Quantum Key Distribution Protocol Research Articles

Quantum key distribution rates from semidefinite programming

Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to a handful of protocols with highly symmetric measurement bases. Numerical methods can handle arbitrary measurement bases, but either use the min-entropy, which gives a loose lower bound to the von Neumann entropy, or rely on cumbersome dedicated algorithms. Based on a recently discovered semidefinite programming (SDP) hierarchy converging to the conditional von Neumann entropy, used for computing the asymptotic key rates in the device independent case, we introduce an SDP hierarchy that converges to the asymptotic secret key rate in the case of characterised devices. The resulting algorithm is efficient, easy to implement and easy to use. We illustrate its performance by recovering known bounds on the key rate and extending high-dimensional QKD protocols to previously intractable cases. We also use it to reanalyse experimental data to demonstrate how higher key rates can be achieved when the full statistics are taken into account.

Polarization bases compensation towards advantages in satellite-based QKD without active feedback

Long-distance photonic implementations of quantum key distribution protocols have gained increased interest due to the promise of information-theoretic security against unauthorized eavesdropping. However, a significant challenge in this endeavor is photon-polarization getting affected due to the birefringence of fibers in fiber-based implementations, or variation of reference frames due to satellite movement in long-haul demonstrations. Conventionally, active feedback-based mechanisms are employed for real-time polarization tracking. Here, we propose and demonstrate an alternative approach via a proof-of-principle experiment over an in-lab entanglement-based (BBM92) protocol. In this approach, we perform a quantum state tomography to arrive at optimal measurement bases for any one party resulting in maximal (anti-)correlation in measurement outcomes of both parties. Our polarization-entangled bi-photons have 94% fidelity with a singlet state and a Concurrence of 0.92. By considering a representative 1 ns coincidence window span, we achieve a quantum-bit-error-rate (QBER) of ≈5%, and a key rate of ≈35 Kbps. The performance of our implementation is independent of any local polarization rotation. Finally, using optimization methods we achieve the best trade-off between the key rate, QBER, and balanced key symmetry. Our approach obviates the need for active polarization tracking. It is also applicable to such demonstrations with non-maximally entangled states and prepare-and-measure-based protocols with partially polarized single-photon sources.

Optimal Statistical Analyses of Bell Experiments

We show how both smaller and more reliable p-values can be computed in Bell-type experiments by using statistical deviations from no-signalling equalities to reduce statistical noise in the estimation of Bell’s S or Eberhard’s J. Further improvement was obtained by using the Wilks likelihood ratio test based on the four tetranomially distributed vectors of counts of the four different outcome combinations, one 4-vector for each of the four setting combinations. The methodology was illustrated by application to the loophole-free Bell experiments of 2015 and 2016 performed in Delft and Munich, at NIST, and in Vienna, respectively, and also to the earlier (1998) Innsbruck experiment of Weihs et al. and the recent (2022) Munich experiment of Zhang et al., which investigates the use of a loophole-free Bell experiment as part of a protocol for device-independent quantum key distribution (DIQKD).

Quantum and Semi–Quantum key Distribution in Networks

In this paper, we utilize the potential offered by multidimensional separable states (MSS) for secure and simultaneous distributions of keys in a layered network. We present protocols for both quantum and semi-quantum key distribution and discuss their robustness against various eavesdropping strategies. We provide a procedure to identify the requisite resource states to generalize these protocols for arbitrary layered networks. Finally, we study the interrelation between the local dimensionalities of states and achievable key rates in a given layer. These proposals are realizable with current technology, thanks to the employment of MSS and many advances in the generation, manipulation, and measurement of higher-dimensional orbital angular momentum states of light.

Simultaneous transmission of hyper-entanglement in three degrees of freedom through a multicore fiber

Entanglement distribution is at the heart of most quantum communication protocols. Inevitable loss of photons along quantum channels is a major obstacle for distributing entangled photons over long distances, as the no-cloning theorem forbids the information to simply be amplified along the way as is done in classical communication. It is therefore desirable for every successfully transmitted photon pair to carry as much entanglement as possible. Spontaneous parametric down-conversion (SPDC) creates photons entangled in multiple high-dimensional degrees of freedom simultaneously, often referred to as hyper-entanglement. In this work, we use a multicore fiber (MCF) to show that energy-time and polarization degrees of freedom can simultaneously be transmitted in multiple fiber cores, even maintaining path entanglement across the cores. We verify a fidelity to the ideal Bell state of at least 95% in all degrees of freedom. Furthermore, because the entangled photons are created with a center wavelength of 1560 nm, our approach can readily be integrated into modern telecommunication infrastructure, thus paving the way for high-rate quantum key distribution and many other entanglement-based quantum communication protocols.

Entanglement based six-state quantum cryptography protocol: exact proof of security

A novel quantum key distribution (QKD) protocol is proposed, which uses six states of three states in two bases. The protocol provides a greater range of key distribution compared to known QKD protocols. The protocol has an accurate proof of secrecy based on fundamental entropy uncertainty relations, the use of which is possible with the entanglement version of the protocol. The implementation of the protocol does not require adjustment of the polarization state at the output of the communication line, since the receiving side does not use active polarization-sensitive elements—phase modulators, which virtually excludes active probing of the active elements of the system.

BB84 quantum key distribution transmitter utilising broadband sources and a narrow spectral filter.

The secure nature of Quantum Key Distribution (QKD) protocols makes it necessary to ensure that the single photon sources are indistinguishable. Any spectral, temporal or spatial discrepancy between the sources would lead to a breach in the security proofs of the QKD protocols. Traditional, weak-coherent pulse implementations of polarization-based QKD protocols have relied on identical photon sources obtained through tight temperature control and spectral filtering. However, it can be challenging to keep the temperature of the sources stable over time, particularly in a real-world setting, meaning photon sources can become distinguishable. In this work, we present an experimental demonstration of a QKD system capable of achieving spectral indistinguishability, over a 10°C range, using a combination of broadband sources, super-luminescent light emitting diodes (SLEDs), along with a narrow band-pass filter. The temperature stability could be useful in a satellite implementation, where there may be temperature gradients over the payload, particularly on a CubeSat.

Practical Demonstration of Quantum Key Distribution Protocol with Error Correction Mechanism

Practical Demonstration of Quantum Key Distribution Protocol with Error Correction Mechanism

Role of Steering Inequality in Quantum Key Distribution Protocol

Violation of Bell's inequality has been the mainspring for secure key generation in an entanglement assisted Quantum Key Distribution (QKD) protocol. Various contributions have relied on the violation of Bell inequalities to build an appropriate QKD protocol. Residing between Bell nonlocality and entanglement, there exists a hybrid trait of correlations, namely correlations exhibited through the violation of steering inequalities. However, such correlations have not been put to use in QKD protocols as much as their stronger counterpart, the Bell violations. In the present work, we show that the violations of the Cavalcanti–Jones–Wiseman–Reid (CJWR) steering inequalities can act as key ingredients in an entanglement assisted QKD protocol. We work with arbitrary two-qubit entangled states, and characterize them by their utility in such protocols. The characterization is based on the quantum bit error rate and violation of the CJWR inequality. Furthermore, we show that subsequent applications of local filtering operations on initially entangled states exhibiting no violation, lead to violations necessary for the successful implementation of the protocol. An additional vindication of our protocol is provided by the use of absolutely Bell–Clauser–Horne–Shimony–Holt (Bell–CHSH) local states, states which remain Bell–CHSH local even under global unitary operations.Quanta 2023; 12: 1–21.

Robust polarization state generation for long-range quantum key distribution.

We present a new compact and robust polarization state transmitter designed to execute the BB84 quantum key distribution protocol. Our transmitter prepares polarization states using a single commercial-off-the-shelf phase modulator. Our scheme does not require global biasing to compensate thermal and mechanical drifts, as both of the system's two time-demultiplexed polarization modes share a single optical path. Furthermore, the transmitter's optical path entails a double-pass through the phase modulation device for each polarization mode, allowing multiple phase rotations to be impinged on each light pulse. We present a proof-of-concept prototype of this transmitter topology and demonstrate a mean intrinsic quantum bit error rate below 0.2% over a 5 hour measurement.

Amplitude damping error on QKD: Effect and a probable bypass

Quantum cryptography was proposed as a counter to the capacity of quantum computers to break classical cryptosystems. A broad subclass of quantum cryptography, called quantum key distribution (QKD), relies on quantum mechanical process for secure distribution of the keys. Quantum channels are inherently noisy, and therefore these protocols will be susceptible to noise as well. In this paper, we study the performance of two QKD protocols — BB84 and E91 under amplitude damping error. We show that while E91 protocol loses its security immediately due to loss of entanglement, the performance of BB84 protocol reduces to random guessing with increasing time. Next, we consider the action of an Eve on the BB84 protocol under amplitude damping noise, who is restricted to guessing the outcome of the protocol only. Under this restriction, we show that Eve can still do better than random guessing when equipped with the characteristics of the noisy channel. Finally, we propose a modification of the BB84 protocol which retains the security of the original protocol, but ensures that Eve cannot get any advantage in guessing the outcome, even with complete channel information.

Scalable high-rate twin-field quantum key distribution networks without constraint of probability and intensity

Implementation of a twin-field quantum key distribution network faces limitations, including the low tolerance of interference errors for phase-matching-type protocols and the strict constraint regarding intensity and probability for sending-or-not-sending-type protocols. Here we propose a two-photon twin-field quantum key distribution protocol and achieve twin-field-type two-photon interference through postmatching phase-correlated single-photon interference events. We exploit the noninterference mode as the code mode to highly tolerate interference errors and the two-photon interference naturally removes the intensity and probability constraint. Therefore, our protocol can transcend the above-mentioned limitations while breaking the secret key capacity of repeaterless quantum key distribution. Simulations show that for a four-user network, under which each node with fixed system parameters can dynamically switch different attenuation links, the key rates of our protocol for all six links can either exceed or approach the secret key capacity. However, the key rates of all links are lower than the key capacity when using phase-matching-type protocols. Additionally, four of the links could not extract the key when using sending-or-not-sending-type protocols. We anticipate that our protocol can facilitate the development of practical and efficient quantum networks.

Application and Development of QKD-Based Quantum Secure Communication.

Quantum key distribution (QKD) protocols have unique advantages of enabling symmetric key sharing with information-theoretic security (ITS) between remote locations, which ensure the long-term security even in the era of quantum computation. QKD-based quantum secure communication (QSC) enhancing the security of key generation and update rate of keys, which could be integrated with a variety of cryptographic applications and communication protocols, has become one of the important solutions to improve information security. In recent years, the research on QKD has been active and productive, the performance of novel protocol systems has been improved significantly, and the feasibility of satellite-based QKD has been experimentally verified. QKD network construction, application exploration, and standardization have been carried out in China as well as other countries and regions around the world. Although QKD-based QSC applications and industrialization are still in the initial stage, the research and exploration momentum is positive and more achievements could be expected in the future.

Nonlocal Temporal Interferometry for Highly Resilient Free-Space Quantum Communication

Entanglement distribution via photons over long distances enables many applications, including quantum key distribution, which provides unprecedented privacy. The inevitable degradation of entanglement through noise accumulated over long distances remains one of the key challenges in this area. Exploiting the potential of higher-dimensional entangled photons promises to address this challenge, but poses extreme demands on the experimental implementation. Here, we present a long-range free-space quantum link, distributing entanglement over 10.2 km with flexible dimensionality of encoding by deploying a phase-stable nonlocal Franson interferometer. With this distribution of multidimensional energy-time entangled photons, we analyze the achievable key rate in a dimensionally adaptive quantum key distribution protocol that can be optimized with respect to any environmental noise conditions. Our approach enables and emphasizes the power of high-dimensional entanglement for quantum communication, yielding a positive asymptotic key rate well into the dawn of the day.Received 15 March 2022Revised 16 January 2023Accepted 13 February 2023DOI:https://doi.org/10.1103/PhysRevX.13.021001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum channelsQuantum communicationQuantum cryptographyQuantum entanglementQuantum information theoryQuantum networksQuantum Information

An Investigation of the Impacts of Available Real Single-photon Sources on Quantum Communication Secure Length

Abstract: One of the most significant applications of single-photon sources is secure quantum communication. In this research, the security of the most famous protocol of quantum key distribution (BB84) has been studied by considering the characteristics of a single-photon source. This paper derives the impact of propagation on photon statistics. The result reveals that the propagation leads to a change in its value, especially in long distances. Besides, the parameter deviation from an ideal source causes a decrease in the confident length. We achieved a difference of up to 1800 km for the safe distance by studying the relation for minimum transmission coefficient in available single-photon sources. Keywords: Quantum communication, Quantum key distribution, Security, Single-photon source.

Quantum Key Distribution Protocols Based on Heisenberg’s Uncertainty

The proposed article is devoted to the analysis of quantum key distribution protocols based on the Heisenberg uncertainty. The peculiarity of this topic lies in the fact that modern methods of key distribution, which use classical calculations at their core, have significant drawbacks, in contrast to quantum key distribution. This problem concerns all types of algorithms and systems for encrypting secret information, both symmetric encryption with a private key and asymmetric encryption with a public key. An example is that in a communication channel protected by quantum key distributions, it is possible to detect an interceptor between two legal network entities using the principles laid down in quantum physics at the beginning of the last century. Principles and theorems such as the Heisenberg principle, quantum entanglement, superposition, quantum teleportation, and the no-cloning theorem. The field of study of this topic is a promising and rapidly developing area in the field of information security and information protection. There are already created commercial products with the implementation of some of the quantum key distribution protocols. Many of the created products are used in various spheres of human activity. The relevance of applying quantum key distribution protocols under ideal conditions without taking into account errors in the form of quantum noise is analyzed. The implementation of two quantum key distribution protocols based on the Heisenberg uncertainty principle is demonstrated, as well as the results of the appearance of keys and the probability of occurrence of each of them. The purpose of the article is aimed at analyzing and researching quantum key distribution protocols based on Heisenberg uncertainty. The article discusses the advantages and disadvantages of the BB84, B92 quantum key distribution protocols.

Surpassing the repeaterless bound with a photon-number encoded measurement-device-independent quantum key distribution protocol

Decoherence is detrimental to quantum key distribution (QKD) over large distances. One of the proposed solutions is to use quantum repeaters, which divide the total distance between the users into smaller segments to minimise the effects of the losses in the channel. Here we introduce a measurement-device-independent protocol which uses high-dimensional states prepared by two distant trusted parties and a coherent total photon number detection for the entanglement swapping measurement at the repeater station. We present an experimentally feasible protocol that can be implemented with current technology as the required states reduce down to the single-photon level over large distances. This protocol outperforms the existing measurement-device-independent and twin-field QKD protocols by achieving better key rates in general and higher transmission distance in total when experimental imperfections are considered. It also surpasses the fundamental limit of the repeaterless bound at a much shorter transmission distance in comparison to the existing TF-QKD protocols.

Alternative schemes for twin-field quantum key distribution with discrete-phase-randomized sources

The twin-field quantum key distribution (TF-QKD) protocol and its variants can overcome the well-known rate-loss bound without quantum repeaters, which have attracted significant attention. Generally, to ensure the security of these protocols, weak coherent states with continuous randomized phases are always assumed in the test mode. However, this assumption is difficult to meet in practice. To bridge the gap between theory and practice, we propose two alternative discrete-phase-randomized (DPR)-twin-field quantum key distribution protocols, which remove the phase sifting procedure in the code mode. Simulation results show that when compared with previous discrete-phase-randomized-twin-field quantum key distribution protocols, our modified protocols can significantly improve the secret key rate in the low channel loss range, which is very promising for practical twin-field quantum key distribution systems.

Plug‐and‐Play Continuous Variable Measurement‐Device‐Independent Quantum Key Distribution

AbstractIn this paper, a continuous variable (CV) measurement‐device‐independent (MDI) quantum key distribution (QKD) protocol using Gaussian modulated coherent states is proposed. The MDI is first proposed to resist the attacks on the detection equipment by introducing an untrusted relay. However, the necessity of propagation of local oscillator between legitimate users and the relay makes the implementation of CV‐MDI‐QKD highly impractical. By introducing the plug‐and‐play (P&P) technique into CV‐MDI‐QKD, the problems of polarization drifts caused by environmental disturbance and the security loopholes during the local oscillator transmission are solved naturally. The proposed scheme is superior to the previous CV‐MDI‐QKD protocol on the aspect of implementation. The security bounds of the P&P CV‐MDI‐QKD under the Gaussian collective attack are analyzed. It is believed that the technique presented in this paper can be extended to quantum network.

Afterpulse effects in quantum key distribution without monitoring signal disturbance.

The round-robin differential phase shift (RRDPS) quantum key distribution (QKD) protocol is the only one that does not require monitoring of signal disturbance. Moreover, it has been proven that RRDPS has excellent performance of resistance to finite-key effects and high error rate tolerance. However, the existing theories and experiments do not take the afterpulse effects into account, which cannot be neglected in high-speed QKD systems. Here, we propose a tight finite-key analysis with afterpulse effects. The results show that the non-Markovian afterpulse RRDPS model optimizes the system performance considering afterpulse effects. The advantage of RRDPS over decoy-state BB84 under short-time communication still holds at typical values of afterpulse.