Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1004.3345 · Physical Review Letters

Quantum Cryptography Approaching the Classical Limit

Christian Weedbrook, Stefano Pirandola, Seth Lloyd, Timothy C. Ralph

Published Sep 8, 2010• 144 citations
arXivHTMLPDF

Abstract

We consider the security of continuous-variable quantum cryptography as we approach the classical limit, i.e., when the unknown preparation noise at the sender's station becomes significantly noisy or thermal (even by as much as 10(4) times greater than the variance of the vacuum mode). We show that, provided the channel transmission losses do not exceed 50%, the security of quantum cryptography is not dependent on the channel transmission, and is therefore incredibly robust against significant amounts of excess preparation noise. We extend these results to consider for the first time quantum cryptography at wavelengths considerably longer than optical and find that regions of security still exist all the way down to the microwave.

DOI
10.1103/physrevlett.105.110501

Related papers

Role of anti-squeezing noise in continuous-variable quantum cryptography

Vladyslav C. Usenko, Akash nag Oruganti

Quadrature squeezing is known to enforce continuous-variable quantum cryptography. However, in practice, squeezed states are never generated perfectly and always contain anti-squeezing quadrature noise concerned with losses in the optical parametric oscillator sources. We therefore address the role of anti-squeezing noise in continuous-variable quantum cryptography over attenuating and noisy quantum channels. We first assume that anti-squeezing noise is trusted, hence, out of control of a potential eavesdropper, capable of collective attacks. In this regime, anti-squeezing noise can be even helpful by tightening the bound on the information leakage in the quantum channel. Moreover, in the asymptotic limit of infinitely strong trusted anti-squeezing noise, the bound can be expressed analytically. We then assume that anti-squeezing noise is controlled by an eavesdropper, thus being a side-channel in the source implementation. In this regime, the anti-squeezing noise leads to the security break both in direct and reverse reconciliation scenarios. We compare the bounds on the untrusted phase-sensitive anti-squeezing noise to the typical phase-insensitive channel excess noise and show that protocols are more robust to the anti-squeezing noise, while the presence of such noise makes the protocol more sensitive to the noise in the main quantum channel. The obtained results reveal the important role of anti-squeezing noise in continuous-variable quantum cryptography and suggest the need of pure squeezed state preparation in the case of untrusted sources.

International Conference on Telecommunications and Signal Processing (TSP)•Jul 1, 2020•2 citations

Feasibility of continuous-variable quantum key distribution with noisy coherent states

Vladyslav C. Usenko, Radim Filip

We address security of the quantum key distribution scheme based on the noisy modulation of coherent states and investigate how it is robust against noise in the modulation regardless of the particular technical implementation. As the trusted preparation noise is shown to be security breaking even for purely lossy channels, we reveal the essential difference between two types of trusted noise, namely sender-side preparation noise and receiver-side detection noise, the latter being security preserving. We consider the method of sender-side state purification to compensate the preparation noise and show its applicability in the realistic conditions of channel loss, untrusted channel excess noise, and trusted detection noise. We show that purification makes the scheme robust to the preparation noise (i.e., even the arbitrary noisy coherent states can in principle be used for the purpose of quantum key distribution). We also take into account the effect of realistic reconciliation and show that the purification method is still efficient in this case up to a limited value of preparation noise.

arXiv:0904.1694•Physical Review A•Feb 19, 2010•105 citations

On a solution to the problem of ensuring the security of quantum cryptography for an infinite communication channel

S. N. Molotkov

Quantum cryptography involves the fundamental question of the existence of secure protocols of quantum key distribution at any length of a communication channel (at any losses in it). A remarkable feature and novelty of the proposed protocol is that it ensures dual control; first, the intensity of a reference (intense) quantum state is controlled classically before the comparison (measurement) of coherent states from different time windows, and, second, the loss of coherence of a state is detected by interference measurements of an information quantum state and the reference quantum state tested against the conservation of the intensity. Thus, this is the only existing protocol stable to any losses in the communication channel. The length of the communication channel is limited only by dark noise in detectors.

Journal of Experimental and Theoretical Physics Letters•Aug 1, 2011•3 citations

Practical Limitation for Continuous-Variable Quantum Cryptography using Coherent States

Ryo Namiki, Takuya Hirano

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.

arXiv:quant-ph/0403115•Physical Review Letters•Mar 16, 2004•71 citations

Two-way quantum cryptography with continuous variables: unconditional security and performances at different wavelengths

Carlo Ottaviani, Stefano Pirandola

In first place we analysed the security of two-way QKD against coherent attacks achieving unconditional security in all encoding/decoding configurations. In second place we studied the security, at different wavelengths, of two-way thermal QKD finding a robust threshold in reverse reconciliation, improving the security distances for continuous variable quantum cryptography in the infrared.

Research in Optical Sciences•Jan 1, 2014•0 citations

Continuous-variable quantum key distribution using thermal states

Christian Weedbrook, Stefano Pirandola, Timothy C. Ralph

We consider the security of continuous-variable quantum key distribution using thermal (or noisy) Gaussian resource states. Specifically, we analyze this against collective Gaussian attacks using direct and reverse reconciliation where both protocols use either homodyne or heterodyne detection. We show that in the case of direct reconciliation with heterodyne detection, an improved robustness to channel noise is achieved when large amounts of preparation noise is added, as compared to the case when no preparation noise is added. We also consider the theoretical limit of infinite preparation noise and show a secure key can still be achieved in this limit provided the channel noise is less than the preparation noise. Finally, we consider the security of quantum key distribution at various electromagnetic wavelengths and derive an upper bound related to an entanglement-breaking eavesdropping attack and discuss the feasibility of microwave quantum key distribution.

arXiv:1110.4617•Physical Review A•Aug 17, 2012•140 citations
We consider the security of continuous-variable quantum cryptography as we approach the classical limit, i.e., when the unknown preparation noise at the sender's station becomes significantly noisy or thermal (even by as much as 10(4) times greater than the variance of the vacuum mode). We show that, provided the channel transmission losses do not exceed 50%, the security of quantum cryptography is not dependent on the channel transmission, and is therefore incredibly robust against significant amounts of excess preparation noise. We extend these results to consider for the first time quantum cryptography at wavelengths considerably longer than optical and find that regions of security still exist all the way down to the microwave.
Quadrature squeezing is known to enforce continuous-variable quantum cryptography. However, in practice, squeezed states are never generated perfectly and always contain anti-squeezing quadrature noise concerned with losses in the optical parametric oscillator sources. We therefore address the role of anti-squeezing noise in continuous-variable quantum cryptography over attenuating and noisy quantum channels. We first assume that anti-squeezing noise is trusted, hence, out of control of a potential eavesdropper, capable of collective attacks. In this regime, anti-squeezing noise can be even helpful by tightening the bound on the information leakage in the quantum channel. Moreover, in the asymptotic limit of infinitely strong trusted anti-squeezing noise, the bound can be expressed analytically. We then assume that anti-squeezing noise is controlled by an eavesdropper, thus being a side-channel in the source implementation. In this regime, the anti-squeezing noise leads to the security break both in direct and reverse reconciliation scenarios. We compare the bounds on the untrusted phase-sensitive anti-squeezing noise to the typical phase-insensitive channel excess noise and show that protocols are more robust to the anti-squeezing noise, while the presence of such noise makes the protocol more sensitive to the noise in the main quantum channel. The obtained results reveal the important role of anti-squeezing noise in continuous-variable quantum cryptography and suggest the need of pure squeezed state preparation in the case of untrusted sources.
We address security of the quantum key distribution scheme based on the noisy modulation of coherent states and investigate how it is robust against noise in the modulation regardless of the particular technical implementation. As the trusted preparation noise is shown to be security breaking even for purely lossy channels, we reveal the essential difference between two types of trusted noise, namely sender-side preparation noise and receiver-side detection noise, the latter being security preserving. We consider the method of sender-side state purification to compensate the preparation noise and show its applicability in the realistic conditions of channel loss, untrusted channel excess noise, and trusted detection noise. We show that purification makes the scheme robust to the preparation noise (i.e., even the arbitrary noisy coherent states can in principle be used for the purpose of quantum key distribution). We also take into account the effect of realistic reconciliation and show that the purification method is still efficient in this case up to a limited value of preparation noise.
Quantum cryptography involves the fundamental question of the existence of secure protocols of quantum key distribution at any length of a communication channel (at any losses in it). A remarkable feature and novelty of the proposed protocol is that it ensures dual control; first, the intensity of a reference (intense) quantum state is controlled classically before the comparison (measurement) of coherent states from different time windows, and, second, the loss of coherence of a state is detected by interference measurements of an information quantum state and the reference quantum state tested against the conservation of the intensity. Thus, this is the only existing protocol stable to any losses in the communication channel. The length of the communication channel is limited only by dark noise in detectors.
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 consider the security of continuous-variable quantum key distribution using thermal (or noisy) Gaussian resource states. Specifically, we analyze this against collective Gaussian attacks using direct and reverse reconciliation where both protocols use either homodyne or heterodyne detection. We show that in the case of direct reconciliation with heterodyne detection, an improved robustness to channel noise is achieved when large amounts of preparation noise is added, as compared to the case when no preparation noise is added. We also consider the theoretical limit of infinite preparation noise and show a secure key can still be achieved in this limit provided the channel noise is less than the preparation noise. Finally, we consider the security of quantum key distribution at various electromagnetic wavelengths and derive an upper bound related to an entanglement-breaking eavesdropping attack and discuss the feasibility of microwave quantum key distribution.