High-dimensional Quantum Key Distribution Research Articles

High-dimensional quantum key distribution using orbital angular momentum of single photons from a colloidal quantum dot at room temperature

High-dimensional quantum key distribution (HDQKD) is a promising avenue to address the inherent limitations of basic quantum key distribution (QKD) protocols. However, experimental realizations of HDQKD to date have relied on indeterministic photon sources that limit the achievable key rate. In this paper, we demonstrate a full emulation of a HDQKD system using a single colloidal giant quantum dot (gQD) as a deterministic, compact, and room-temperature single-photon source (SPS). We demonstrate a practical protocol by encoding information in a high-dimensional space (d = 3) of the orbital angular momentum of the photons. Our experimental configuration incorporates two spatial light modulators for encoding and decoding the spatial information carried by individual photons. Our experimental demonstration establishes the feasibility of utilizing high radiative quantum yield gQDs as practical SPSs for HDQKD. We also experimentally demonstrate surpassing the traditional d = 2 QKD capacity with comparable error rates, indicating a significant improvement in performance while maintaining reliability.

Hyperentanglement quantum communication over a 50 km noisy fiber channel

High-dimensional entanglement not only offers a high security level for quantum communication but also promises improved information capacity and noise resistance of the system. However, due to various constraints on different high-dimensional degrees of freedom, whether these advantages can bring improvement to the actual implementation is still not well proven. Here we present a scheme to fully utilize these advantages over long-distance noisy fiber channels. We exploit polarization and time-bin hyperentanglement to achieve high-dimensional coding, and observe significant enhancements in secure key rates and noise tolerance that surpass the capabilities of qubit systems. Moreover, the demonstration achieves a distribution up to 50 km, which is the longest distance for high-dimensional entanglement-based quantum key distribution up to date, to our knowledge. Our demonstration validates the potential of high-dimensional entanglement for quantum communications over long-distance noisy channels, paving the way for a resilient and resource-efficient quantum network.

An intelligent threshold selection method to improve orbital angular momentum-encoded quantum key distribution under turbulence

High-dimensional quantum key distribution (HD-QKD) encoded by orbital angular momentum (OAM) presents significant advantages in terms of information capacity. However, perturbations caused by free-space atmospheric turbulence decrease the performance of the system by introducing random fluctuations in the transmittance of OAM photons. Currently, the theoretical performance analysis of OAM-encoded QKD systems exists a gap when concerning the statistical distribution under the free-space link. In this article, we analyzed the security of QKD systems by combining probability distribution of transmission coefficient (PDTC) of OAM with decoy-state BB84 method. To address the problem that the invalid key rate is calculated in the part transmittance interval of the post-processing process, an intelligent threshold method based on neural network is proposed to improve OAM-encoded QKD, which aims to conserve computing resources and enhance system efficiency. Our findings reveal that the ratio of root mean square (RMS) OAM-beam radius to Fried constant plays a crucial role in ensuring secure key generation. Meanwhile, the training error of neural network is at the magnitude around 10−3, indicating the ability to predict optimization parameters quickly and accurately. Our work contributes to the advancement of parameter optimization and prediction for free-space OAM-encoded HD-QKD systems. Furthermore, it provides valuable theoretical insights to support the development of free-space experimental setups.

Efficient information reconciliation for high-dimensional quantum key distribution

The information reconciliation phase in quantum key distribution has significant impact on the range and throughput of any QKD system. We explore this stage for high-dimensional QKD implementations and introduce two novel methods for reconciliation. The methods are based on nonbinary LDPC codes and the Cascade algorithm, respectively, and achieve efficiencies close the Slepian–Wolf bound on q-ary symmetric channels.

Generation of true quantum random numbers with on-demand probability distributions via single-photon quantum walks

Random numbers are at the heart of diverse fields, ranging from simulations of stochastic processes to classical and quantum cryptography. The requirement for true randomness in these applications has motivated various proposals for generating random numbers based on the inherent randomness of quantum systems. The generation of true random numbers with arbitrarily defined probability distributions is highly desirable for applications, but it is very challenging. Here we show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions, when the required “coin” parameters are found with the gradient descent (GD) algorithm. Our theoretical and experimental results exhibit high fidelity for various selected distributions. This GD-enhanced single-photon system provides a convenient way for building flexible and reliable quantum random number generators. Multi-bit random numbers are a necessary resource for high-dimensional quantum key distribution.

State-dependent misalignment and turbulence effects on high-dimensional quantum key distribution with orbital angular momentum

High-dimensional quantum key distribution (HD-QKD) is a topic of growing interest in the quantum communication community, not only for its inherent properties but also for its possible applications. As the typical freedom in HD-QKD, orbital angular momentum (OAM) has made significant advancements in experiments recently. However, in the airborne scenario, different states suffer different amounts of misalignment and turbulence. A complete theoretical analysis model for the transmission characteristics of OAM in atmospheric channels is lacking. In this paper, we systematically analyze the extent to which degeneration including channel power loss and mode crosstalk are influenced by misalignment and turbulence effects. Furthermore, the performance of OAM-encoded HD-QKD system in different dimensions is evaluated while incorporating finite-key effects. We demonstrate that the performance of OAM-encoded HD-QKD will be better at short range, which provide a reference to implement QKD based on task requirements. Since OAM is desired to increase the capacity of QKD system and experiments have already been carried out, our work can not only bridge the gap between theory and practice, but also optimize experimental parameters and improve system performance.

Practical high-dimensional quantum key distribution protocol over deployed multicore fiber

Quantum key distribution (QKD) is a secure communication scheme for sharing symmetric cryptographic keys based on the laws of quantum physics, and is considered a key player in the realm of cyber-security. A critical challenge for QKD systems comes from the fact that the ever-increasing rates at which digital data are transmitted require more and more performing sources of quantum keys, primarily in terms of secret key generation rate. High-dimensional QKD based on path encoding has been proposed as a candidate approach to address this challenge. However, while proof-of-principle demonstrations based on lab experiments have been reported in the literature, demonstrations in realistic environments are still missing. Here we report the generation of secret keys in a 4-dimensional hybrid time-path-encoded QKD system over a 52-km deployed multicore fiber link forming by looping back two cores of a 26-km 4-core optical fiber. Our results indicate that robust high-dimensional QKD can be implemented in a realistic environment by combining standard telecom equipment with emerging multicore fiber technology.

Experimental high-dimensional quantum key distribution with orbital angular momentum

The development and practical applications of quantum key distribution are limited by the channel capacity and high error rate during long-distance transmission. High-dimensional quantum key distribution protocols solve these problems effectively. In this paper, a high-dimensional quantum key distribution protocol based on polarization-orbit angular momentum is achieved, using a decoy state method to ensure the security of the protocol. The experimental results show that the high-dimensional quantum key distribution protocol improves the encoding efficiency and the upper bound of the quantum bit error rate.

High-dimensional Encoding in the Round-Robin Differential-Phase-Shift Protocol

In quantum key distribution (QKD), protocols are tailored to adopt desirable experimental attributes, including high key rates, operation in high noise levels, and practical security considerations. The round-robin differential phase shift protocol (RRDPS), falling in the family of differential phase shift protocols, was introduced to remove restrictions on the security analysis, such as the requirement to monitor signal disturbances, improving its practicality in implementations. While the RRDPS protocol requires the encoding of single photons in high-dimensional quantum states, at most, only one bit of secret key is distributed per sifted photon. However, another family of protocols, namely high-dimensional (HD) QKD, enlarges the encoding alphabet, allowing single photons to carry more than one bit of secret key each. The high-dimensional BB84 protocol exemplifies the potential benefits of such an encoding scheme, such as larger key rates and higher noise tolerance. Here, we devise an approach to extend the RRDPS QKD to an arbitrarily large encoding alphabet and explore the security consequences. We demonstrate our new framework with a proof-of-concept experiment and show that it can adapt to various experimental conditions by optimizing the protocol parameters. Our approach offers insight into bridging the gap between seemingly incompatible quantum communication schemes by leveraging the unique approaches to information encoding of both HD and DPS QKD.

Large-alphabet time-bin quantum key distribution and Einstein–Podolsky–Rosen steering via dispersive optics

Quantum key distribution (QKD) has established itself as a groundbreaking technology, showcasing inherent security features that are fundamentally proven. Qubit-based QKD protocols that rely on binary encoding encounter an inherent constraint related to the secret key capacity. This limitation restricts the maximum secret key capacity to one bit per photon. On the other hand, qudit-based QKD protocols have their advantages in scenarios where photons are scarce and noise is present, as they enable the transmission of more than one secret bit per photon. While proof-of-principle entangled-based qudit QKD systems have been successfully demonstrated over the years, the current limitation lies in the maximum distribution distance, which remains at 20 km fiber distance. Moreover, in these entangled high-dimensional QKD systems, the witness and distribution of quantum steering have not been shown before. Here we present a high-dimensional time-bin QKD protocol based on energy-time entanglement that generates a secure finite-length key capacity of 2.39 bit/coincidences and secure cryptographic finite-length keys at 0.24 Mbits s−1 in a 50 km optical fiber link. Our system is built entirely using readily available commercial off-the-shelf components, and secured by nonlocal dispersion cancellation technique against collective Gaussian attacks. Furthermore, we set new records for witnessing both energy-time entanglement and quantum steering over different fiber distances. When operating with a quantum channel loss of 39 dB, our system retains its inherent characteristic of utilizing large-alphabet. This enables us to achieve a secure key rate of 0.30 kbits s−1 and a secure key capacity of 1.10 bit/coincidences, considering finite-key effects. Our experimental results closely match the theoretical upper bound limit of secure cryptographic keys in high-dimensional time-bin QKD protocols (Mower et al 2013 Phys. Rev. A 87 062322; Zhang et al 2014 Phys. Rev. Lett. 112 120506), and outperform recent state-of-the-art qubit-based QKD protocols in terms of secure key throughput using commercial single-photon detectors (Wengerowsky et al 2019 Proc. Natl Acad. Sci. 116 6684; Wengerowsky et al 2020 npj Quantum Inf. 6 5; Zhang et al 2014 Phys. Rev. Lett. 112 120506; Zhang et al 2019 Nat. Photon. 13 839; Liu et al 2019 Phys. Rev. Lett. 122 160501; Zhang et al 2020 Phys. Rev. Lett. 125 010502; Wei et al 2020 Phys. Rev. X 10 031030). The simple and robust entanglement-based high-dimensional time-bin protocol presented here provides potential for practical long-distance quantum steering and QKD with multiple secure bits-per-coincidence, and higher secure cryptographic keys compared to mature qubit-based QKD protocols.

High-dimensional quantum key distribution using energy-time entanglement over 242 km partially deployed fiber

Entanglement-based quantum key distribution (QKD) is an essential ingredient in quantum communication, owing to the property of source-independent security and the potential on constructing large-scale quantum communication networks. However, implementation of entanglement-based QKD over long-distance optical fiber links is still challenging, especially over deployed fibers. In this work, we report an experimental QKD using energy-time entangled photon pairs that transmit over optical fibers of 242 km (including a section of 19 km deployed fibers). The QKD is realized through the protocol of dispersive-optics QKD (DO-QKD) with high-dimensional encoding to utilize coincidence counts more efficiently. A reliable, high-accuracy time synchronization technology for long-distance entanglement-based QKD is developed based on the distribution of optical pulses in quantum channels. Our system operates continuously for more than 7 d without active polarization or phase calibration. We ultimately generate secure keys with secure key rates of 0.22 bps and 0.06 bps in the asymptotic and finite-size regimes, respectively. It shows that entanglement-based DO-QKD is reliable for long-distance realization in the field if its high requirement on time synchronization is satisfied.

Compact implementation of high-dimensional mutually partially unbiased bases protocol

Transverse spatial mode of light is crucial in high-dimensional quantum key distribution (QKD). However, applications in realistic scenarios suffer from mode-dependent loss and the complexity of system, making it impractical to achieve higher-dimensional, longer-distance and low-cost communications. A mutually partially unbiased bases (MPUBs) protocol has been proposed to fundamentally eliminate the effects induced by mode-dependent loss for long propagation distances and limited sizes of apertures. Here, we demonstrate the first implementation of the MPUBs protocol in dimensions of and 6. By performing a controlled unitary transformation, we can actively switch the measurement basis and enable a compact measurement system. In consequence, a higher encoding dimension is available under finite system resources, resulting in higher key rates and stronger noise resistance. Our work enhances the practicability of MPUBs protocol, and may promote the applications of high-dimensional QKD in quantum networks.

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.

Hybrid High-Dimensional Quantum Key Distribution for a Composable Quantum Network

High-dimensional quantum key distribution (HD-QKD) possesses a higher noise-tolerance ability and secure key rate. In the work presented here, by developing a mapping method for multiple degrees of freedom (DOFs), we propose and implement a HD-QKD system with a quantum bit error rate as low as 0.57%. Our HD-QKD system can stably achieve high secure key rates and is composable, allowing one to build HD quantum networks compatible with multiple DOFs. The results indicate that the proposed scheme could bridge HD and two-dimensional terminals encoded in different DOFs and could support large-scale deployment of quantum networks with high performance. Our work significantly enhances the performance of HD-QKD and strengthens the practical applications of large-scale quantum networks in a hybrid way.

Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States

Temporal modes (TMs) of photons provide an appealing high-dimensional encoding basis for quantum information. While techniques to generate TM states have been established, high-dimensional decoding of single-photon TMs remains an open challenge. In this work, we experimentally demonstrate demultiplexing of five-dimensional TMs of single photons with an average fidelity of 0.96±0.01, characterized via measurement tomography. This is achieved with use of a newly developed device, the multi-output quantum pulse gate (MQPG). We demonstrate a proof-of-principle complete decoder based on the MQPG that operates on any basis from a set of six five-dimensional mutually unbiased bases and is therefore suitable as a receiver for high-dimensional quantum key distribution. Furthermore, we confirm the high-quality operation of the MQPG by performing resource-efficient state tomography with an average fidelity of 0.98±0.02.3 MoreReceived 20 September 2022Accepted 15 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020306Published 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 AreasIntegrated opticsNonlinear waveguidesOptical quantum information processingQuantum communicationQuantum gatesQuantum opticsQuantum tomographyQuantum Information

High-dimensional quantum key distribution implemented with biphotons

We present a high-dimensional measurement device-independent (MDI) quantum key distribution (QKD) protocol employing biphotons to encode information. We exploit the biphotons as qutrits to improve the tolerance to error rate. Qutrits have a larger quantum system; hence they carry more bits of classical information and have improved robustness against eavesdropping compared to qubits. Notably, our proposed protocol is independent of measurement devices, thus eliminating the possibility of side-channel attacks. Also, we employ the finite key analysis approach to study the performance of our proposed protocol under realistic conditions where finite resources are used. Furthermore, we simulated the secret key rate for the proposed protocol in terms of the transmission distance for different fixed amounts of signals. The results prove that this protocol achieves a considerable secret key rate for a moderate transmission distance of 90 km by using 10^{16} signals. Moreover, the expected secret key rate was simulated to examine our protocol’s performance at various intrinsic error rate values, Q=(0.3%,0.6%,1%) caused by misalignment and instability due to the optical system. These results show that reasonable key rates are achieved with a minimum data size of about 10^{14} signals which are realizable with the current technology. Thus, implementing MDI-QKD using finite resources while allowing intrinsic errors due to the optical system makes a giant step forward toward realizing practical QKD implementations.

Time-division technique for quantum optical receivers utilizing single-photon detector array technology and spatial-multiplexing.

Free-space quantum key distribution (QKD) has been gaining popularity in recent years due to its advantages in creating networking options for the quantum internet. One of the main challenges to be addressed in QKD is the achievable secret key rate, which must meet current and future demand. Some of the existing solutions include the use of higher bandwidth electronics, untrusted relay architectures such as Twin-Field QKD, or high dimensional QKD. In this work, we proposed the use of a combination of spatial-multiplexing and time-division techniques, together with the use of 2D single-photon avalanche diode arrays to increase the final throughput. The main challenge in a free-space scenario is the effects introduced by turbulence. This paper demonstrates how appropriate time-division of the spatial-modes can reduce the quantum bit error rate due to optical crosstalk from 36% to 0%. With this technique, we believe the future need for superconducting nanowires single photon detectors, in some free-space QKD applications, can be relaxed, obtaining more cost-effective receiver systems.

Performance evaluation of high-dimensional quantum key distribution with single-photon detector based on avalanche photodiode

The current theoretical analysis model for high-dimensional quantum key distribution (QKD) was developed without carefully considering the dead time and after-pulse of the single-photon detectors. Here, we propose a new model that accounts for these two effects. With this model, we analyze the effects of various properties of the single-photon detector on the performance of the high-dimensional quantum key distribution and show numerically that the high-dimensional quantum key distribution can be achieved up to 180 km with InGaAs/InP-type single-photon detectors. This work can improve our understanding of the factors that determine the performance of high-dimensional quantum key distribution and will help to promote the application of single-photon detectors based on avalanche photodiodes in high-dimensional quantum key distribution.

Scalable implementation of (d+1) mutually unbiased bases for d -dimensional quantum key distribution

A high-dimensional quantum key distribution (QKD) can improve error rate tolerance and the secret key rate. Many $d$-dimensional QKDs have used two mutually unbiased bases (MUBs), while $(d+1)$ MUBs enable a more robust QKD, especially against correlated errors. However, a scalable implementation has not been achieved because the setups have required $d$ devices even for two MUBs or a flexible convertor for a specific optical mode. Here, we propose a scalable and general implementation of $(d+1)$ MUBs using $\log_p d$ interferometers in prime power dimensions $d=p^N$. We implemented the setup for time-bin states and observed an average error rate of 3.8% for phase bases, which is lower than the 23.17% required for a secure QKD against coherent attack in $d=4$.

Security analysis for a mutually partially unbiased bases–based protocol

The recently proposed mutually partially unbiased bases (MPUB)–based protocol, which encodes with Laguerre–Gaussian modes and Hermite–Gaussian modes of the same mode order, can close the security loophole caused by state-dependent diffraction. However, its pessimistic security proof limits the performance, and some practical issues, such as finite-key size and imperfect sources, have not been considered. Here, we improve the key rates of the MPUB-based protocol by accurately estimating the phase error rate. Moreover, the effect of finite-key size and its performance when combined with the decoy state method are demonstrated. Our work broadens the application scope of the MPUB-based protocol, and thereby advances the development of high-dimensional quantum key distribution using spatial modes.