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arXiv:quant-ph/0506193 · Physical Review A

Security of continuous-variable quantum cryptography using coherent states: Decline of postselection advantage

Ryo Namiki, Takuya Hirano

Published Aug 5, 2005• 20 citations
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Abstract

We investigate the security of continuous-variable (CV) quantum key distribution (QKD) using coherent states in the presence of quadrature excess noise. We consider an eavesdropping attack that uses a linear amplifier and a beam splitter. This attack makes a link between the beam-splitting attack and the intercept-resend attack (classical teleportation attack). We also show how postselection loses its efficiency in a realistic channel.

DOI
10.1103/physreva.72.024301

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We investigate the security of continuous-variable (CV) quantum key distribution (QKD) using coherent states in the presence of quadrature excess noise. We consider an eavesdropping attack that uses a linear amplifier and a beam splitter. This attack makes a link between the beam-splitting attack and the intercept-resend attack (classical teleportation attack). We also show how postselection loses its efficiency in a realistic channel.
In this Letter, first, we investigate the security of a continuous-variable quantum cryptographic scheme with a postselection process against individual beam splitting attack. It is shown that the scheme can be secure in the presence of the transmission loss owing to the postselection. Second, we provide a loss limit for continuous-variable quantum cryptography using coherent states taking into account excess Gaussian noise on quadrature distribution. Since the excess noise is reduced by the loss mechanism, a realistic intercept-resend attack which makes a Gaussian mixture of coherent states gives a loss limit in the presence of any excess Gaussian noise.
We demonstrate that secure quantum key distribution systems based on continuous variable implementations can operate beyond the apparent 3 dB loss limit that is implied by the beam splitting attack. The loss limit was established for standard minimum uncertainty states such as coherent states. We show that, by an appropriate postselection mechanism, we can enter a region where Eve's knowledge on Alice's key falls behind the information shared between Alice and Bob, even in the presence of substantial losses.
Quantum Key Distribution (QKD) provides a method for securely sharing a secret key between two distant parties, Alice and Bob, by leveraging the principles of quantum mechanics. This thesis focuses on Continuous-Variable (CV) QKD, a variant of QKD where information is encoded in the quadrature components of coherent light states, allowing for efficient and cost-effective detection using homodyne or heterodyne receivers. The thesis is divided into three main parts: an introduction to quantum cryptography concepts, the presentation of a CV-QKD protocol, and a detailed security proof of the protocol against different types of attacks. The security proof considers both finite and infinite symbol transmission and tackles various eavesdropping attacks, including individual, collective, and coherent attacks. The use of Gaussian states and operations provides a promising approach to enhance QKD security, particularly in the context of practical quantum cryptography. The final sections provide a mathematical framework for the optimization of secure key rates and strategies for addressing the photon-number cutoff assumption in practical implementations.
We extend the security analysis of continuous variable quantum-key-distribution protocols using a family of post selection schemes to account for arbitrary eavesdropping attacks. We show that the postselection protocol is equivalent to a virtual entanglement-based protocol including a distillation stage. We introduce a particular `Gaussian' post selection and demonstrate that the security can be calculated using only experimentally accessible quantities. Finally, we explicitly evaluate the performance for the case of a noisy Gaussian channel in the limit of unbounded key length and find improvements over all pre-existing continuous variable protocols in realistic regimes.
Quantum continuous variables (CV) have been explored as an alternative to qubits for quantum key distribution (QKD). More specifically, protocols using coherent states and homodyne or heterodyne measurements have been proposed and experimentally demonstrated (Grosshans et al., 2003). Relying on technologies allowing much higher rates than allowed by the single photon detectors used in qubit based QKD, those protocols are the only ones which could allow key rates in the GHz range in the foreseeable future. Furthermore, their security proofs have recently been extendend to generic attacks in the case of gaussian modulation. However, to our knowledge, all security analyses up to know have implicitely assumed Bob's measurement setup to use a homo- or heterodyne detection with an external classical phase reference, while the experimental realizations use a lightbeam for this role. This beam doesn't carry any information useful to the spy, and any attack on its phase could equally be carried on the signal beam. However, the intensity of this beam is used in experimental implementations to calibrate the quantum noise level. This calibration is then used to determine the channel gain, which is an important parameter of Eve's attack. We show that this allows Eve to implement an intercepte resend attack forbiding QKD as soon as the losses are above 3dB. We also give simple countermeasures to this new class of attacks.
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.