Continuous-variable Quantum Key Distribution Scheme Research Articles

Quantum relay schemes for continuous-variable quantum key distribution

We propose several concatenated quantum relay continuous-variable quantum key distribution schemes based on the parametric amplifier (PA) and the beam splitter (BS). Instead of using only one BS in the traditional relay scheme, the proposed schemes provide two operations that involve both PA and BS, activating the beam splitting and recombining operations in turn. These schemes would benefit the system performance improvement by providing signal amplification and establishing quantum correlations. We show that the different effects of the relay schemes will cause different system performances because of the varied signal-to-noise ratio (SNR) of output fields. The system's secret key rate will be increased when equipping with the PA-BS relay scheme, because the output fields of the PA are entangled with the correlated quantum noises while input fields of the BS are superimposed, subsequently leading to the quantum noise reduction of the total output fields of relay station, while the reversed BS-PA relay scheme has little advantage over the traditional counterpart that contains only one BS in relay data postprocessing because it will not cause any SNR improvement. Moreover, the reinforced PA-PA relay scheme results in a slight improvement due to the increased SNR. These quantum relay schemes can be performed through the beam splitting, the recombining operations, and the relay data postprocessing, such that it would be suitable for secret information exchange in complex networks with intermediate stations.

Single-quadrature continuous-variable quantum key distribution

Most continuous-variable quantum key distribution schemes are based on the Gaussian modulation of coherent states followed by continuous quadrature detection using homodyne detectors. In all previous schemes, the Gaussian modulation has been carried out in conjugate quadratures thus requiring two independent modulators for their implementations. Here, we propose and experimentally test a largely simplified scheme in which the Gaussian modulation is performed in a single quadrature. The scheme is shown to be asymptotically secure against collective attacks, and considers a specific attack using asymmetric preparation and excess noise. We find that this protocol is considerably more sensitive to noise than other CVQKD schemes, as a consequence of the simplified implementation. A single-quadrature modulation approach renders the need for a costly amplitude modulator unnecessary, and thus facilitates commercialization of continuous-variable quantum key distribution, provided that the low noise requirement can be achieved.

Continuous-variable quantum key distribution under the local oscillator intensity attack with noiseless linear amplifier

An improved continuous-variable quantum key distribution (CVQKD) protocol is proposed to improve the performance of CVQKD system under the local oscillator intensity attack by using a suitable noiseless linear amplifier (NLA) at the destination. This method can enhance the efficiency of the CVQKD scheme in terms of the maximum transmission distance, no matter whether the direct or reverse reconciliation is used. Simulation results show that there is a considerable increase in the transmission distance for the NLA-based CVQKD by adjusting the values of the parameters.

Security of Continuous-Variable Quantum Key Distribution with Imperfect Phase Compensation

Phase compensation is a necessary procedure in practical application of continuous-variable quantum key distribution (CVQKD) for the reason of unavoidable phase drifts of quantum signals in quantum channel. However, the phase compensation may become imperfect in practical applications. The security of CVQKD scheme with imperfect phase compensation is investigated under realistic conditions of quantum channel and detector. In particular, a tight security bound to the phase noise of the imperfect phase compensation are derived for reverse reconciliation and realistic homodyne detection. Moreover, the phase noise is analyzed experimentally and a practical phase compensation procedure is applied to simulate the imperct processing. The simulation results show its coincidence to the security bound, and reveal the sensitivity of the security of the reverse reconciliation CVQKD protocol to the noise arising from imperfect phase compensation.

Spacetime effects on satellite-based quantum communications

We investigate the consequences of space-time being curved on space-based quantum communication protocols. We analyze tasks that require either the exchange of single photons in a certain entanglement distribution protocol or beams of light in a continuous-variable quantum key distribution scheme. We find that gravity affects the propagation of photons, therefore adding additional noise to the channel for the transmission of information. The effects could be measured with current technology.

Geometrical analysis of physically allowed quantum cloning transformations for quantum cryptography

The security of quantum key distribution (QKD) relies on the no-cloning theorem, which allows no to copy perfectly a quantum system. An eavesdropping activity on the quantum channel perturbs the state of the quantum states, which results in noise at the receiver. The physical layer detection of the eavesdropping activity of the quantum channel requires tomography, which is intractable in experiment. An adequate and equivalent answer for the problem can be proposed through the logical layer. We propose an efficient algorithmical tool to study the eavesdropping activity on the quantum channel and characterize the properties of a quantum cloning-based attack for DV and CVQKD protocols. The physically allowed quantum cloning transformations on a quantum system can be described in terms of information geometry. We propose a computational geometrical method to analyze the cloning activity on the quantum channel and to characterize the noise properties. The security analysis studies the DV (discrete variable) and CV (continuous variable) QKD schemes through the four-state (BB84) and six-state DVQKD protocols and the two-way CVQKD protocol. The proposed geometrical method provides a useful tool to analyze the most powerful attacks against quantum cryptography and the effects of the physically allowed quantum cloning transformations.

Single-photon-detection attack on the phase-coding continuous-variable quantum cryptography

The phase-coding quantum cryptographic scheme using the homodyne detection and weak coherent state [Hirano et al.,Phys. Rev. A 68, 042331 (2003)] provides the simplest continuous-variable quantum key distribution scheme from the experimental side. However, the inherent loss of the practical system will not only increase the bit error rate (BER) but also affect the security of the final key. In this paper, we propose a single-photon-detection attack, and then the security of the final key will be compromised in some parameter regimes. Our results show that the BER induced by Eve can be lower than the inherent BER induced by the loss of the system in some parameter regimes. Furthermore, our attack gives the maximal communication distance of this scheme for given experimental parameters.

Security analysis of continuous-variable quantum key distribution scheme

In this paper security of the quantum key distribution scheme using correlations of continuous variable Einstein–Podolsky–Rosen (EPR) pairs is investigated. A new approach for calculating the secret information rate ΔI is proposed by using the Shannon information theory. Employing an available parameter F which is associated with the entanglement of the EPR pairs, one can detect easily the eavesdropping. Results show that the proposed scheme is secure against individual beam splitter attack strategy with a proper squeeze parameter.

Cloning and cryptography with quantum continuous variables

The cloning of quantum variables with continuous spectra is investigated. We define a Gaussian 1-to-2 cloning machine that copies equally well two conjugate variables such as position and momentum or the two quadrature components of a light mode. The resulting cloning fidelity for coherent states, namely F = 2/3, is shown to be optimal. An asymmetric version of this Gaussian cloner is then used to assess the security of a continuous-variable quantum key distribution scheme that allows two remote parties to share a Gaussian key. The information versus disturbance tradeoff underlying this continuous quantum cryptographic scheme is then analyzed for the optimal individual attack. Methods to convert the resulting Gaussian keys into secret key bits are also studied. Finally, the extension of the Gaussian cloner to optimal N-to-M continuous cloners is discussed, and it is shown how to implement these cloners for light modes using a phase-insensitive optical amplifier and beam splitters. In addition, a phase-conjugate input cloner is defined, yielding M clones and M' anticlones from N replicas of a coherent state and N' replicas of its phase-conjugate (with M' - M = N' - N). This novel kind of cloners is shown to outperform the standard N-to-M cloners in some cases.