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arXiv:2009.02665

Phase noise-immune unconditionally secured classical key distribution using doubly coupled Mach-Zehnder interferometer

Byoung Seung HAM

Published Sep 6, 2020• 0 citations
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Abstract

Recently, new physics for unconditional security in a classical key distribution (USCKD) in a frame of a double Mach-Zehnder interferometer has been proposed and demonstrated as a proof of principle, where the unconditional security is unaffected by the no-cloning theorem of quantum key distribution protocols. Due to environmental phase fluctuations caused by temperature variations, atmospheric turbulences, or mechanical vibrations, active phase locking seems to be necessary for the two-channel transmission layout of USCKD. Here, the two-channel layout of USCKD is demonstrated to be an environmental noise-immune protocol especially for free space optical links, where the transmission distance is potentially unlimited if random phase noises are considered.

DOI
10.48550/arxiv.2009.02665

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Recently, new physics for unconditional security in a classical key distribution (USCKD) in a frame of a double Mach-Zehnder interferometer has been proposed and demonstrated as a proof of principle, where the unconditional security is unaffected by the no-cloning theorem of quantum key distribution protocols. Due to environmental phase fluctuations caused by temperature variations, atmospheric turbulences, or mechanical vibrations, active phase locking seems to be necessary for the two-channel transmission layout of USCKD. Here, the two-channel layout of USCKD is demonstrated to be an environmental noise-immune protocol especially for free space optical links, where the transmission distance is potentially unlimited if random phase noises are considered.
Recently, new physics for unconditional security in a classical key distribution (USCKD) has been proposed and demonstrated in a frame of a double Mach-Zehnder interferometer (MZI) as a proof of principle, where the unconditional security is rooted in MZI channel superposition. Due to environmental phase noise caused by temperature variations, atmospheric turbulences, and mechanical vibrations, free-space optical links have been severely challenged for both classical and quantum communications. Here, the double MZI scheme of USCKD is analyzed for greatly subdued environment-caused phase noise via double unitary transformation, resulting in potential applications of free-space optical links, where the free-space optical link has been a major research area from fundamental physics of atomic clock and quantum key distribution to potential applications of geodesy, navigation, and MIMO technologies in mobile communications systems.
The unconditionally secured classical key distribution (USCKD) has been presented for an air turbulent free-space optical link. Even in the noisy air channels, the USCKD has shown nearly unconditionally secure communications in data transmission owing to double unitary transformation in a round-trip scheme, where the absolute phase noises in both air channels are replaced by a relative phase noise between them. Unlike classical cryptography, USCKD is based on basis randomness and thus resistant to the attack of quantum computers. Unlike quantum key distributions, USCKD is free from nonclassical light requirement such as a single photon, which is sensitive to quantum loopholes of channel loss and imperfect detectors.
So far, unconditional security in key distribution processes has been confined to quantum key distribution (QKD) protocols based on the no-cloning theorem of nonorthogonal bases. Recently, a completely different approach, the unconditionally secured classical key distribution (USCKD), has been proposed for unconditional security in the purely classical regime. Unlike QKD, both classical channels and orthogonal bases are key ingredients in USCKD, where unconditional security is provided by deterministic randomness via path superposition-based reversible unitary transformations in a coupled Mach-Zehnder interferometer. Here, the first experimental demonstration of the USCKD protocol is presented.
Over decades quantum cryptography has been intensively studied for unconditionally secured key distribution in a quantum regime. Due to the quantum loopholes caused by imperfect single photon detectors and/or lossy quantum channels, however, the quantum cryptography is practically inefficient and even vulnerable to eavesdropping. Here, a method of unconditionally secured key distribution potentially compatible with current fiber-optic communications networks is proposed in a classical regime for high-speed optical backbone networks. The unconditional security is due to the quantum superposition-caused measurement indistinguishability between paired transmission channels and its unitary transformation resulting in deterministic randomness corresponding to the no-cloning theorem in a quantum key distribution protocol.
As a practical version of twin-field quantum key distribution (TF-QKD), phase-matching quantum key distribution (PM-QKD) is able to surpass the linear bound without quantum repeaters. Implementing PM-QKD through free space can guarantee two parties to share unconditionally secure keys between ground stations and mobile platforms. However, atmospheric turbulence decreases the free-space secure key rate as the result of fluctuations of transmittances caused by it. This paper includes two works we do. First, for generality, we derive the secure key rate formula of 4-intensity PM-QKD based on asymmetric channel transmittances. Second, we numerically simulate the performance of PM-QKD in free space and ideal circumstance to study the effect of the atmospheric turbulence.
Continuous-variable quantum key distribution is a practical application of quantum information theory that is aimed at generation of secret cryptographic key between two remote trusted parties and that uses multi-photon quantum states as carriers of key bits. Remote parties share the secret key via a quantum channel, that presumably is under control of of an eavesdropper, and which properties must be taken into account in the security analysis. Well-studied fiber-optical quantum channels commonly possess stable transmittance and low noise levels, while free-space channels represent a simpler, less demanding and more flexible alternative, but suffer from atmospheric effects such as turbulence that in particular causes a non-uniform transmittance distribution referred to as fading. Nonetheless free-space channels, providing an unobstructed line-of-sight, are more apt for short, mid-range and potentially long-range (using satellites) communication and will play an important role in the future development and implementation of QKD networks. It was previously theoretically shown that coherent-state CV QKD should be in principle possible to implement over a free-space fading channel, but strong transmittance fluctuations result in the significant modulation-dependent channel excess noise. In this regime the post-selection of highly transmitting sub-channels may be needed, which can even restore the security of the protocol in the strongly turbulent channels. We now report the first proof-of-principle experimental test of coherent state CV QKD protocol using different levels Gaussian modulation over a mid-range (1.6-kilometer long) free-space atmospheric quantum channel. The transmittance of the link was characterized using intensity measurements for the reference but channel estimation using the modulated coherent states was also studied. We consider security against Gaussian collective attacks, that were shown to be optimal against CV QKD protocols . We assumed a general entangling cloner collective attack (modeled using data obtained from the state measurement results on both trusted sides of the protocol), that allows to purify the noise added in the quantum channel . Our security analysis of coherent-state protocol also took into account the effect of imperfect channel estimation, limited post-processing efficiency and finite data ensemble size on the performance of the protocol. In this regime we observe the positive key rate even without the need of applying post-selection. We show the positive improvement of the key rate with increase of the modulation variance, still remaining low enough to tolerate the transmittance fluctuations. The obtained results show that coherent-state CV QKD protocol that uses real free-space atmospheric channel can withstand negative influence of transmittance fluctuations, limited post-processing efficiency, imperfect channel estimation and other finite-size effects, and be successfully implemented. Our result paves the way to the full-scale implementation of the CV QKD in real free-space channels at mid-range distances.