Variable Quantum Key Distribution Protocol Research Articles

Unidimensional Continuous Variable Quantum Key Distribution under Fast Fading Channel

AbstractIn this paper, the performance of a unidimensional continuous variable quantum key distribution protocol is analyzed using Gaussian modulated coherent state under fast fading channel. In the fast fading channel, both parties are connected in free space, resulting in a harsh propagation environment and pollution caused by atmospheric turbulence. This pollution makes it difficult for the communicators to determine the channel transmittance, which can only be estimated based on a probability distribution. To address this, only one modulator is used to code, which demonstrates performance equivalent to that of the symmetric modulated Gaussian coherent state protocol. The security of the protocol in the face of collective attacks is analyzed and it is proved that it can accept a certain amount of excessive channel noise while simplifying operations. Simultaneously, the impact of finite‐key length effects on the protocol is analyzed. It is also demonstrated that this protocol can reduce costs within an acceptable range of performance losses, making it more practical.

Measurement-device-independent continuous variable quantum key distribution protocol operation in optical transport networks

Measurement-device-independent continuous variable quantum key distribution protocol operation in optical transport networks

Optical transmitter for time-bin encoding quantum key distribution

We introduce an electro-optical arrangement that can produce time-bin encoded symbols with the decoy state method over a standard optical fiber in the C-band telecom window. The device consists of a specifically designed pulse pattern generator for pulse production and a field-programmable gate array that controls timing and synchronization. The electrical pulse output drives a sequence of intensity modulators acting on a continuous laser that deliver bursts of weak optical pulse pairs of discrete intensity values. Such a transmitter allows for the generation of all the quantum states needed to implement a discrete variable quantum key distribution (QKD) protocol over a single-mode fiber channel. Symbols are structured in bursts; the minimum relative delay between pulses is 1.25 ns, and the maximum symbol rate within a burst is 200 MHz. We tested the transmitter on simulated optical channels of 7 dB and 14 dB loss, obtaining maximum extractable secure key rates of 3.0 kb/s and 0.57 kb/s, respectively. Time-bin-state parameters such as the symbol rate, pulse separation, and intensity ratio between the signal and decoy states can be easily accessed and changed, allowing the transmitter to adapt to different experimental conditions and contributing to the standardization of QKD implementations.

Plug-and-play discrete modulation continuous variable quantum key distribution based on non-Gaussian state-discrimination detection

Plug-and-play discrete modulation continuous variable quantum key distribution can generate local oscillator light locally without using two independent lasers, and both signal light and local oscillator are generated from the same laser, which can effectively ensure the practical security of the system and have a completely identical frequency characteristic. In addition, this scheme has good compatibility with efficient error correction codes, and can achieve high reconciliation efficiency even at low signal-to-noise ratio. However, there exists large excess noise in the plug-and-play configuration based on the untrusted source model, which seriously limits the maximum transmission distance of the discrete modulation scheme. To solve this problem, we propose a plug-and-play discrete modulation continuous variable quantum key distribution based on non-Gaussian state-discrimination detection. That is to say, a non-Gaussian state-discrimination detector is deployed at the receiver. With adaptive measurement method and Bayesian inference, four non-orthogonal coherent states which are based on four-state discrete modulation can be unconditionally distinguished on condition that the error probability is lower than the standard quantum limit. We analyze the security of the proposed protocol by considering both asymptotic limit and finite-size effect. Simulation results show that the secret key rate and maximum transmission distance are significantly enhanced by using no-Gaussian state-discrimination detection even under the influence of the untrusted source noise compared with the original plug-and-play discrete modulation continuous variable quantum key distribution. These results indicate that the proposed scheme can effectively reduce the negative influence of the untrust source noise on the performance of the plug-and-play discrete modulation continuous variable quantum key distribution protocol. The proposed protocol can not only ensure the practical security of the system, but also achieve more efficient and longer transmission distance quantum key distribution.

Improving source-in-the-middle continuous-variable quantum key distribution using a heralded hybrid linear amplifier

A hybrid linear amplifier is inserted at the output of the source-in-the-middle distribution protocol to overcome the shortcomings of the transmission distance. The modified protocol aims to maintain a high key rate for long-distance transmission under high noise. It has the potential to significantly broaden the application range of the continuous variable quantum key distribution protocol. The effects of amplifier parameters and noise on the modified protocol are analyzed in detail with regard to applying it to a practical system. To make the simulation more realistic, the effect of finite size on the new protocol is taken into account. It will serve as a guideline for the future use of hybrid linear amplifiers. Different parameters can be adjusted to achieve the best performance for key rates of different quantum channels.

Networking Feasibility of Quantum Key Distribution Constellation Networks.

Quantum key distribution constellation is the key to achieve global quantum networking. However, the networking feasibility of quantum constellation that combines satellite-to-ground accesses selection and inter-satellite routing is faced with a lack of research. In this paper, satellite-to-ground accesses selection is modeled as problems to find the longest paths in directed acyclic graphs. The inter-satellite routing is interpreted as problems to find a maximum flow in graph theory. As far as we know, the above problems are initially understood from the perspective of graph theory. Corresponding algorithms to solve the problems are provided. Although the classical discrete variable quantum key distribution protocol, i.e., BB84 protocol, is applied in simulation, the methods proposed in our paper can also be used to solve other secure key distributions. The simulation results of a low-Earth-orbit constellation scenario show that the Sun is the leading factor in restricting the networking. Due to the solar influence, inter-planar links block the network periodically and, thus, the inter-continental delivery of keys is restricted significantly.

Thermal state quantum key distribution

We analyse a central broadcast continuous variable quantum key distribution protocol in which a beam produced by a thermal source is used to create a secret key between two parties, Alice and Bob. A beam splitter divides the initial beam into a pair of output beams, which are sent to Alice and Bob, with Eve intercepting Bob’s beam. We investigate the protocol in detail, calculating mutual informations through a pair of analytic methods and comparing the results to the outputs of a Monte Carlo simulation of the protocol. In a lossless system, we find that a lower bound on the key rate remains positive in the protocol under a beam splitter attack, provided Bob receives a nonzero proportion of the beam initially sent to him. This suggests that the thermal state protocol could be used experimentally to produce secure keys.

Adaptable transmitter for discrete and continuous variable quantum key distribution

We present a versatile transmitter capable of performing both discrete variable and continuous variable quantum key distribution protocols (DV-QKD and CV-QKD, respectively). Using this transmitter, we implement a time-bin encoded BB84 DV-QKD protocol over a physical quantum channel of 47 km and a GG02 CV-QKD protocol with true local oscillator over a 10.5 km channel, achieving secret key rates of 4.1 kbps and 1 Mbps for DV- and CV-QKD, respectively. The reported transmitter scheme is particularly suitable for re-configurable optical networks where the QKD protocol is selected to optimize the performance according to the parameters of the links.

A continuous variable quantum key distribution protocol based on multi-dimensiondata reconciliation with Polar code

The continuous variable quantum key distribution protocol (CV-QKD) has the advantages of easy generation of quantum signals, convenient measurement and high communication capacity. However, the multi-dimensional data reconciliation is mainly implemented by binary LDPC code as quantum error correction code, which is greatly affected by complex environments and the bit error rate is high. In order to solve this problem, acontinuous variable quantum key distribution protocol based onmulti-dimension data reconciliation with Polar code, that can be applied to long-distance transmission in power systems, is proposed. First, we prepare an EPR quantum state, and perform heterodyne detection on one of the quantum states, and obtain the values of two orthogonal components at the same time which is the coherent state of the information carrier. Then the continuous variable quantum key distribution is realized by six steps (i.e., quantum state preparation, gaussian random detection, data filtering, calculation of bit error rate, data reconciliation, privacy amplification).In data reconciliation, we use Polar code as the error correction code and use reverse coding technology to achieve key error correction, which can effectively improve the negotiation efficiency. Numerical simulation verifies the feasibility of the protocol, and the protocol is more efficient than the multi-dimensiondata reconciliation protocol based on LDPC code under the same conditions.

基于离散调制的三态连续变量量子密钥分发协议的安全性分析

基于离散调制的三态连续变量量子密钥分发协议的安全性分析

Continuous variable B92 quantum key distribution protocol using single photon added and subtracted coherent states

In this paper, a continuous variable B92 quantum key distribution (QKD) protocol is proposed using single photon added and subtracted coherent states, which are prepared by adding and subsequently subtracting a single photon on a coherent state. It is established that in contrast to the traditional discrete variable B92 protocol, this protocol for QKD is intrinsically robust against the unambiguous state discrimination attack, which circumvents the requirement for any uninformative states or entanglement used in corresponding discrete variable case as a remedy for this attack. Further, it is shown that the proposed protocol is intrinsically robust against the eavesdropping strategies exploiting classical communication during basis reconciliation, such as beam splitter attack. Security against some individual attacks, key rate, and bit-error rate estimation for the proposed scheme are also provided. Specifically, the proposed scheme ensures very small bit-error rate due to properties of the states used. Thus, the proposed scheme is shown to be preferable over the corresponding discrete variable B92 protocol as well as some similar continuous variable quantum key distribution schemes.

Coherence-assisted non-Gaussian measurement-device-independent quantum key distribution

Non-Gaussian operations on two mode squeezed vacuum states (TMSV) in continuous variable measurement device independent quantum key distribution (CV-MDI-QKD) protocols have been shown to effectively increase the total transmission distances drastically. In this paper we show that photon subtraction on a two mode squeezed coherent (PSTMSC) state can further improve the transmission distances remarkably. To that end we also provide a generalized covariance matrix corresponding to PSTMSC, which has not been attempted before. We show that coherence, defined as the amount of displacement of vacuum state, along with non-Gaussianity can help improve the performance of prevalent CV-MDI-QKD protocols. Furthermore, since we use realistic parameters, our technique is experimentally feasible and can be readily implemented

Generation of Gaussian-modulated entangled states for continuous variable quantum communication

We present and demonstrate a high-efficiency and compact scheme for generating Gaussian-modulated Einstein-Podolsky-Rosen (EPR) entangled optical fields by injecting a modulated signal field into a non-degenerate optical parametric amplifier (NOPA). We perform a quantum analysis of the scheme and derive the variance of the output signal (idler) mode and the quantum entanglement between the signal and idler modes from the NOPA. An experimental study is presented with different Gaussian modulation depths, showing that the modulation of the injected signal field successfully enlarges the distribution of the field quadratures of the EPR source in phase space and has a negligible effect on the entanglement quality. The experimental observations have good agreement with the theoretical analysis. Our scheme can be used readily in continuous variable quantum key distribution protocol.

Improving Eight-State Continuous Variable Quantum Key Distribution by Applying Photon Subtraction

We propose a new method to effectively improve the performance of a quantum key distribution with eight-state continuous variables by the photon subtraction method. This operation is effective in increasing and distilling Gaussian entanglement between quantum states, and can be easily realized by existing technology. Simulation results show that the channel-loss tolerance of the eight-state continuous variable quantum key distribution (CVQKD) protocol can be extended by the appropriate photon subtraction algorithm; namely, single-photon subtraction.

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.

Noise-enhanced CVQKD with untrusted source

The performance of one-way and two-way continuous variable quantum key distribution (CVQKD) protocols can be increased by adding some noise on the reconciliation side. In this paper, we propose to add noise at the reconciliation end to improve the performance of CVQKD with untrusted source. We derive the key rate of this case and analyze the impact of the additive noise. The simulation results show that the optimal additive noise can improve the performance of the system in terms of maximum transmission distance and tolerable excess noise.

On the problem of non-zero word error rates for fixed-rate error correction codes in continuous variable quantum key distribution

The maximum operational range of continuous variable quantum key distribution protocols has shown to be improved by employing high-efficiency forward error correction codes. Typically, the secret key rate model for such protocols is modified to account for the non-zero word error rate of such codes. In this paper, we demonstrate that this model is incorrect: firstly, we show by example that fixed-rate error correction codes, as currently defined, can exhibit efficiencies greater than unity. Secondly, we show that using this secret key model combined with greater than unity efficiency codes, implies that it is possible to achieve a positive secret key over an entanglement breaking channel—an impossible scenario. We then consider the secret key model from a post-selection perspective, and examine the implications for key rate if we constrain the forward error correction codes to operate at low word error rates.

Estimation of output-channel noise for continuous-variable quantum key distribution

Estimation of channel parameters is important for extending the range and increasing the key rate of continuous variable quantum key distribution protocols. We propose a new estimator for the channel noise parameter based on the method of moments. The method of moments finds an estimator from the moments of the output distribution of the protocol. This estimator has the advantage of being able to use all of the states shared between Alice and Bob. Other estimators are limited to a smaller publicly revealed subset of the states. The proposed estimator has a lower variance for high loss channel than what has previously been proposed. We show that the method of moments estimator increases the key rate by up to an order of magnitude at the maximum transmission of the protocol.

Macro-micro entanglement in optical system and its application in quantum key distribution

Macro-micro entanglement originates from the Schrodinger's Cat paradox. The paradox has been attracting the interest of the physicists since it was proposed. Schrodinger's Cat paradox is a thought experiment that entangles a cat with some decay atoms, in which the entanglement between the macroscopic object and the microscopic atoms is established. Mac-micro entanglement relates to some important problems in quantum physics. It is more likely to interact with the surroundings for the quantum system as its size increases, which is the reason why we hardly observe the macroscopic superposition state. Can the superposition state theory of quantum physics be used in macro domain? Is there a limitation to the scale for the objects in the superposition states? These questions need studying and verifying in experiment. In addition, the preparation of the macro-micro entanglement state provides a new possibility to study the decoherence model. Macro-micro entanglement can be realized in many physical systems, such as atomic ensembles, superconducting circuits, electro-mechanical and opto-mechanical systems. Here in this paper we will introduce the development of macro-micro entanglement in optical system. The initial approach to creating the macro-micro entanglement in the context of optical system is quantum cloning by simulating the emission. Then the quantum-injected optical parametric amplification is used to amplify single photon to a macroscopic level. Afterwards, the displacement in phase space is proposed to create the macro-micro entanglement. Since the photon number of the macro-micro entanglement with the optical parametric amplification approach can be about 104, the studies towards the detection of this type of entanglement with human eyes have been extensively conducted. But it is realized that the coarse-grained measurements, such as those with the human eye, generally cannot judge whether macro-micro entanglement exists, and hence cannot be used to prove the considered type of micro-macro entanglement. A way of overcoming this difficulty is to invert the amplification process, bringing the macro system back to the micro level. The entanglement can then be verified by using single-photon detectors. Because local operation and classical communication cannot create entanglement, the de-amplification process will not increase the entanglement and the presence of the entanglement in the end shows that entanglement is present between the amplification and de-amplification process. Inspired by this thought, two groups create and verify mac-micro entanglement between one photon and 108 photons. What they used to amplify the micro states is the displacement operation in phase space, which can be realized by combining a single photon state and a coherent state with a highly asymmetric beam splitter. Because the entanglement is a precondition for a secure quantum key distribution, and the macro-micro entanglement has more photons than the traditional micro entanglement, we will discuss the possibility whether the macro-micro entanglement can be used in quantum key distribution and improve the distance of the quantum key distribution. We point out that the mac-micro entanglement and the binary reverse reconciliation continuous variable quantum key distribution protocol are the same in physics essence. We will introduce a quantum key distribution scheme with two phase entangled coherent states. Although the security proof of the scheme is not complete, it still provides us with the possibility to use the macro-micro entanglement in quantum key distribution.

A Continuous Variable Quantum Key Distribution Protocol Based on Entanglement Swapping of Quasi-Bell Entangled Coherent States

A continuous variable quantum key distribution protocol with entanglement swapping of quasi-Bell entangled coherent states is proposed. As the preliminary step, a sender shares quasi-Bell entangled coherent states with a receiver. After their measurements to distinguish the cases of a zero response, a nonzero even-photon response and an odd-photon response, two legitimate participants fulfill the task of key distribution. The correlations resulting from entanglement swapping of quasi-Bell entangled coherent states and the order rearrangement of transmitted states provide the possibility to protect secret key distribution. In the ideal channel, the success probability increases with the amplitude of the coherent state, and approaches unity when the amplitude of the coherent state is larger than two. However, in the loss channel, the decoherence will introduce error in the generated key, and the error rate increases with the amplitude of the coherent state. When the amplitude of the coherent state is smaller than 0.2 (or so), the error rate approaches zero, although the success probability is less than 0.5 in this case.