Continuous-variable entanglement distillation and noncommutative central limit theorems

Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced.

The rate at which quantum communication tasks can be performed using direct transmission is fundamentally hindered by the channel loss. Quantum repeaters allow, in principle, to overcome these limitations, but their introduction necessarily adds an additional layer of complexity to the distribution of entanglement. This additional complexity - along with the stochastic nature of processes such as entanglement generation, Bell swaps, and entanglement distillation - makes finding good quantum repeater schemes non-trivial. We develop an algorithm that can efficiently perform a heuristic optimisation over a subset of quantum repeater schemes for general repeater platforms. We find a strong improvement in the generation rate in comparison to an optimisation over a simpler class of repeater schemes based on BDCZ repeater schemes. We use the algorithm to study three different experimental quantum repeater implementations on their ability to distribute entanglement, which we dub \emph{information processing} implementations, \emph{multiplexed} implementations, and combinations of the two. We perform this heuristic optimisation of repeater schemes for each of these implementations for a wide range of parameters and different experimental settings. This allows us to make estimates on what are the most critical parameters to improve for entanglement generation, how many repeaters to use, and which implementations perform best in their ability to generate entanglement.

Purpose of the study: systematization and critical analysis of existing approaches to error suppression in quantum repeaters, as well as to assess their advantages and limitations for the implementation of scalable quantum networks and the quantum internet. Methods of research: the paper provides a detailed analysis of modern literature, including a comparison of various quantum repeater schemes, as well as an assessment of resource costs and performance. Result(s): quantum repeaters can be divided into three generations, each of which demonstrates optimal efficiency under certain conditions. The first generation, implementing probabilistic error suppression by generating heralded entanglement and two-way entanglement distillation, is easy to implement and provides the basic functionality of a quantum network, but requires significant time due to the need to exchange classical signals and long-term storage of quantum states. The second generation combines probabilistic entanglement generation with deterministic operation error suppression using quantum error correction, which reduces the requirements for long-term quantum memory, although the exchange of classical signals between neighboring nodes remains mandatory. The third generation relies entirely on deterministic error suppression using one-way classical communication, which allows for a significant reduction in time delays and high entanglement generation rates, despite the need for a denser arrangement of repeaters and high-quality local gates. In addition, the review covers new areas such as memoryless repeaters and all-photonic repeaters. The conducted comparative analysis of resource costs demonstrates that optimization of repeater operating parameters is a key factor for the implementation of scalable quantum networks, which is of direct importance for quantum key distribution, quantum metrology, and distributed quantum computing. Scientific novelty: the scientific novelty lies in the integration of disparate approaches to the implementation of quantum repeaters into a single holistic representation, which allows for an objective assessment of their efficiency by key parameters. The review highlights the potential for new classes of repeaters, such as memoryless repeaters and all-photonic circuits, to become important elements in the development of a quantum internet.

Shor and Preskill (see Phys. Rev. Lett., vol.85, p.441, 2000) have provided a simple proof of security of the standard quantum key distribution scheme by Bennett and Brassard (1984) by demonstrating a connection between key distribution and entanglement purification protocols (EPPs) with one-way communications. Here, we provide proofs of security of standard quantum key distribution schemes, Bennett and Brassard and the six-state scheme, against the most general attack, by using the techniques of two-way entanglement purification. We demonstrate clearly the advantage of classical post-processing with two-way classical communications over classical post-processing with only one-way classical communications in quantum key distribution (QKD). This is done by the explicit construction of a new protocol for (the error correction/detection and privacy amplification of) Bennett and Brassard that can tolerate a bit error rate of up to 18.9%, which is higher than what any Bennett and Brassard scheme with only one-way classical communications can possibly tolerate. Moreover, we demonstrate the advantage of the six-state scheme over Bennett and Brassard by showing that the six-state scheme can strictly tolerate a higher bit error rate than Bennett and Brassard. In particular, our six-state protocol can tolerate a bit error rate of 26.4%, which is higher than the upper bound of 25% bit error rate for any secure Bennett and Brassard protocol. Consequently, our protocols may allow higher key generation rate and remain secure over longer distances than previous protocols. Our investigation suggests that two-way entanglement purification is a useful tool in the study of advantage distillation, error correction, and privacy amplification protocols.

In this section, I wish to put quantum key distribution (QKD) in the wider context of a cryptosystem. I shall discuss informally some aspects that are considered important. The questions I wish to answer here are: “What are the ingredients needed to make a QKD-based cryptosystem work? What services does it bring? What are its limitations?”

Quantum correlations or entanglement is a basic ingredient for many applications of quantum information theory.One important application using quantum entanglement exploits the correlation nature of entangled photon states is quantum key distribution, which is proven unbreakable in principle and provides the highest possible security that is impossible in classical information theory. However, generating entangled photon pairs is not a simple task -- only approximately one out of a million pump photons decay into a signal and idler photon pair. This low rate of entangled photon pairs is further reduced by the overhead required in order for the rectification of the inevitable errors due to channel imperfections or caused by potential eavesdroppers. As a consequence, quantum key distribution suffers from a low bit rate, which is in the order of hundreds to thousands bits per second or below. On the other hand, the classical public key distribution does not impose a tight limit on the transmission rate. However, it is subject to the risks of eavesdroppers sitting in the middle of the insecure channel. In this paper, we propose a hybrid key distribution method which uses public key distribution method to generate a raw key, and then uses entanglement assisted communication to modify the raw key by inserting a number of quantum bits in the raw key. Building upon the foundation of the unconditional security of quantum key distribution, we use the privacy amplification to make the affection of inserted bits expand to a whole key. Our quantum entanglement assisted key distribution scheme greatly improves the efficiency of key distribution while without compromising the level of security achievable by quantum cryptography.

Although the quantum technology introduces an unprecedented threat to the classical encryption field, the combination of Quantum Key Distribution (QKD) and one-time pad makes the absolutely secure encryption possible. However the key distribution rate of most QKD systems still cannot meet the requirements of practical applications. The complex QKD post-processing is one of the largest obstacles to improving the key distribution rate. In this paper, the design and implementation of a multi-thread QKD post-processing software is introduced, including the motivation, architecture and communication protocol. The QKD post processing software is flexible, efficient and easy to implement.

Security is an increasingly growing concern for network communications and video is an emerging segment of network traffic that uses large amounts of bandwidth. Streaming video, vs. downloading a video for later viewing, requires a continuous, high data rate. The data rate will vary depending on the quality of the video. Video surveillance is a streaming video application that in addition may require securing the data stream to prevent others from viewing it as well as prevent any tampering of that video stream. There are two parts to secure communication, key distribution and ciphers. A cipher requires a secret key that is used to encrypt data (plaintext), transforming it into an unreadable form (ciphertext) and then to decrypt it back into its original form. Key distribution is the method used to exchange the secret key between the desired end users and no one else. Current block ciphers are relatively slow compared to existing bandwidth because they require a substantial amount of processing that must compete for CPU cycles with the video encoding and compression processing. Frequently changing keys is thought to increase security, but the public key exchange method requires even more processing than the cipher. Cipher and key exchange processing can be off-loaded from the CPU, when the communication end point is the other end of the link, by using dedicated hardware called a link encryptor. Current classical security algorithms are based on the perceived computational complexity of certain mathematical functions and have not been proved secure. The public key algorithm is at risk from future quantum computers, whereas block ciphers are only weakened and an easy fix is to double the length of the key. Both are constantly at risk from a potential break through algorithm. Communications channels that exploit properties unique to quantum systems have been shown to enable functionality that cannot be achieved by classical means. If a high level of security is deemed necessary for the video stream, one might consider the use of a One-Time-Pad cipher [Wikipedia 2010], the only provably secure cipher, along with Quantum Key Distribution (QKD), also a provably secure method of exchanging the secret keys used by a cipher. QKD is a protocol based on the quantum laws of physics and is provably information theoretically secure to accomplish key distribution [Gisin, et al., 2002]. QKD keys, when used with a One-Time-Pad cipher, can provide secure communications. A One-Time-Pad cipher algorithm performs an Exclusive OR (XOR) on a random secret key and the message. This is a simple operation that incurs little overhead compared to the more common

For the past few years, the security of practical quantum key distribution systems has attracted a lot of attention. Device-independent quantum key distribution was proposed to design a real-life secure quantum key distribution system with imperfect and untrusted quantum devices. In this paper, we analyzed the security of BB84 protocol in a device-independent scenario based on the entanglement distillation method. Since most of the reported loopholes are in receivers of quantum key distribution systems, we focus on condition that the transmitter of the system is perfectly coincident with the requirement of the BB84 protocol, while the receiver can be controlled by eavesdropper. Finally, the lower bound of the final secret-key rate was proposed and we explained why the secure-key rate is similar to the well-known result for the original entanglement distillation protocol.

Quantum cryptography, and especially quantum key distribution (QKD), is steadily progressing to become a viable tool for cryptographic services. In recent years we have witnessed a dramatic increase in the secure bit rate of QKD, as well as its extension to ever longer fibre- and air-based links and the emergence of metro-scale trusted networks. In the foreseeable future even global-scale communications may be possible using quantum repeaters or Earth–satellite links. A handful of start-ups and some bigger companies are already active in the field. The launch of an initiative to form industrial standards for QKD, under the auspices of the European Telecommunication Standards Institute, described in the paper by Laenger and Lenhart in this Focus Issue, can be taken as a sign of the growing commercial interest.

With the development of quantum computers, that can break current classical encryption schemes, unconditionally secure quantum key distribution (QKD) will become very important. Current fiber-based QKD implementations are limited to a few hundred kilometers due to optical losses in fiber and cannot be used with mobile platforms. A free space QKD system has recently been demonstrated over very large distances using entangled photons. However, due to the extremely high pointing accuracy required, the implementation of this QKD approach is very challenging and power demanding. Here we describe a new type of QKD link that uses modulating retro-reflectors. Our approach reduces pointing requirements by orders of magnitude, allowing an increase in pointing tolerance from microradians to tens of milliradians. Additionally, it reduces power requirements on the moving platform and has potential of reducing some influence of turbulence on the secure key distribution rate. Our approach relies on new, high extinction surface-normal multiple quantum well modulators with a maximum modulation rate of 100 MHz. We report on a BB84 QKD link using our system in the laboratory.

Quantum key distribution (QKD) provides the opportunity to deliver unconditional communication security. The most robust version of QKD relies on quantum entanglement. Very recently, ubiquitous deployment of such entanglement-based QKD over large distances has moved closer to reality, as verified by quantum entanglement distribution from a low Earth orbit satellite. We will demonstrate that this robust form of QKD via space will require a renewed focus on short-block length error-correcting codes in order to facilitate the reconciliation phase of the key distribution. Focusing on discrete variable QKD and adopting the low data rates consistent with measured entanglement distribution from space, we quantify the benefits of state-of-the-art short- block length codes in the context of device- independent QKD. Our results highlight the trade- off between the attainable key throughput vs the communication latency encountered in space-based implementations of this ultra-secure technology.

How to improve the key distribution efficiency is key technique in quantum key distribution. An efficient quantum key distribution (QKD) protocol based on Orbital Angular Momentum (OAM) states in the d-dimension Hilbert space is presented in this paper. In the protocol, each photon carries log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> d bits information, and the key distribution efficiency is improved greatly. In addition, the numerical simulation for this key distribution protocol are also given to show the availability of the protocol.

Large-scale quantum networks with thousands of nodes require scalable network protocols and physical hardware to realize. In this paper, we introduce packet switching as a paradigm for quantum data transmission in both future and near-term quantum networks. We propose a classical-quantum data frame structure and explore methods of frame generation and processing. Further, we present conceptual designs for a quantum reconfigurable optical add-drop multiplexer to realize the proposed transmission scheme. Packet switching allows for a universal design for a next-generation Internet where classical and quantum data share the same network protocols and infrastructure. In this quantum networking paradigm, entanglement distribution, as with quantum key distribution, is an application built on top of the quantum network rather than as a network designed especially for those purposes. For analysis of the network model, we simulate the feasibility of quantum packet switching for some preliminary models of quantum key and entanglement distribution. Finally, we discuss how our model can be integrated with other network models toward a realization of the quantum Internet.

Quantum key distribution (QKD) is a cornerstone of secure communication in the quantum era, yet most existing protocols are designed for point-to-point transmission, limiting their scalability in networked environments. In this work, we introduce Loop-Back QKD, a novel QKD protocol that supports both two-party linear configurations and scalable multiuser ring topologies. By leveraging a structured turn-based mechanism and bidirectional pulse propagation, the protocol enables efficient key distribution while reducing the quantum bit error rate (QBER) through a multi-pulse approach. Unlike trusted-node QKD networks, Loop-Back QKD eliminates intermediate-node vulnerabilities, as secret keys are never processed by intermediate nodes. Furthermore, unlike Measurement-Device-Independent (MDI-QKD) and Twin-Field QKD (TF-QKD), which require complex entanglement-based setups, Loop-Back QKD relies solely on direct polarization transformations, reducing vulnerability to side-channel attacks and practical implementation challenges. Additionally, our analysis indicates that multi-pulse Loop-Back QKD can tolerate higher QBER thresholds. However, this increased robustness comes at the cost of a lower key rate efficiency compared to standard QKD schemes. This design choice enhances its robustness against real-world adversarial threats, making it a strong candidate for secure multiuser communication in local and metropolitan-scale quantum networks.