Reverse Reconciliation Research Articles

Enhancing Performance of Continuous-Variable Quantum Key Distribution (CV-QKD) and Gaussian Modulation of Coherent States (GMCS) in Free-Space Channels under Individual Attacks with Phase-Sensitive Amplifier (PSA) and Homodyne Detection (HD).

In recent research, there has been a significant focus on establishing robust quantum cryptography using the continuous-variable quantum key distribution (CV-QKD) protocol based on Gaussian modulation of coherent states (GMCS). Unlike more stable fiber channels, one challenge faced in free-space quantum channels is the complex transmittance characterized by varying atmospheric turbulence. This complexity poses difficulties in achieving high transmission rates and long-distance communication. In this article, we thoroughly evaluate the performance of the CV-QKD/GMCS system under the effect of individual attacks, considering homodyne detection with both direct and reverse reconciliation techniques. To address the issue of limited detector efficiency, we incorporate the phase-sensitive amplifier (PSA) as a compensating measure. The results show that the CV-QKD/GMCS system with PSA achieves a longer secure distance and a higher key rate compared to the system without PSA, considering both direct and reverse reconciliation algorithms. With an amplifier gain of 10, the reverse reconciliation algorithm achieves a secure distance of 5 km with a secret key rate of 10-1 bits/pulse. On the other hand, direct reconciliation reaches a secure distance of 2.82 km.

Refined finite-size analysis of binary-modulation continuous-variable quantum key distribution

Recent studies showed the finite-size security of binary-modulation CV-QKD protocols against general attacks. However, they gave poor key-rate scaling against transmission distance. Here, we extend the security proof based on complementarity, which is used in the discrete-variable QKD, to the previously developed binary-modulation CV-QKD protocols with the reverse reconciliation under the finite-size regime and obtain large improvements in the key rates. Notably, the key rate in the asymptotic limit scales linearly against the attenuation rate, which is known to be optimal scaling but is not achieved in previous finite-size analyses. This refined security approach may offer full-fledged security proofs for other discrete-modulation CV-QKD protocols.

Zero-photon catalysis based eight-state discrete modulated measurement-device-independent continuous-variable quantum key distribution

Zero-photon catalysis (ZPC) introduces noiseless attenuation and can be implemented by existing technologies in quantum key distribution (QKD) protocols. In this paper, we present a ZPC-based eight-state measurement-device-independent continuous-variable QKD (MDI-CV-QKD) combined with discrete modulation and reverse reconciliation. This ZPC-involved eight-state protocol shows better efficiency in terms of optimal modulation variances, secret key rates, transmission distances, tolerable excess noises, and reconciliation efficiency compared to the eight-state protocol without ZPC, the four-state protocol without ZPC, and the four-state protocol with ZPC, at a low signal-to-noise ratio (SNR).

Using a multi‐staged translation method to develop socio‐culturally and language‐sensitive study materials: Lessons learned from an Asian cohort for Alzheimer’s disease

AbstractBackgroundAlzheimer’s disease (AD) is a global health crisis on multiple levels. A major impediment to AD research is the availability of socio‐culturally and language appropriate study materials and instruments and inclusion of under‐represented minorities. To fulfill this need, we apply best practices and lessons learned to translate study materials for use in the Asian Cohort for Alzheimer’s Disease’s (ACAD) study of AD in Asian Americans and Asian Canadians (ASAC) with the overarching goal in inclusivity of these populations to better understand the etiology of AD.MethodOur multi‐stag translation process is guided by the World Health Organization’s (WHO) process of translation (forward and reverse translation, consensus verification and reconciliation) to achieve parity with the English materials for our target groups (Chinese (simplified and traditional; Mandarin and Cantonese), Korean and Vietnamese). ACAD’s collective experience partnering with aging Asian adults has revealed not only a language barrier, but also issues with socio‐cultural communication traits, and literal translations that stigmatize AD and dementia. Consequently, we have taken into account the varying perceptions and expressions of words in a social context. The translation process was implemented by a team of multi‐lingual researchers/clinicians/community leaders with extensive practical translation experience. Since language influences how a speaker views the world, we employed a cross‐section of translators and emphasized conceptual (vs. literal) culturally appropriate translations for the community.ResultsTo date, we have developed Asian language versions of ACAD documents (informed consent, data collection, community and social media outreach materials, website) for all our target groups and continue the process of beta‐testing our study materials (including the cognitive assessment instruments).ConclusionThe multi‐stage translation process accounts for distinctive Asian socio‐cultural‐language backgrounds, providing an important guideline for AD researchers to promote health literacy in the health and general community in an effort to reduce health disparities in underrepresented groups, like Asians. In order to ensure fidelity across languages, we will continue validating the original English version in Chinese, Korean, and Vietnamese versions in the ACAD study.

Performance improvement of self-referenced continuous-variable quantum key distribution via optical amplifiers

Self-referenced continuous-variable quantum key distribution (SR-CVQKD) protocols, which operate with a real local local oscillator (LLO) at the receiver side, provide the major advantage that they can defend against all attacks associated with the local oscillator. We propose a method to enhance the performance of the SR-CVQKD by adding an optical parametric amplifier into the receiver’s apparatus. Considering reverse reconciliation, the secret key rate against collective eavesdropping attacks is calculated. For the plug-and-play dual-phase-modulated coherent-states (DPMCS) SR-CVQKD protocol, we demonstrate that an ideal phase-sensitive amplifier (PSA) can enhance the efficiency of a homodyne detector, and the compensation ability of a realistic phase-insensitive amplifier (PIA) for heterodyne detection varies according to different values of N, which indicates the noise variance of the PIA. Moreover, these arrangements of optical amplifiers also have applications in one-way SR-CVQKD systems.

Imperfect basis choice in continuous-variable quantum key distribution

In the Gaussian-modulated coherent states (GMCS) quantum key distribution (QKD), basis choice is a necessary procedure if homodyne detector is used. However, finite bandwidth of the digital-to-analog convertor (DAC) at the receiver’s side may lead to the imperfection of the basis choice, namely, maybe Bob can not exactly modulate 0 or on the phase modulator to implement the homodyne detection.We investigate the GMCS QKD scheme with imperfect basis choice under realistic conditions of quantum channel and detector.We show that the imperfection causes a misestimate of the transmittance and the excess noise, the secret key rate and the security of the system are dramatically decreased consequently. To achieve a reliable quantum key distribution, a security bound to the noise induced by the imperfect basis choice is derived for reverse reconciliation and homodyne detector. Besides, we propose and demonstrate a countermeasure against the noise due to imperfect basis choice.

Hybrid linear amplifier-involved detection for continuous variable quantum key distribution with thermal states**Project supported by the National Natural Science Foundation of China (Grant Nos. 61572529 and 61871407).

Continuous-variable quantum key distribution (CVQKD) can be integrated with thermal states for short-distance wireless quantum communications. However, its performance is usually restricted with the practical thermal noise. We propose a method to improve the security threshold of thermal-state (TS) CVQKD by employing a heralded hybrid linear amplifier (HLA) at the receiver. We find the effect of thermal noise on the HLA-involved scheme in near-and-mid infrared band or terahertz band for direct and reverse reconciliation. Numerical simulations show that the HLA-involved scheme can compensate for the detriment of thermal noise and hence increase the security threshold of TS-CVQKD. In near-and-mid infrared band, security threshold can be extended by 2.1 dB in channel loss for direct reconciliation and 1.6 dB for reverse reconciliation, whereas in terahertz band, security threshold can be slightly enhanced for the gain parameter less than 1 due to the rise in thermal noise.

Terahertz Quantum Cryptography

A well-known empirical rule for the demand of wireless communication systems is that of Edholm's law of bandwidth. It states that the demand for bandwidth in wireless short-range communications doubles every 18 months. With the growing demand for bandwidth and the decreasing cell size of wireless systems, terahertz (THz) communication systems are expected to become increasingly important in modern day applications. With this expectation comes the need for protecting users' privacy and security in the best way possible. With that in mind, we show that quantum key distribution can operate in the THz regime and we derive the relevant secret key rates against realistic collective attacks. In the extended THz range (from 0.1 to 50 THz), we find that below 1 THz, the main detrimental factor is thermal noise, while at higher frequencies it is atmospheric absorption. Our results show that high-rate THz quantum cryptography is possible over distances varying from a few meters using direct reconciliation, to about 220m via reverse reconciliation. We also give a specific example of the physical hardware and architecture that could be used to realize our THz quantum key distribution scheme.

Asymptotic Security Analysis of Discrete-Modulated Continuous-Variable Quantum Key Distribution

Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discrete-modulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus on two variants of the CV QKD protocol with quaternary modulation. Interestingly, thanks to the tightness of our proof method, we show that this protocol is capable of achieving much higher key rates over significantly longer distances with experimentally feasible parameters compared with previous security proofs of binary and ternary modulation schemes and also yielding key rates comparable to Gaussian modulation schemes. Furthermore, as our security analysis method is versatile, it allows us to evaluate variations of the discrete-modulated protocols, including direct and reverse reconciliation, and postselection strategies. In particular, we demonstrate that postselection of data in combination with reverse reconciliation can improve the key rates.

Security bound of continuous-variable measurement-device-independent quantum key distribution with imperfect phase reference calibration

Phase reference calibration is a necessary procedure in practical continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) for the need of Bell-State Measurement (BSM). However, the phase reference calibration may become imperfect in practical applications. We explored the practical security of CV-MDI-QKD with imperfect phase reference calibration under realistic conditions of lossy and noisy quantum channel. Specifically, a comprehensive framework is developed to model and characterize the imperfection of practical phase reference calibration operation, which is mainly caused by the non-synchronization of two remote lasers in senders. Security analysis shows that the imperfect phase reference calibration has significant side effects on the performance and security of the CV-MDI-QKD protocol. A tight security bound to excess noise introduced by imperfect phase reference calibration is derived for reverse reconciliation against arbitrary collective attacks in the asymptotic limit, and the tolerance of the CV-MDI-QKD protocol to this excess noise is also obtained. This security analysis framework can eliminate the security hazards caused by imperfect phase reference calibration without changing the existing CV-MDI-QKD system structure.

Laser beam propagation effects on secure key rates for satellite-to-ground discrete modulation CV-QKD.

The increasing prevalence of satellite-to-ground laser communications necessitates unconditional security measures that so far can only be provided by quantum key distribution. However, in a free-space optical channel, the diffraction of laser beams along with turbulence effects can reduce the initially high secure key rates potentially provided by continuous variable quantum key distribution (CV-QKD). Using derived formulas from four-state discrete modulation CV-QKD with reverse reconciliation, we highlight parameters that yield key rates on the order of 50Mbps, and then describe the possible factors that can cause its reduction in a free-space optical channel. Numerical beam propagation simulations are performed to supplement the analyses.

Framework for covert and secret key expansion over classical-quantum channels

Covert and secret quantum key distribution aims at generating information-theoretically secret bits between distant legitimate parties in a manner that remains provably undetectable by an adversary. We propose a framework in which to precisely define and analyze such an operation, and we show that covert and secret key expansion is possible. For fixed and known classical-quantum channels, we develop and analyze protocols based on forward and reverse reconciliation. When the adversary applies the same quantum channel independently on each transmitted quantum state, akin to a collective attack in the quantum key distribution literature, we propose a protocol that achieves covert and secret key expansion under mild restrictions. The crux of our approach is the use of information reconciliation and privacy amplification techniques that are able to process the sparse signals required for covert operation and whose Shannon entropy scales as the square root of their length. % diffuse information content quantified through Shannon entropy induced by the sparse signaling required for covert operation. In particular, our results show that the coordination required between legitimate parties to achieve covert communication can be achieved with a negligible number of secret key bits.

Information reconciliation for continuous variable QKD systems based on permutation modulation

This paper is focused on the problem of Information Reconciliation (IR) for continuous variable Quantum Key Distribution (QKD). The main problem is quantization and assignment of labels to the samples of the Gaussian variables observed at Alice and Bob. Trouble is that most of the samples, assuming that the Gaussian variable is zero mean which is de-facto the case, tend to have small magnitudes and are easily disturbed by noise. Transmission over longer and longer distances increase the losses corresponding to a lower effective Signal to Noise Ratio (SNR) exasperating the problem. In previous work [1], [2] we approach the IR problem in a fundamentally different way than how it is addressed in published literature. At very low SNR, one can focus exclusively on the sign of the Gaussian samples at Alice and Bob and perform Reverse Reconciliation (RR) on sign of the samples given their quantized magnitudes as side information Alice and Bob share in the open. In this paper we demonstrate that the weighted sum capacity of the Binary Symmetric Channels (BSCs) derived from magnitude dependent sign error probabilities of the Gaussian samples shared between Alice and Bob approaches the mutual information between Alice and Bob at very low SNR regimes. Thus, when SNR is very low, one could just as well ignore any common randomness that may be obtained from magnitude of the Gaussian samples and focus exclusively on their sign. The caveat is, to get close to this mutual information, Unequal Error Protection (UEP) must be employed based on magnitude of the observed samples at Bob in RR.

Longer distance continuous variable quantum key distribution protocol with photon subtraction at the receiver

One of the limitations of continuous variable quantum key distribution is the relatively short transmission distance of secure keys. Some solutions have been proposed to overcome the limitation including reverse reconciliation, trusted noise concept, and non-Gaussian operation. In this paper, we propose a protocol using photon subtraction at the receiver, which combines the synergetic benefits of the aforementioned approaches. Using simulations, we show that the performance of the proposed protocol outperforms other conventional protocols. The results showed that an improvement in secure key distance can be obtained using a non-Gaussian operation, depending on the position where the operation is performed, similar to the trusted noise concept. Furthermore, the result implies existence of some Gaussian operations which increases security without using a beam splitter.

Secret key rate proof of multicarrier continuous‐variable quantum key distribution

SummaryWe prove the secret key rate formulas and derive security threshold parameters of multicarrier continuous‐variable quantum key distribution CVQKD. In a multicarrier CVQKD scenario, the Gaussian input quantum states of the legal parties are granulated into Gaussian subcarrier continuous variables (CVs). The multicarrier communication formulates Gaussian subchannels from the physical quantum channel, each dedicated to the transmission of a subcarrier CV. The Gaussian subcarriers are decoded by a unitary CV operation, which results in the recovered single‐carrier Gaussian CVs. We derive the formulas through the adaptive multicarrier quadrature division (AMQD) scheme, the singular value decomposition (SVD)–assisted AMQD, and the multiuser AMQD multiuser quadrature allocation (MQA). We prove that the multicarrier CVQKD leads to improved secret key rates and higher tolerable excess noise in comparison with single‐carrier CVQKD. We derive the private classical capacity of a Gaussian subchannel and the security parameters of an optimal Gaussian collective attack in the multicarrier setting. We reveal the secret key rate formulas for one‐way and two‐way multicarrier CVQKD protocols, assuming homodyne and heterodyne measurements and direct and reverse reconciliation. The results reveal the physical boundaries of physically allowed Gaussian attacks in a multicarrier CVQKD scenario and confirm that the improved transmission rates lead to enhanced secret key rates and security thresholds.

Improving the lower bound to the secret-key capacity of the thermal amplifier channel

We consider the noisy thermal amplifier channel, where signal modes are amplified together with environmental thermal modes. We focus on the secret-key capacity of this channel, which is the maximum amount of secret bits that two remote parties can generate by means of the most general adaptive protocol, assisted by unlimited and two-way classical communication. For this channel only upper and lower bounds are known, and in this work we improve the lower bound. We consider a protocol based on squeezed states and homodyne detections, in both direct and reverse reconciliation. In particular, we assume that trusted thermal noise is mixed on beam splitters controlled by the parties in a way to assist their homodyne detections. The new improved lower bounds to the secret-key capacity are obtained by optimizing the key rates over the variance of the trusted noise injected, and the transmissivity of the parties’ beam splitters. Our results confirm that there is a separation between the coherent information of the thermal amplifier channel and its secret key capacity.Graphical abstract

Quantum key distribution with phase-encoded coherent states: Asymptotic security analysis in thermal-loss channels

We consider discrete-alphabet encoding schemes for coherent-state quantum key distribution. The sender encodes the letters of a finite-size alphabet into coherent states whose amplitudes are symmetrically distributed on a circle centered in the origin of the phase space. We study the asymptotic performance of this phase-encoded coherent-state protocol in direct and reverse reconciliation assuming both loss and thermal noise in the communication channel. In particular, we show that using just four phase-shifted coherent states is sufficient for generating secret key rates of the order of $4 \times 10^{-3}$ bits per channel use at about 15 dB loss in the presence of realistic excess noise.

Hybrid quantum key distribution using coherent states and photon-number-resolving detectors

We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. In the presence of direct reconciliation, the PNR strategy is still the best one against individual attacks, but for the collective ones the homodyne-based scheme is still to be preferred as the channel transmissivity decreases.

Secret key rates for intensity-modulated dual-threshold detection key distribution under individual beam splitting attacks.

We investigate the secret key rates for the recently proposed intensity-modulated dual-threshold key distribution [T. Ikuta and K. Inoue, New J. Phys. 18 (2016)] under beam splitting attacks. We show that previous assumptions on an eavesdropper that performs hard decision measurements on the channel, overestimates the secret key rate. We discuss the impact of an eavesdropper that can measure full soft information and give the secret key rates under forward and reverse reconciliation. Further, we perform simulations for different system assumptions and show the optimal modulation depths for these systems. We also outline an attack on this protocol based on photon counting that prohibits secret key generation.

Composable security analysis of continuous-variable measurement-device-independent quantum key distribution with squeezed states for coherent attacks

Measurement-device-independent quantum key distribution protocol, whose security analysis does not rely on any assumption on the detection system, can immune the attacking against detectors. We give a first composable security analysis for continuous-variable measurement-device-independent quantum key distribution using squeezed states against general coherent attacks. The security analysis is derived based on the entanglement-based scheme considering finite size effect. A version of entropic uncertainty relation is exploited to give a lower bound on the conditional smooth min-entropy by trusting Alice's and Bob's devices. The simulation results indicate that, in the universal composable security framework, the protocol can tolerate 2.5 dB and 6.5 dB channel loss against coherent attacks with direct and reverse reconciliation, respectively.