mutual information, and secure key gain.
We address the effect of classical correlations, introduced to a quantum resource used for the continuous-variable quantum key distribution. The set-up is based on an entangled source with two trusted parties performing homodyne measurements on their modes, thus corresponding to the preparation of squeezed states, while one of the modes is traveling to the remote party through lossy and noisy channel. The security of the scheme is considered against individual and collective eavesdropping attacks. It is shown that the classical correlations added to the entangled source increase the performance of the scheme both quantatively in terms of the secure key rate and qualitatively in terms of the security region with respect to the tolerable excess noise for both types of attacks and the improvement is essentially significant for sources possessing low degree of nonclassicality.
As quantum key distribution becomes a mature technology, it appears clearly that some assumptions made in the security proofs cannot be justified in practical implementations. This might open the door to possible side-channel attacks. We examine several discrepancies between theoretical models and experimental setups in the case of continuous-variable quantum key distribution. We study in particular the impact of an imperfect modulation on the security of Gaussian protocols and show that approximating the theoretical Gaussian modulation with a discrete one is sufficient in practice. We also address the issue of properly calibrating the detection setup and in particular the value of the shot noise. Finally, we consider the influence of phase noise in the preparation stage of the protocol and argue that taking this noise into account can improve the secret key rate because this source of noise is not controlled by the eavesdropper.