Measurement-device-independent Research Articles

Comparative Study of Fast Optimization Method for Four‐Intensity Measurement‐Device‐Independent Quantum Key Distribution Through Machine Learning

AbstractThe four‐intensity protocol for measurement‐device‐independent (MDI) quantum key distribution (QKD) is renowned for its excellent performance and extensive experimental implementation. To enhance this protocol, a machine learning‐driven rapid parameter optimization method is developed. This initial step involved a speed‐up technique that quickly pinpoints the worst‐case scenarios with minimal data points during the optimization phase. This is followed by a detailed scan in the key rate calculation phase, streamlining data collection to fit machine learning timelines effectively. Several machine learning models are assessed—Generalized Linear Models (GLM), k‐Nearest Neighbors (KNN), Decision Trees (DT), Random Forests (RF), XGBoost (XGB), and Multilayer Perceptron (MLP)—with a focus on predictive accuracy, efficiency, and robustness. RF and MLP were particularly noteworthy for their superior accuracy and robustness, respectively. This optimized approach significantly speeds up computation, enabling complex calculations to be performed in microseconds on standard personal computers, while still achieving high key rates with limited data. Such advancements are crucial for deploying QKD under dynamic conditions, such as in fluctuating fiber‐optic networks and satellite communications.

Measurement-device-independent detection of beyond-quantum state

Abstract In quantum theory, a quantum state on a composite system of two parties realizes a non-negative probability with any measurement element with a tensor product form. However, there also exist non-quantum states which satisfy the above condition. Such states are called beyond-quantum states, and cannot be detected by standard Bell tests. To distinguish a beyond-quantum state from quantum states, we propose a measurement-device-independent (MDI) test for beyond-quantum state detection, which is composed of quantum input states on respective parties and quantum measurements across the input system and the target system on respective parties. The performance of our protocol is independent of the forms of the tested states and the measurement operators, which provides an advantage in practical scenarios. We also discuss the importance of tomographic completeness of the input sets to the detection.

One-Photon-Interference Quantum Secure Direct Communication.

Quantum secure direct communication (QSDC) is a quantum communication paradigm that transmits confidential messages directly using quantum states. Measurement-device-independent (MDI) QSDC protocols can eliminate the security loopholes associated with measurement devices. To enhance the practicality and performance of MDI-QSDC protocols, we propose a one-photon-interference MDI QSDC (OPI-QSDC) protocol which transcends the need for quantum memory, ideal single-photon sources, or entangled light sources. The security of our OPI-QSDC protocol has also been analyzed using quantum wiretap channel theory. Furthermore, our protocol could double the distance of usual prepare-and-measure protocols, since quantum states sending from adjacent nodes are connected with single-photon interference, which demonstrates its potential to extend the communication distance for point-to-point QSDC.

Hybrid quantum key distribution: A novel approach for secure end-to-end communication in network infrastructure

The Quantum Key Distribution (QKD) network approach has emerged as a promising solution and has garnered significant interest across various domains. QKD networks can be broadly categorized into two main types: those based on measurement-device-dependent (MDD) protocols and those based on measurement-device-independent (MDI) protocols. A novel network scheme is proposed combining these two protocols to guarantee end-to-end secure communication. It comprises two interconnected networks — the first uses a measurement-device-dependent protocol to connect routers with nearby nodes, while the second employs a measurement-device-independent protocol to interconnect the routers. In the first network, the process begins with Alice (Router) generating two types of weak quantum signals — the first has intensity, frequency and polarization or phase randomly varied, while the second with different delay times. Alice randomly transmits either signal states carrying information or decoy states with varying properties to the receivers (Bobs) over the quantum channels. She also sends a synchronization signal along with the quantum signals. At the receiver end, the synchronization pulse timestamps the incoming quantum signals. Each Bob then randomly shifts the frequencies of the received signals and measures their phase/polarization of the first signal and measures the delay times of the second signal. The secret key is derived by combining the frequency, the delay time and the phase/polarization information of the quantum signals, resulting in longer key lengths. Encoding information across multiple degrees of freedom enables extended key generation for secure communication. However, between the routers, MDI-QKD protocols are used to securely share the keys. This hybrid approach aims to ensure secure end-to-end communication across the network.

Hong–Ou–Mandel Interference in Quantum Optics, Monogamy of Entanglement, Nonorthogonality, and Untrusted Nodes

Quantum key distribution systems with an untrusted intermediate node described by the so-called measurement device independent (MDI) protocol have been actively studied in the last decade. In early works, it was only argued why such a quantum key distribution system ensures the security of distributed keys mentioning that the security proof of the MDI protocol, which was not presented, is similar to that for the basic Bennett‒Brassard 84 (BB84) protocol. For this reason, despite the existing experimental implementations of the MDI quantum key distribution system, physical reasons for the protocol security are still questionable. Such quantum key distribution systems provide a common key between two network nodes connected through the intermediate untrusted node, which does not require protection of the equipment on it, and an eavesdropper sees the entire operation of the equipment, including the results of the operation of photodetectors. In this work, the MDI protocol has been analyzed. It has been shown that the physical reasons for the protocol security are based on fundamental properties such as the interference of photons from different sources, monogamy of entanglement, and nonorthogonality of states. A simple and explicit derivation is given showing the equivalence of the MDI and BB84 protocols and physical reasons for the identity of the corresponding expressions for the length of the final key.

Measurement-device-independent quantum random number generation over 23 Mbps with imperfect single-photon sources

Quantum randomness relies heavily on the accurate characterization of the generator implementation, where the device imperfection or inaccurate characterization can lead to incorrect entropy estimation and practical bias, significantly affecting the reliability of the generated randomness. Measurement-device-independent (MDI) quantum random number generation (QRNG) endeavors to produce certified randomness, utilizing uncharacterized and untrusted measurement devices that are vulnerable to numerous attack schemes targeting measurement loopholes. However, existing implementations have shown insufficient performance thus far. Here, we propose a high-speed MDI-QRNG scheme based on a robust measurement tomography approach against the imperfection of single-photon sources. Compared with the conventional approach, the decoy-state method is introduced to obtain more accurate tomography results and a tighter lower bound of randomness. Finally, by using a high-speed time-bin encoding system, we experimentally demonstrated the scheme and obtained a reliable min-entropy lower bound of 7.37×10−2 bits per pulse, corresponding to a generation rate over 23 Mbps, which substantially outperforms the existing realizations and makes a record in discrete-variable semi-device-independent QRNGs.

Passive Continuous Variable Measurement-Device-Independent Quantum Key Distribution Predictable with Machine Learning in Oceanic Turbulence.

Building an underwater quantum network is necessary for various applications such as ocean exploration, environmental monitoring, and national defense. Motivated by characteristics of the oceanic turbulence channel, we suggest a machine learning approach to predicting the channel characteristics of continuous variable (CV) quantum key distribution (QKD) in challenging seawater environments. We consider the passive continuous variable (CV) measurement-device-independent (MDI) QKD in oceanic scenarios, since the passive-state preparation scheme offers simpler linear elements for preparation, resulting in reduced interaction with the practical environment. To provide a practical reference for underwater quantum communications, we suggest a prediction of transmittance for the ocean quantum links with a given neural network as an example of machine learning algorithms. The results have a good consistency with the real data within the allowable error range; this makes the passive CVQKD more promising for commercialization and implementation.

Verification of continuous-variable quantum memories

A proper quantum memory is argued to consist in a quantum channel which cannot be simulated with a measurement followed by classical information storage and a final state preparation, i.e. with an entanglement breaking (EB) channel. The verification of quantum memories (non-EB channels) is a task in which an honest user wants to test the quantum memory of an untrusted, remote provider. This task is inherently suited for the class of protocols with trusted quantum inputs, sometimes called measurement-device-independent (MDI) protocols. Here, we study the MDI certification of non-EB channels in continuous variable (CV) systems. We provide a simple witness based on adversarial metrology, and describe an experimentally friendly protocol that can be used to verify all non Gaussian incompatibility breaking quantum memories. Our results can be tested with current technology and can be applied to test other devices resulting in non-EB channels, such as CV quantum transducers and transmission lines.

Measurement-device-independent quantum secure multiparty summation based on entanglement swapping

In this paper, we propose a measurement-device-independent (MDI) quantum secure multiparty summation protocol based on entanglement swapping. The protocol is capable of providing a secure modulo-2 summation method for n parties. Our protocol uses Bell states as the information vehicle and establishes encryption through entanglement swapping, and each party encodes the information orderly to complete the summation process through the simple single-qubit operation. In contrast to previous protocols, there is no pre-shared private key sequence and key storage process in our protocol, which helps to reduce the possibility of information leakage in transmission. Our protocol supports multiple summations by n participants, which improves quantum resource utilization. The protocol can be implemented with linear-optical devices. Furthermore, it can resist multiple attack modes including the intercept-resend attack, entangle-and-measure attack, dishonest third-party attack, and parties’ attack. Most significantly, the protocol enables to eliminate all side-channel attacks against detectors based on the MDI principle. Therefore, the protocol has advantages of high security, high efficiency, and good feasibility.

Single-Photon-Memory Measurement-Device-Independent Quantum Secure Direct Communication—Part II: A Practical Protocol and its Secrecy Capacity

In Part I of this two-part letter on single-photon-memory measurement-device-independent quantum secure direct communication (SPMQC), we reviewed the fundamentals and evolution of quantum secure direct communication (QSDC). In this Part II, we propose a practical protocol and analyze its secrecy capacity. In order to eliminate the security loopholes resulting from practical detectors, the measurement-device-independent (MDI) QSDC protocol has been proposed. However, block-based transmission of quantum states is utilized in MDI-QSDC, which requires practical quantum memory that is still unavailable at the time of writing. For circumventing this impediment, we propose the SPMQC protocol for dispensing with high-performance quantum memory. The performance of the proposed protocol is characterized by simulations considering realistic experimental parameters, and the results show that it is feasible to implement SPMQC by relying on existing technology.

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.

Dynamic generation of photonic spatial quantum states with an all-fiber platform.

Photonic spatial quantum states are a subject of great interest for applications in quantum communication. One important challenge has been how to dynamically generate these states using only fiber-optical components. Here we propose and experimentally demonstrate an all-fiber system that can dynamically switch between any general transverse spatial qubit state based on linearly polarized modes. Our platform is based on a fast optical switch based on a Sagnac interferometer combined with a photonic lantern and few-mode optical fibers. We show switching times between spatial modes on the order of 5 ns and demonstrate the applicability of our scheme for quantum technologies by demonstrating a measurement-device-independent (MDI) quantum random number generator based on our platform. We run the generator continuously over 15 hours, acquiring over 13.46 Gbits of random numbers, of which we ensure that at least 60.52% are private, following the MDI protocol. Our results show the use of photonic lanterns to dynamically create spatial modes using only fiber components, which due to their robustness and integration capabilities, have important consequences for photonic classical and quantum information processing.

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.

Measurement-device-independent quantum key distribution with passive time-dependent source side channels

While measurement-device-independent (MDI) quantum key distribution (QKD) allows two trusted parties to establish a shared secret key from a distance without needing to trust a central detection node, their quantum sources must be well characterized, with side channels at the source posing the greatest loophole to the protocol's security. In this paper, we identify a time-dependent side channel in a common polarization-based QKD source that employs a Faraday mirror for phase stabilization. We apply a recently developed numerical proof technique [Phys. Rev. A 99, 062332 (2019)] to quantify the sensitivity of the secret key rate to the quantum optical model for the side channel, and to develop strategies to mitigate the information leakage. In particular, we find that the MDI three-state and BB84 protocols, while yielding the same key rate under ideal conditions, have diverging results in the presence of a side channel, with BB84 proving more advantageous. While we consider only a representative case example, we expect the strategies developed and key rate analysis method to be broadly applicable to other leaky sources.

Https://journals.scholarpublishing.org/index.php/AIVP/issue/view/425

In this paper, we prove the security of the LM05’s two-way quantum key distribution (TWQKD) under the assumption that detector devices in both Alice’s and Bob’s sides are controlled by eavesdroppers. Using a relatively simple method, more practical, we give an analytical proof that LM05’s TWQKD is measurement-device-independent (MDI) security in both the quantum forward channel and the quantum backward channel. This is the first work shows that TWQKD has fully MDI characteristic, thus makes it immune to all possible detector-device-attacks in two-quantum-way in actual implementations.

Simultaneous two-way classical communication and measurement-device-independent quantum key distribution on oceanic quantum channels

Simultaneous two-way classical and quantum (STCQ) communication combines both continuous classical coherent optical communication and continuous-variable quantum key distribution (CV-QKD), which eliminates all detection-related imperfections by being measurement-device-independent (MDI). In this paper, we propose a protocol relying on STCQ communication on the oceanic quantum channel, in which the superposition-modulation-based coherent states depend on the information bits of both the secret key and the classical communication ciphertext. We analyse the encoding combination in classical communication and consider the probability distribution transmittance under seawater turbulence with various interference factors. Our numerical simulations of various practical scenarios demonstrate that the proposed protocol can simultaneously enable two-way classical communication and CV-MDI QKD with just a slight performance degradation transmission distance compared to the original CV-MDI QKD scheme. Moreover, the asymmetric situation outperforms the symmetric case in terms of transmission distance and optical modulation variance. We further take into consideration the impact of finite-size effects to illustrate the applicability of the proposed scheme in practical scenarios. The results show the feasibility of the underwater STCQ scheme, which contributes toward developing a global quantum communication network in free space.

Numerical security proof for the decoy-state BB84 protocol and measurement-device-independent quantum key distribution resistant against large basis misalignment

In this work, we incorporate decoy-state analysis into a well-established numerical framework for key rate calculation, and we apply the numerical framework to decoy-state BB84 and measurement-device-independent (MDI) QKD protocols as examples. Additionally, we combine with these decoy-state protocols what is called ``fine-grained statistics,'' which is a variation of existing QKD protocols that makes use of originally discarded data to get a better key rate. We show that such variations can grant protocols resilience against any unknown and slowly changing rotation along one axis, similar to reference-frame-independent QKD, but without the need for encoding physically in an additional rotation-invariant basis. Such an analysis can easily be applied to existing systems, or even data already recorded in previous experiments, to gain a significantly higher key rate when considerable misalignment is present, extending the maximum distance for BB84 and MDI-QKD and reducing the need for manual alignment in an experiment.

Continuous variable measurement device independent quantum conferencing with postselection

A continuous variable (CV), measurement device independent (MDI) quantum key distribution (QKD) protocol is analyzed, enabling three parties to connect for quantum conferencing. We utilise a generalised Bell detection at an untrusted relay and a postselection procedure, in which distant parties reconcile on the signs of the displacements of the quadratures of their prepared coherent states. We derive the rate of the protocol under a collective pure-loss attack, demonstrating improved rate-distance performance compared to the equivalent non-post-selected protocol. In the symmetric configuration in which all the parties lie the same distance from the relay, we find a positive key rate over 6 km. Such postselection techniques can be used to improve the rate of multi-party quantum conferencing protocols at longer distances at the cost of reduced performance at shorter distances.

Measurement-device-independent one-step quantum secure direct communication

The one-step quantum secure direct communication (QSDC) (Sci. Bull. 67, 367 (2022)) can effectively simplify QSDC’s operation and reduce message loss. For enhancing its security under practical experimental condition, we propose two measurement-device-independent (MDI) one-step QSDC protocols, which can resist all possible attacks from imperfect measurement devices. In both protocols, the communication parties prepare identical polarization-spatial-mode two-photon hyperentangled states and construct the hyperentanglement channel by hyperentanglement swapping. The first MDI one-step QSDC protocol adopts the nonlinear-optical complete hyperentanglement Bell state measurement (HBSM) to construct the hyperentanglement channel, while the second protocol adopts the linear-optical partial HBSM. Then, the parties encode the photons in the polarization degree of freedom and send them to the third party for the hyperentanglement-assisted complete polarization Bell state measurement. Both protocols are unconditionally secure in theory. The simulation results show the MDI one-step QSDC protocol with complete HBSM attains the maximal communication distance of about 354 km. Our MDI one-step QSDC protocols may have potential applications in the future quantum secure communication field.

Robust and adaptable quantum key distribution network without trusted nodes

Quantum key distribution (QKD) networks are promising to serve large numbers of users with information-theoretic secure communication. In QKD networks, the detection-safe protocol, termed measurement-device-independent (MDI) QKD, can naturally enhance realistic security by supporting untrusted measurement nodes. However, the environmental disturbances to quantum states degrade the performance of multi-user communication. Here we propose an MDI-QKD networking scheme with robustness against environmental disturbance and adaptability to multi-user access, where more than two users can generate keys simultaneously regardless of aligning reference frames and compensating channel disturbance on polarization. To achieve this, we introduce the reference-frame-independent protocol as well as a polarization-compensation-free method, design a multi-user measurement unit, and combine it with original two-user units. The scheme is experimentally demonstrated for the improvement of network robustness and adaptability in multi-user scenarios, and the time and device costs of disturbance compensation can be saved from O ( N ) to O ( 1 ) for an N-user network.