Trusted Noise in Continuous-Variable Quantum Key Distribution: A Threat and a Defense

Demonstration of microwave single-shot quantum key distribution

Security of modern classical data encryption often relies on computationally hard problems, which can be trivialized with the advent of quantum computers. A potential remedy for this is quantum communication which takes advantage of the laws of quantum physics to provide secure exchange of information. Here, quantum key distribution (QKD) represents a powerful tool, allowing for unconditionally secure quantum communication between remote parties. At the same time, microwave quantum communication is set to play an important role in future quantum networks because of its natural frequency compatibility with superconducting quantum processors and modern near-distance communication standards. To this end, we present an experimental realization of a continuous-variable QKD protocol based on propagating displaced squeezed microwave states. We use superconducting parametric devices for generation and single-shot quadrature detection of these states. We demonstrate unconditional security in our experimental microwave QKD setting. The security performance is shown to be improved by adding finite trusted noise on the preparation side. Our results indicate feasibility of secure microwave quantum communication with the currently available technology in both open-air (up to  ~ 80 m) and cryogenic (over 1000 m) conditions.

Low-complexity continuous-variable quantum key distribution with true local oscillator using pilot-assisted frequency locking

In the domain of continuous variable quantum key distribution (CV-QKD), a significant challenge arises in achieving precise frequency synchronization, an issue commonly termed as frequency locking. This involves matching the optical frequencies of both the quantum signal laser and the local oscillator laser for accurate symbol demodulation during the exchange of quantum keys. As such, implementations today still grapple with maintaining precise synchronization between sender and receiver frequencies, occasionally hindering the efficiency and reliability of the information exchange. Addressing this challenge, we present and empirically validate a novel approach to CV-QKD by incorporating a pilot tone-assisted frequency locking algorithm to enhance stability when using a locally generated local oscillator (LLO) at the receiver. The proposed design leverages software-based optimization techniques, thereby eliminating the need for high-speed electronic stabilization devices and achieving efficient performance at typical repetition rates. Specifically, the introduction of the pilot tone algorithm allows us to effectively mitigate phase fluctuations and preserve the integrity of the quantum signals during transmission without resorting to time-multiplexed reference pulses or fast-locking electronics in the lasers. Our results suggest the potential for achieving secure key rates of up to 1 Mb/s over a 50 km single-mode fiber when using these techniques, offering promising insights into the feasibility of high-rate, low-complexity CV-QKD implementations under realistic conditions.

Types, sources, socioeconomic impacts, and control strategies of environmental noise: a review

Noise exposure has reached an alarming degree over the years because of rapid growth in the industry, transportation, and urbanization. Therefore, it is a dire need to provide awareness of the sources and mitigation strategies of noise, and to highlight the health, and socio-economic impacts of noise. A few research studies have documented this emerging issue; however, there is no comprehensive document describing all types of noise, their impacts on living organisms, and control strategies. This review article summarizes the sources of noise; their effects on industrial workers, citizens, and animals; and the value of property in noisy areas. The plethora of literature is showing an increased level of noise in various cities of the world, which have various health consequences such as high blood pressure, insomnia, nausea, heart attack, exhaustion, dizziness, headache, and triggered hearing loss. Apart from humans, noise also affects animal habitat, preying, and reproduction ability; increases heart rate and hearing loss to even death and loss in property value; and impairs the hospital environment. Finally, we have discussed the possible strategies to mitigate the noise problem, policy statements, and regulations to be followed, with future research directions based on the identified research gaps.

Redundancy and Synergy of an Entangling Cloner in Continuous-Variable Quantum Communication

We address minimization of information leakage from continuous-variable quantum channels. It is known, that regime of minimum leakage can be accessible for the modulated signal states with variance equivalent to a shot noise, i.e., vacuum fluctuations, in the case of collective attacks. Here we derive the same condition for the individual attacks and analytically study the properties of the mutual information quantities in and out of this regime. We show that in such regime a joint measurement on the modes of a two-mode entangling cloner, being the optimal individual eavesdropping attack in a noisy Gaussian channel, is no more effective that independent measurements on the modes. Varying variance of the signal out of this regime, we observe the nontrivial statistical effects of either redundancy or synergy between the measurements of two modes of the entangling cloner. The result reveals the non-optimality of entangling cloner individual attack for sub-shot-noise modulated signals. Considering the communication between the cloner modes, we show the advantage of knowing the residual noise after its interaction with the cloner and extend the result to a two-cloner scheme.

Discrete-modulation measurement-device-independent continuous-variable quantum key distribution with a quantum scissor: exact non-Gaussian calculation

In this paper, we study non-Gaussian discrete-modulated measurement-device-independent continuous-variable quantum key distribution protocol equipped with a proposed quantum scissor at the receiver side. Our suggested scissor truncates all multiphoton number states with four or more photons and amplifies remaining photon number states in a probabilistic way. Using exact non-Gaussian calculation, we find that quantum scissor meliorates the fidelity and entanglement between two legitimate parties Alice and Bob, at long distances. Therefore, quantum scissor enhances the continuous-variable quantum key distribution protocol range. Examination of the system for different values of the excess noise reveals that this improvement disappears at high noisy channels.

Security analysis of continuous variable quantum key distribution based on entangled states with biased correlations

Einstein-Podolsky-Rosen (EPR) entangled states can significantly enhance the secret key rate and secure distance of continuous-variable quantum key distribution (CV-QKD). In practical imperfections always exist in the preparation of two-mode squeezing (entangled states), which present an asymmetrical variance for the two quadratures. The imperfections induced by the bias effect of the entangled states are commonly treated as part of the untrusted channel to decrease the performance of the system. Here, we theoretically quantify the influence of bias effect on the secret key rate and secure distance, and propose a solution of generating unbiased entangled states protocol. The results demonstrated that the unbiased entangled states protocol guarantees the longest secure distance and highest key rate compared to that of coherent and biased entangled states.

Applicability of Squeezed- and Coherent-State Continuous-Variable Quantum Key Distribution over Satellite Links

We address the applicability of quantum key distribution with continuous-variable coherent and squeezed states over long-distance satellite-based links, considering low Earth orbits and taking into account strong varying channel attenuation, atmospheric turbulence and finite data ensemble size effects. We obtain tight security bounds on the untrusted excess noise on the channel output, which suggest that substantial efforts aimed at setup stabilization and reduction of noise and loss are required, or the protocols can be realistically implemented over satellite links once either individual or passive collective attacks are assumed. Furthermore, splitting the satellite pass into discrete segments and extracting the key from each rather than from the overall single pass allows one to effectively improve robustness against the untrusted channel noise and establish a secure key under active collective attacks. We show that feasible amounts of optimized signal squeezing can substantially improve the applicability of the protocols allowing for lower system clock rates and aperture sizes and resulting in higher robustness against channel attenuation and noise compared to the coherent-state protocol.

High Efficiency Continuous-Variable Quantum Key Distribution Based on ATSC 3.0 LDPC Codes

Due to the rapid development of quantum computing technology, encryption systems based on computational complexity are facing serious threats. Based on the fundamental theorem of quantum mechanics, continuous-variable quantum key distribution (CVQKD) has the property of physical absolute security and can effectively overcome the dependence of the current encryption system on the computational complexity. In this paper, we construct the spatially coupled (SC)-low-density parity-check (LDPC) codes and quasi-cyclic (QC)-LDPC codes by adopting the parity-check matrices of LDPC codes in the Advanced Television Systems Committee (ATSC) 3.0 standard as base matrices and introduce these codes for information reconciliation in the CVQKD system in order to improve the performance of reconciliation efficiency, and then make further improvements to final secret key rate and transmission distance. Simulation results show that the proposed LDPC codes can achieve reconciliation efficiency of higher than 0.96. Moreover, we can obtain a high final secret key rate and a long transmission distance through using our proposed LDPC codes for information reconciliation.

CV-MDI-QKD with coherent state: beyond one-mode Gaussian attacks

A general security proof of continuous variable (CV) measurement device independent (MDI) quantum key distribution (QKD) should not be automatically reduced to the analysis of one-mode Gaussian attacks (in particular, independent entangling-cloner attacks). To stress this point, the present work provides a very simple (almost trivial) argument, showing that there are an infinite number of two-mode Gaussian attacks that cannot be reduced to or simulated by one-mode Gaussian attacks. This result further confirms that the security analysis of CV-MDI-QKD must generally involve a careful minimization over two-mode attacks as originally performed in (Pirandola et al, 2015 Nature Photon. 9, 397–402; arXiv:1312.4104 (2013)).

Long-Distance Continuous-Variable Quantum Key Distribution over 202.81 km of Fiber

Quantum key distribution provides secure keys resistant to code-breaking quantum computers. The continuous-variable version of quantum key distribution offers the advantages of higher secret key rates in metropolitan areas, as well as the use of standard telecom components that can operate at room temperature. However, the transmission distance of these systems (compared with discrete-variable systems) are currently limited and considered unsuitable for long-distance distribution. Herein, we report the experimental results of long distance continuous-variable quantum key distribution over 202.81 km of ultralow-loss optical fiber by suitably controlling the excess noise and employing highly efficient reconciliation procedures. This record-breaking implementation of the continuous-variable quantum key distribution doubles the previous distance record and shows the road for long-distance and large-scale secure quantum key distribution using room-temperature standard telecom components.

Plug-and-play continuous-variable quantum key distribution for metropolitan networks

We report a plug-and-play continuous variable quantum key distribution system (CV-QKD) with Gaussian modulated quadratures and a true local oscillator. The proposed configuration avoids the need for frequency locking two narrow line-width lasers. To minimize Rayleigh back-scattering, we utilize two independent fiber strands for the distribution of the laser and the transmission of the quantum signals. We further demonstrate the quantum-classical co-existing capability of our system by injecting high-power classical light in both fibers. A secret key rate up to 0.88 Mb/s is obtained by using two fiber links of 13 km and up to 0.3 Mb/s when adding 4 mW of classical light in the optical fiber used for transmitting the quantum signal. The reported performance indicates that the proposed QKD scheme has the potential to become an effective low-cost solution for metropolitan optical networks.

Feasibility of quantum key distribution with macroscopically bright coherent light

We address feasibility of continuous-variable quantum key distribution using bright multimode coherent states of light and homodyne detection. We experimentally verify the possibility to properly select signal modes by matching them with the local oscillator and this way to decrease the quadrature noise concerned with unmatched bright modes. We apply the results to theoretically predict the performance of continuous-variable quantum key distribution scheme using multimode coherent states in scenarios where modulation is applied either to all the modes or only to the matched ones, and confirm that the protocol is feasible at high overall brightness. Our results open the pathway towards full-scale implementation of quantum key distribution using bright light, thus bringing quantum communication closer to classical optics.

Security Analysis of Discrete-Modulated Continuous-Variable Quantum Key Distribution over Seawater Channel

We investigate the optical absorption and scattering properties of four different kinds of seawater as the quantum channel. The models of discrete-modulated continuous-variable quantum key distribution (CV-QKD) in free-space seawater channel are briefly described, and the performance of the four-state protocol and the eight-state protocol in asymptotic and finite-size cases is analyzed in detail. Simulation results illustrate that the more complex is the seawater composition, the worse is the performance of the protocol. For different types of seawater channels, we can improve the performance of the protocol by selecting different optimal modulation variances and controlling the extra noise on the channel. Besides, we can find that the performance of the eight-state protocol is better than that of the four-state protocol, and there is little difference between homodyne detection and heterodyne detection. Although the secret key rate of the protocol that we propose is still relatively low and the maximum transmission distance is only a few hundred meters, the research on CV-QKD over the seawater channel is of great significance, which provides a new idea for the construction of global secure communication network.

Stabilization of transmittance fluctuations caused by beam wandering in continuous-variable quantum communication over free-space atmospheric channels

Transmittance fluctuations in turbulent atmospheric channels result in quadrature excess noise which limits applicability of continuous-variable quantum communication. Such fluctuations are commonly caused by beam wandering around the receiving aperture. We study the possibility to stabilize the fluctuations by expanding the beam, and test this channel stabilization in regard of continuous-variable entanglement sharing and quantum key distribution. We perform transmittance measurements of a real free-space atmospheric channel for different beam widths and show that the beam expansion reduces the fluctuations of the channel transmittance by the cost of an increased overall loss. We also theoretically study the possibility to share an entangled state or to establish secure quantum key distribution over the turbulent atmospheric channels with varying beam widths. We show the positive effect of channel stabilization by beam expansion on continuous-variable quantum communication as well as the necessity to optimize the method in order to maximize the secret key rate or the amount of shared entanglement. Being autonomous and not requiring adaptive control of the source and detectors based on characterization of beam wandering, the method of beam expansion can be also combined with other methods aiming at stabilizing the fluctuating free-space atmospheric channels.

Quantum communication based on two-mode entangled state with quantum noise locking method

The two-mode entangled state is an important basic non-classical state and it has been used in many quantum communication projects. We propose a new quantum communication scheme with a two-mode entangled state which can transmit signals encoded by a thermal-state light field. Also, instead of locking several phases in the whole process, we use only one locking servo system at the final stage. The locking error signal comes from the measured quantum variances by using the quantum noise locking method. A proof-of-principle derivation shows that it is very convenient to achieve the secure condition against individual attacks. It would be utilized in practical quantum information process.