Key Generation Rate Research Articles

Cryptographic robustness of practical quantum cryptography: BB84 key distribution protocol

In real fiber-optic quantum cryptography systems, the avalanche photodiodes are not perfect, the source of quantum states is not a single-photon one, and the communication channel is lossy. For these reasons, key distribution is impossible under certain conditions for the system parameters. A simple analysis is performed to find relations between the parameters of real cryptography systems and the length of the quantum channel that guarantee secure quantum key distribution when the eavesdropper’s capabilities are limited only by fundamental laws of quantum mechanics while the devices employed by the legitimate users are based on current technologies. Critical values are determined for the rate of secure real-time key generation that can be reached under the current technology level. Calculations show that the upper bound on channel length can be as high as 300 km for imperfect photodetectors (avalanche photodiodes) with present-day quantum efficiency (η ≈ 20%) and dark count probability (p dark ∼ 10−7).

Quantum key distribution with triggering parametric down-conversion sources

Parametric down-conversion (PDC) sources can be used as triggered single photon sources in quantum key distribution (QKD). Recently, there have been several practical proposals of the decoy state QKD with triggering PDC sources. In this paper, we generalize the passive decoy state idea, originally proposed by Mauerer and Silberhorn. The generalized passive decoy state idea can be applied to cases where either threshold detectors or photon-number-resolving detectors are used. The decoy state protocol proposed by Adachi, Yamamoto, Koashi and Imoto (AYKI) can be treated as a special case of the generalized passive decoy state method. By simulating a recent PDC experiment, we compare various practical decoy state protocols with the infinite decoy state protocol and also compare the cases using threshold detectors and photon-number-resolving detectors. Our simulation result shows that with the AYKI protocol, one can achieve a key generation rate that is close to the theoretical limit of an infinite decoy state protocol. Furthermore, our simulation result shows that a photon-number-resolving detector appears to be not very useful for improving QKD performance in this case. Although our analysis is focused on QKD with PDC sources, we emphasize that it can also be applied to QKD setups with other triggered single photon sources.

Decoy State Quantum Key Distribution with Odd Coherent State

We propose a decoy state quantum key distribution scheme with odd coherent state which follows sub-Poissonian distributed photon count and has low probability of the multi-photon event and vacuum event in each pulse. The numerical calculations show that our scheme can improve efficiently the key generation rate and secure communication distance. Furthermore, only one decoy state is necessary to approach to the perfect asymptotic limit with infinite decoy states in our scheme, but at least two decoy states are needed in other scheme.

Implementation of polarization-coded free-space BB84 quantum key distribution

We report on the implementation of a Bennett-Brassard 1984 quantum key distribution protocol over a free-space optical path on an optical table. Attenuated laser pulses and Pockels cells driven by a pseudorandom number generator are employed to prepare polarization-encoded photons. The sifted key generation rate of 23.6 kbits per second and the quantum bit error rate (QBER) of 3% have been demonstrated at the average photon number per pulse μ = 0.16. This QBER is sufficiently low to extract final secret keys from shared sifted keys via error correction and privacy amplification. We also tested the long-distance capability of our system by adding optical losses to the quantum channel and found that the QBER remains the same regardless of the loss.

Wireless Information-Theoretic Security

This paper considers the transmission of confidential data over wireless channels. Based on an information-theoretic formulation of the problem, in which two legitimates partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through a second independent quasi-static fading channel, the important role of fading is characterized in terms of average secure communication rates and outage probability. Based on the insights from this analysis, a practical secure communication protocol is developed, which uses a four-step procedure to ensure wireless information-theoretic security: (i) common randomness via opportunistic transmission, (ii) message reconciliation, (iii) common key generation via privacy amplification, and (iv) message protection with a secret key. A reconciliation procedure based on multilevel coding and optimized low-density parity-check (LDPC) codes is introduced, which allows to achieve communication rates close to the fundamental security limits in several relevant instances. Finally, a set of metrics for assessing average secure key generation rates is established, and it is shown that the protocol is effective in secure key renewal-even in the presence of imperfect channel state information.

Quantum key distribution with an unknown and untrusted source

The security of a standard bidirectional ``plug-and-play'' quantum key distribution (QKD) system has been an open question for a long time. This is mainly because its source is equivalently controlled by an eavesdropper, which means the source is unknown and untrusted. Qualitative discussion on this subject has been made previously. In this paper, we solve this question directly by presenting the quantitative security analysis on a general class of QKD protocols whose sources are unknown and untrusted. The securities of standard Bennett-Brassard 1984 protocol, $\text{weak}+\text{vacuum}$ decoy state protocol, and one-decoy state protocol, with unknown and untrusted sources are rigorously proved. We derive rigorous lower bounds to the secure key generation rates of the above three protocols. Our numerical simulation results show that QKD with an untrusted source gives a key generation rate that is close to that with a trusted source.

Unconditionally secure quantum key distribution with relatively strong signal pulse

We propose an unconditionally secure quantum key distribution protocol, which uses a relatively strong signal pulse. While our protocol shares similar security bases as the Bennett 1992 protocol with a strong reference pulse, our scheme uses a smaller number of detectors and it is robust against Rayleigh scattering in an optical fiber. We derive a lower bound of secret key generation rate of our protocol and show that our protocol can cover relatively long distances, assuming precise phase modulations and stable interferometers.

Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source

We have experimentally demonstrated a decoy-state quantum key distribution scheme (QKD) with a heralded single-photon source based on parametric down-conversion. We used a one-way Bennett-Brassard 1984 protocol with a four states and one-detector phase-coding scheme, which is immune to recently proposed time-shift attacks, photon-number splitting attacks, and can also be proven to be secure against Trojan horse attacks and any other standard individual or coherent attacks. In principle, the setup can tolerate the highest losses or it can give the highest secure key generation rate under fixed losses compared with other practical schemes. This makes it a quite promising candidate for future quantum key distribution systems.

Fast quantum key distribution with decoy number states

We investigate the use of photon number states to identify eavesdropping attacks on quantum key distribution (QKD) schemes. The technique is based on the fact that different photon numbers traverse a channel with different transmittivity. We then describe two QKD schemes that utilize this method, one of which overcomes the upper limit on the key generation rate imposed by the dead time of detectors when using a heralded source of photons.

New method of decoy state quantum key distribution with a heralded single-photon source

We propose a new method of decoy state quantum key distribution with a heralded single-photon source. Alice uses the parametric down-conversion to generate entangled photon-pairs, one of the pair is used as heralding photon. According to the results of the trigger detector the heralded photons are divided into trigger and non-trigger sets.The states of the photons in the trigger set are used as the signal states and the ones in the non-trigger sets are used as the decoy states. Because of the efficiency of the trigger detector, the two sets both have photons. The yield and error rate of the single-photon are estimated through the yield and error rate of the two sets. This method does not need changing the intensity of the photon source, is easy to implement. Analysis results show that this method can reach the same security distance as with a perfect single photon source; the key generation rate is increased a lot compared with the method with a heralded photon source and is approximately two thirds the rate of the three intensities decoy state quantum key distribution with a heralded photon source.

Study on quantum cryptography using orbital angular momentum states of photons

We present a simple quantum cryptographic scheme that encodes information in two orthogonal orbital angular momentum states. The states used in this scheme are invariant under rotations of the propagation direction，making this implementation independent of the alignment between the reference frames of Alice and Bob. Besides，since the two orbital angular momentum states are orthogonal，100% use of the photons is attained，which increases the key generation rate of the protocol.

Simple and Efficient Quantum Key Distribution with Parametric Down-Conversion

We propose an efficient quantum key distribution protocol based on the photon-pair generation from parametric down-conversion (PDC). It uses the same experimental setup as the conventional protocol, but a refined data analysis enables detection of photon-number splitting attacks by utilizing information from a built-in decoy state. Assuming the use of practical detectors, we analyze the unconditional security of the new scheme and show that it improves the secure key generation rate by several orders of magnitude at long distances, using a high intensity PDC source.

General theory for decoy-state quantum key distribution with an arbitrary number of intensities

We develop a general theory for quantum key distribution (QKD) in both the forward error correction and the reverse error correction cases when the QKD system is equipped with phase-randomized coherent light with an arbitrary number of decoy intensities. For this purpose, generalizing Wang's expansion, we derive a convex expansion of the phase-randomized coherent state. We also numerically check that the asymptotic key generation rates are almost saturated when the number of decoy intensities is three.

Upper bounds of eavesdropper’s performances in finite-length code with the decoy method

Security formulas of quantum key distribution (QKD) with imperfect resources are obtained for finite-length code when the decoy method is applied. This analysis is useful for guaranteeing the security of implemented QKD systems. Our formulas take into account the effect of the vacuum state and dark counts in the detector. We compare the asymptotic key generation rate in presence of dark counts with that without.

Photon-number-resolved heralded-photon source for improved quantum key distribution

We have suppressed multiphoton probability of a heralded-photon source, which is vital for quantum key distribution with a higher secure key generation rate. It is accomplished by utilizing a practical photon-number-resolving detector for triggering resulting in an important step for improved practical quantum key distribution. Heralded-photon source and a practical photon-number-resolving detector capable of real-time processed multiphoton rejection are stably operable at room temperature and enable us to generate a secure key at a distance as long as an ideal single photon source is used.

Differential phase shift quantum key distribution using single-photon detectors based on a sinusoidally gated InGaAs∕InP avalanche photodiode

The authors report a quantum key distribution experiment, in which they implemented a differential phase shift quantum key distribution protocol, using single-photon detectors based on InGaAs∕InP avalanche photodiodes operated with a sinusoidal gating. The single-photon detectors were operated at a repetition frequency of 500MHz with low after pulsing probabilities and low dark counts. A sifted key generation rate of 1.5Mbit∕s was achieved over a communication distance of 15km. Taking account of the security of the protocol against general individual attacks, secure keys can be generated with a rate of 0.33Mbit∕s.

Security of quantum key distribution using weak coherent states with nonrandom phases

We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the key information is encoded in the relative phase of a coherent-state reference pulse and a weak coherent-state signal pulse, as in some practical implementations of the protocol. In contrast to previous work, our proof applies even if the eavesdropper knows the phase of the reference pulse, provided that this phase is not modulated by the source, and even if the reference pulse is bright. The proof also applies to the case where the key is encoded in the photon polarization of a weak coherent-state pulse with a known phase, but only if the phases of the four BB84 signal states are judiciously chosen. The achievable key generation rate scales quadratically with the transmission in the channel, just as for BB84 with phase-randomized weak coherent-state signals (when decoy states are not used). For the case where the phase of the reference pulse is strongly modulated by the source, we exhibit an explicit attack that allows the eavesdropper to learn every key bit in a parameter regime where a protocol using phase-randomized signals is provably secure.

Quantum key distribution with passive decoy state selection

We propose a quantum key distribution scheme which closely matches the performance of a perfect single photon source. It nearly attains the physical upper bound in terms of key generation rate and maximally achievable distance. Our scheme relies on a practical setup based on a parametric downconversion source and present day, nonideal photon-number detection. Arbitrary experimental imperfections which lead to bit errors are included. We select decoy states by classical postprocessing. This allows one to improve the effective signal statistics and achievable distance.

Differential-phase quantum key distribution experiment using a series of quantum entangled photon pairs

We report what we believe to be the first differential-phase quantum key distribution experiment using a series of quantum entangled photon pairs. We employed two outstanding techniques. As an entangled photon source, we used a 1.5 microm band entangled photon pair source based on spontaneous four-wave mixing in a cooled dispersion-shifted fiber. As receivers, photon pairs were actively phase modulated with LiNbO3 phase modulators followed by very stable planar light-wave circuit Mach-Zehnder interferometers, which provided two nonorthogonal measurements. As a consequence, we successfully generated sifted keys with a quantum bit error rate of 8.3% and a key generation rate of 0.3 bit/s and revealed the feasibility of this QKD scheme.

Field trial of differential-phase-shift quantum key distribution using polarization independent frequency up-conversion detectors

We report a field trial of differential phase shift quantum key distribution (QKD) using polarization independent frequency up-conversion detectors. A frequency up-conversion detector is a promising device for achieving a high key generation rate when combined with a high clock rate QKD system. However, its polarization dependence prevents it from being applied to practical QKD systems. In this paper, we employ a modified polarization diversity configuration to eliminate the polarization dependence. Applying this method, we performed a long-term stability test using a 17.6-km installed fiber. We successfully demonstrated stable operation for 6 hours and achieved a sifted key generation rate of 120 kbps and an average quantum bit error rate of 3.14 %. The sifted key generation rate was not the estimated value but the effective value, which means that the sifted key was continuously generated at a rate of 120 kbps for 6 hours.