Information Reconciliation (IR) in QKD is a fundamental step in ensuring Alice and Bob share identical set of bits (reconciled key). IR could be done by one-way or two-way channel coding using an auxiliary public authenticated channel to send parities to correct the actual labels so that the sample labels at Alice and Bob match. We assume that communication is performed through an Optical Wireless (OW) or Free Space Optics (FSO) channel, which effects the received signal by a stochastic fading due to jitter in pointing. The effect is that the received samples do not match with the transmitted ones, this is the reason why IR is necessary in such a system. In a previous work, we analyzed the system performance over FSO channel, uncovering the dependence between performance and system parameters such as fading variance or the telescope gain. In this paper we want to study the overall performance and try to obtain optimal values for the parameters that influence the sign error probability.
Information Reconciliation (IR) in QKD is a fundamental step in ensuring Alice and Bob share identical set of bits (reconciled key). IR could be done by one-way or two-way channel coding using an auxiliary public authenticated channel to send parities to correct the actual labels so that the sample labels at Alice and Bob match. We assume that communication is performed through an Optical Wireless (OW) or Free Space Optics (FSO) channel, which effects the received signal by a stochastic fading due to jitter in pointing. The effect is that the received samples do not match with the transmitted ones, this is the reason why IR is necessary in such a system. In a previous work, we analyzed the system performance over FSO channel, uncovering the dependence between performance and system parameters such as fading variance or the telescope gain. In this paper we want to study the overall performance and try to obtain optimal values for the parameters that influence the sign error probability.
Quantum Key Distribution (QKD) is a communication method which exchanges secret keys using cryptographic protocols involving elements from quantum science. Continuous Variable (CV) QKD is a method to implement key exchange using sampling of Gaussian signals. Reconciliation in CV-QKD is fundamentally realized via coding of the Alice or Bob binary labels of the Gaussian samples using either one-way or interactive communications between the parties, Alice and Bob, over a public authenticated channel. We assume that the communication is performed through an Optical Wireless (OW) or Free Space Optics (FSO) channel. In that case the received signal suffers from stochastic fading due to pointing jitter or atmospheric turbulence. As a result of the channel fading and noise Alice and Bob Gaussian samples will not match. Information Reconciliation (IR) is the phase of the CV-QKD protocol that makes sure that Alice and Bob agree on a common and identical labeling of their samples, i.e. agree on a common stream of bits that we denote as “reconciled key.” The information reconciliation in CV-QKD could be done by one-way or two-way channel coding to correct the actual labels so that they do match. To do so Bob generates a sequence of parity bits using a systematic code. These bits are sent to Alice over an authenticated public channel. Alice then uses her own sequence of labels she obtains after quantization with the redundancy provided by Bob to recover Bob’s binary sequence. In this work we analyze the problem of information reconciliation for continuous variable quantum key distribution over a free space optics channel.
Continuous-variable quantum key distribution (CV-QKD) has been proposed as a method for securely exchanging keys to protect against the security concerns caused by potential advancements in quantum computing. In addition to optical fibre transmission, the free-space optical (FSO) channel is an interesting channel for CV-QKD, as it is possible to share keys over this channel wirelessly. The instability of the FSO channel caused by turbulence-induced fading, however, can cause a degradation in the system's performance. One of the most important aspects of CV-QKD is the reconciliation step, which significantly impacts the performance of the CV-QKD system. Hence, rate-adaptive reconciliation is necessary for CV-QKD over FSO to combat the fluctuations in the channel and improve secret key rates (SKRs). Therefore, in this paper, we simulate the impact of discrete modulation on the reconciliation efficiency and consider the use ofd-dimensional reconciliation withd>8to mitigate this impact, improving reconciliation efficiencies by up to 3.4%. We validate our results by experimentally demonstrating CV-QKD over a turbulent FSO link and demonstrate SKR gains by up to 165%. Furthermore, we optimise the reconciliation efficiency for FSO links, achieving additional SKR gains of up to 7.6%.
This paper studies a multiple-input multiple-output (MIMO) free-space optical (FSO) communication system employing continuous-variable quantum key distribution (CV-QKD), with the goal to support secret key transmission between two legitimate users, Alice and Bob. All involved wireless channels are subjected to atmospheric turbulence leading to beam spreading, pointing error, and turbulence-induced fading, which along with the presence of hybrid quantum noise negatively impact secret key exchange. Furthermore, the legitimate MIMO FSO system faces the threat of compromise from an eavesdropper, Eve, employing a collective Gaussian attack to intercept the secret key exchange. Novel one- and two-way protocols for enhancing the security of the transmitted keys are proposed. To this end, the transmissivity of the FSO channels is mathematically formulated and bounds on the mutual information between the transmitted and received coherent states are obtained, which are then used for deriving novel expressions for the secret key rates (SKRs) for both one- and two-way protocols. The presented numerical results corroborate the proposed analytical secrecy framework, quantifying the SKR gains obtained by employing MIMO and the two-way protocol for FSO CV-QKD systems.
This paper is focused on the problem of Information Reconciliation (IR) for continuous variable Quantum Key Distribution (QKD). The main problem is quantization and assignment of labels to the samples of the Gaussian variables observed at Alice and Bob. Trouble is that most of the samples, assuming that the Gaussian variable is zero mean which is de-facto the case, tend to have small magnitudes and are easily disturbed by noise. Transmission over longer and longer distances increase the losses corresponding to a lower effective Signal to Noise Ratio (SNR) exasperating the problem. In previous work [1], [2] we approach the IR problem in a fundamentally different way than how it is addressed in published literature. At very low SNR, one can focus exclusively on the sign of the Gaussian samples at Alice and Bob and perform Reverse Reconciliation (RR) on sign of the samples given their quantized magnitudes as side information Alice and Bob share in the open. In this paper we demonstrate that the weighted sum capacity of the Binary Symmetric Channels (BSCs) derived from magnitude dependent sign error probabilities of the Gaussian samples shared between Alice and Bob approaches the mutual information between Alice and Bob at very low SNR regimes. Thus, when SNR is very low, one could just as well ignore any common randomness that may be obtained from magnitude of the Gaussian samples and focus exclusively on their sign. The caveat is, to get close to this mutual information, Unequal Error Protection (UEP) must be employed based on magnitude of the observed samples at Bob in RR.
In this paper, the free-space optics (FSO) quantum backscatter communication (QBC), inspired by the quantum illumination concept, is described. In this method, the transmitter generates entangled photon pairs. The signal photon is transmitted in the direction of the modulated retro reflector (MRR) or the tag antenna, and the idler photon is moved to the receiver. The MRR communicates by modulating the received photon and retro-reflecting it back to the receiver. QBC could provide performance improvement in comparison to conventional backscatter communications. In this work, a mathematical model of the FSO QBC systems is derived. In an FSO system, the pointing direction jitter is a stochastic process that reduces the communication performance. In this paper, optimization of FSO QBC performance is proposed to minimize the error probability. This could be done by adapting the telescope gain to jitter a standard deviation amplitude.
The distribution of symmetric keys over optical networks is possible through the implementation of continuous variables quantum key distribution (CV-QKD) systems. Despite the rate of key extraction in CV-QKD being maximized for Gaussian modulation (GM), its practical implementation is demanding due to the finite extinction ratio of the electro-optic modulators. The use of discrete modulation (DM) allows for a simpler practical implementation. Provided that higher-order constellations can be used, DM can approximate the performances of GM. Higher-order DM has been shown to be feasible experimentally in CV-QKD. Notwithstanding, such implementations are usually obtained in offline without applying all the post-processing steps, particularly the information reconciliation, turning the validity of the results dependent on a null frame error rate after information reconciliation. Besides that, a fixed value is typically assumed for the reconciliation efficiency value, being the modulation variance optimized under such assumptions. This disregarding the dependency of the reconciliation efficiency parameter on the method for information reconciliation and on the modulation variance. In this work we study the impact that such assumptions have on the optimization of the modulation variance in a CV-QKD system using probabilistic shaped higher-order DM. Moreover, we analyse how optimizing the modulation variance can affect the extraction key rates of symmetric keys at the output of the CV-QKD system. Besides the assumptions of null frame error rate and of the reconciliation efficiency, we study how different code rates may also affect the optimization of the modulation variance. This considering M-symbol quadrature amplitude modulation and multidimensional reconciliation.