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arXiv:2308.11320

Continuous Variable Quantum Key Distribution in Multiple-Input Multiple-Output Settings

Shradhanjali Sahu, Ahmed Q. Lawey, Mohsen Razavi

Published Aug 22, 2023• 1 citation
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Abstract

We investigate quantum key distribution (QKD) in optical multiple-input-multiple-output (MIMO) settings. Such settings can prove useful in dealing with harsh channel conditions as in, e.g., satellite-based QKD. We study a $2\times2$ setting for continuous variable (CV) QKD with Gaussian encoding and heterodyne detection and reverse reconciliation. We present our key rate analysis for this system and compare it with single-mode and multiplexed CV QKD scenarios. We show that we can achieve multiplexing gain using multiple transmitters and receivers even if there is some crosstalk between the two channels. In certain cases, when there is nonzero correlated excess noise in the two received signals, we can even surpass the multiplexing gain.

DOI
10.48550/arxiv.2308.11320

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We investigate quantum key distribution (QKD) in optical multiple-input-multiple-output (MIMO) settings. Such settings can prove useful in dealing with harsh channel conditions as in, e.g., satellite-based QKD. We study a 2×22\times22×2 setting for continuous variable (CV) QKD with Gaussian encoding and heterodyne detection and reverse reconciliation. We present our key rate analysis for this system and compare it with single-mode and multiplexed CV QKD scenarios. We show that we can achieve multiplexing gain using multiple transmitters and receivers even if there is some crosstalk between the two channels. In certain cases, when there is nonzero correlated excess noise in the two received signals, we can even surpass the multiplexing gain.
Continuous-variable (CV) quantum key distribution (QKD) in optical multiple-antenna settings can be useful in harsh channel conditions despite the presence of cross-talk between channels. This is, for instance, relevant to satellite-based QKD with multiple transmitting antennas on the satellite and multiple ground stations. In such a case, each transmitter independently exchanges data with its intended receiver, where the received signal may contain components from other transmitters. In particular, for a 2×2 multiple-input multiple-output (MIMO) setting with Gaussian encoding and heterodyne detection, preliminary key rate analysis has recently been presented and compared with single-mode and multiplexed CV-QKD scenarios. In this work, we study the effect of different MIMO channels on the performance by accounting for the cross-talk parameter in slow fading channels.
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.
We present novel one-way and two-way continuous-variable quantum key distribution frameworks integrating multiple-input multiple-output (MIMO) and free-space optical systems to enhance secret key rates (SKRs) and extend transmission distance between the legitimate transceiver pair. Our models are subjected to an eavesdropper employing Gaussian collective attacks, and the receiver using homodyne detection for secret key reception. Novel expressions for the SKRs for both frameworks are computed, and asymptotic results demonstrate that both the SKR gains from employing MIMO and the two-way protocol are proportional to half the MIMO channels.
With the vastly growing need for secure communication, quantum key distribution (QKD) has been developed to provide high security for communications against potential attacks from the fast-developing quantum computers. Among different QKD protocols, continuous variable (CV-) QKD employing Gaussian modulated coherent states has been promising for its complete security proof and its compatibility with current communication systems in implementation with homodyne or heterodyne detection. Since satellite communication has been more and more important in developing global communication networks, there have been concerns about the security in satellite communication and how we should evaluate the security of CV-QKD in such scenarios. To better analyse the secure key rate (SKR) in this case, in this invited paper we investigate the CV-QKD SKR lower bounds under realistic assumptions over a satellite-to-satellite channel. We also investigate the eavesdropper's best strategy to apply in these scenarios. We demonstrate that for these channel conditions with well-chosen carrier centre frequency and receiver aperture size, based on channel parameters, we can optimize SKR correspondingly. The proposed satellite-based QKD system provides high security level for the coming 5G and beyond networks, the Internet of things, self-driving cars, and other fast-developing applications.
Currently, quantum key distribution (QKD) using continuous variable (CV) technology has only been demonstrated over short-range terrestrial links. Here, we attempt to answer whether CV-QKD over the much longer satellite-to-Earth channel is feasible. To this end, we first review the concepts and technologies that will enable CV-QKD over the satellite-to-Earth channels. We then consider, in the infinite key limit, the simplest-to-deploy QKD protocols, the coherent state (CS) QKD protocol with homodyne detection and the CS-QKD protocol with heterodyne detection. We then focus on the CS-QKD protocol with heterodyne detection in the pragmatic setting of finite keys, where complete security against general attacks is known. We pay particular attention to the relevant noise terms in the satellite-to-Earth channel and their impact on the secret key rates. In system set-ups where diffraction dominates losses, we find that the main components of the total excess noise are the intensity fluctuations due to scintillation, and the time-of-arrival fluctuations between signal and local oscillator. We conclude that for a wide range of pragmatic system models, CS-QKD with information-theoretic security in the satellite-to-Earth channel is feasible.
In this paper, we propose a quantum code division multiple access (q-CDMA) based continuous-variable quantum key distribution (CV-QKD) system. In the proposed system, the quantum states of two senders (Alice1,2) are chaotically encoded through chaotic phase shifters and then transmitted over a quantum channel. At the receiver, the quantum states are decoded via chaos synchronization to separate the quantum states sent by the different senders and received by the two receivers (Bob1,2) separately. We characterize the input-output relation of the quadrature between the two senders and receivers and then analyze the secret key rate (SKR) of the q-CDMA-based CV-QKD system. Our numerical results reveal that the q-CDMA approach can significantly enhance the SKR for both users when compared to the single-user case without the q-CDMA approach.