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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Continuous Variable Quantum Cryptography: Post-Selection with Thermal Noise

Syed M. Assad, Daniel J. Alton, Thomas Symul, Ping Koy Lam, Christian Weedbrook, Timothy C. Ralph

Published Jun 1, 2007• 2 citations
Publisher

Abstract

Continuous variable quantum key distribution (CVQKD) utilizes bright beams to establish secure communication between two parties via an optical quantum channel such as an optical fiber. One of the main protocols that are practical and promising involves a selection process after the transmission of quantum states, called post-selection based CVQKD. The security of CVQKD using post-selection has been investigated both theoretically (Silberhorn et al., 2002) and demonstrated experimentally (Lance et al., 2002). However, it was subject to one fundamental assumption, namely that the quantum channel must have strictly zero excess noise (i.e. it is shot-noise-limited). In reality, nonlinearities in optical fibers and classical noise of laser beams commonly introduce Gaussian excess noise. The authors considered an eavesdropping attack based on entangling cloner setup where the channel was replaced with a lossless and shot-noise-limited line and remain undetectible. Two-way reconciliation was considered in the security analysis.The paper presents experiments based on the protocol developed by the authors.

DOI
10.1109/cleoe-iqec.2007.4386770

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Continuous variable quantum key distribution (CVQKD) utilizes bright beams to establish secure communication between two parties via an optical quantum channel such as an optical fiber. One of the main protocols that are practical and promising involves a selection process after the transmission of quantum states, called post-selection based CVQKD. The security of CVQKD using post-selection has been investigated both theoretically (Silberhorn et al., 2002) and demonstrated experimentally (Lance et al., 2002). However, it was subject to one fundamental assumption, namely that the quantum channel must have strictly zero excess noise (i.e. it is shot-noise-limited). In reality, nonlinearities in optical fibers and classical noise of laser beams commonly introduce Gaussian excess noise. The authors considered an eavesdropping attack based on entangling cloner setup where the channel was replaced with a lossless and shot-noise-limited line and remain undetectible. Two-way reconciliation was considered in the security analysis.The paper presents experiments based on the protocol developed by the authors.
Abstract Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) offers a practical path to quantum-secured communication owing to its compatibility with existing optical fibre networks and use of mature security proofs. Achieving high secret key rates in real-time systems, however, requires post-processing schemes that are both information-theoretically efficient and computationally scalable. In previous experimental work 1 , we have demonstrated record real-time key rates using a one-round sliced reconciliation scheme with guard-band post-selection. Here, we present the corresponding theoretical framework and provide an asymptotic security analysis that considers arbitrary collective attacks, a much broader class of attacks than the usually assumed Gaussian collective attacks. The security analysis applies the entropic continuity of quantum channels justified by a quantum channel estimation procedure. In conditions of high noise, our scheme uses 500 times less classical communication than multidimensional reconciliation.
In realistic continuous variable quantum key distribution protocols, an eavesdropper may exploit the additional Gaussian noise generated during transmission to mask her presence. We present a theoretical framework for a post-selection based protocol which explicitly takes into account excess Gaussian noise. We derive a quantitative expression of the secret key rates based on the Levitin and Holevo bounds. We experimentally demonstrate that the post-selection based scheme is still secure against both individual and collective Gaussian attacks in the presence of this excess noise.
In realistic continuous variable quantum key distribution protocols, an eavesdropper may exploit the additional Gaussian noise generated during transmission to mask her presence. We present a theoretical framework for a post-selection based protocol which explicitly takes into account excess Gaussian noise. We derive a quantitative expression of the secret key rates based on the Levitin and Holevo bounds. We experimentally demonstrate that the post-selection based scheme is still secure against both individual and collective Gaussian attacks in the presence of this excess noise.
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.
The performance of a continuous-variable quantum key distribution (CVQKD) protocol depends on the efficiency of the post-processing of measurement results. The post-processing methods extract statistical information from the raw data, establish the mutual knowledge between the parties, and produce a final key that provides absolute security. The post-processing phase is a bottleneck in CVQKD with crucial importance to the efficiency and protocol attributes. Post-processing uses the raw data of the parties generated by the quantum-level transmission and a classical authenticated channel to generate a secret key between the parties. The current reconciliation procedures require high-complexity coding with moderate resulting efficiency. Here we define an optimization method for post-processing in continuous-variable quantum key distribution. The reconciliation method achieves additive Gaussian noise on the random secret for arbitrarily low dimensional blocks. The model consumes all information from the raw data blocks to provide maximal efficiency and security via standard operations. The results can be realized by generic Gaussian coding schemes, allowing an easily implementation for experimental CVQKD protocols.
In realistic continuous-variable quantum key distribution protocols, an eavesdropper may exploit the additional Gaussian noise generated during transmission to mask her presence. We present a theoretical framework for a post-selection-based protocol which explicitly takes into account excess Gaussian noise. We derive a quantitative expression of the secret key rates based on the Levitin and Holevo bounds. We experimentally demonstrate that the post-selection-based scheme is still secure against both individual and collective Gaussian attacks in the presence of this excess noise.