Advances in Quantum Cryptography (1906.01645v1)

Abstract: Quantum cryptography is arguably the fastest growing area in quantum information science. Novel theoretical protocols are designed on a regular basis, security proofs are constantly improving, and experiments are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. In this review, we provide both a general introduction and a state of the art description of the recent advances in the field, both theoretically and experimentally. We start by reviewing protocols of quantum key distribution based on discrete variable systems. Next we consider aspects of device independence, satellite challenges, and high rate protocols based on continuous variable systems. We will then discuss the ultimate limits of point-to-point private communications and how quantum repeaters and networks may overcome these restrictions. Finally, we will discuss some aspects of quantum cryptography beyond standard quantum key distribution, including quantum data locking and quantum digital signatures.

• The paper surveys quantum key distribution protocols, emphasizing improved security via decoy states and device-independent approaches.
• It rigorously analyzes both discrete and continuous-variable QKD, highlighting experimental implementations like satellite-based and fiber-optic systems.
• The review outlines ultimate rate-loss trade-offs and quantum repeater designs, offering actionable insights for building scalable secure networks.

Comprehensive Review of Advances in Quantum Cryptography

Introduction and Motivation

The field of quantum cryptography has experienced significant development, driven largely by the interplay between foundational quantum information principles—such as entanglement, the no-cloning theorem, and teleportation—and the practical necessity of secure communication in the presence of advancing computational and cryptanalytic threats. This review comprehensively covers theoretical protocols, experimental progress, security proofs, side-channel attacks, and the ultimate limits and networking prospects of quantum cryptography. It also addresses practical aspects, such as scalability, hardware integration, and deployment over both terrestrial and satellite networks.

Quantum Key Distribution: Protocols and Security Foundations

Discrete-Variable Protocols

The review provides a detailed treatment of the canonical DV-QKD protocols such as BB84, the six-state, and B92 protocols, along with their security proofs against individual, collective, and coherent attacks. The Csiszár-Körner framework and the Holevo bound are emphasized as fundamental tools for estimating key rates under different reconciliation strategies (direct and reverse). The trade-off between key rate, distance, and practical assumptions—especially in the presence of multiphoton pulses, photon-number-splitting (PNS) attacks, and imperfect single-photon sources—leads to the development and rigorous analysis of decoy state protocols and SARG04, both yielding notably improved security and practicality.

Device-independent and measurement-device-independent paradigms are discussed in depth, with an explicit connection made to Bell inequality violations, the role of composable security, and mitigation against side-channel attacks (e.g., detector vulnerabilities). The text underscores that fully device-independent security requires prohibitively high detection efficiencies (notably, the detection loophole threshold for CHSH-based protocols is $\eta > 2/3$), constraining practicality.

Continuous-Variable Protocols

CV-QKD is analyzed, starting from seminal theoretical proposals (protocols based on squeezed or coherent states, Gaussian or discrete modulation, homodyne/heterodyne detection), to present-day implementations. The review formalizes security against general attacks via reduction to collective Gaussian attacks by exploiting the extremality of Gaussian states and the quantum de Finetti theorem. The authors highlight that ideal coherent-state protocols with RR and large modulation can closely approach the secret-key capacity of the pure-loss channel. One- and two-way schemes, trusted-noise-enhanced protocols, as well as unidimensional and discrete-modulation approaches, are rigorously presented within an asymptotic and finite-size framework, and their practical limitations are quantified.

Explicitly, the limits of trusted reconciliation efficiency, block size requirements, and parameter estimation are considered, noting the exponential scaling of block size to achieve protocol composability at high loss. Practical issues surrounding local oscillator manipulation—both from an attack (LO calibration or saturation) and technological perspective (locally generated LO, pilot tones)—are analyzed, with proposed countermeasures and their impact on the security analysis.

Quantum Cryptography Beyond Key Distribution

Quantum Hacking

A rigorous categorization of practical quantum hacking techniques is provided, encompassing attacks on sources (Trojan horse, unambiguous state discrimination), detectors (blinding, faked states, DEM), authenticated channels, and calibration procedures. These illustrate the continued arms race between protocol designers and adversaries, thus motivating composable and device-independent frameworks and the shift toward MDI implementations.

Digital Signatures and Bounded Memory

Quantum digital signatures (QDS) are discussed extensively, tracing the progression from the Gottesman-Chuang proposal (employing quantum one-way functions and SWAP tests, but reliant on quantum memory and authenticated channels) to memoryless and photonic implementations leveraging coherent states and quantum state elimination. Protocols are detailed under settings with multiple parties, including the challenges of universal verifiability, classical ITS signature schemes, and network scaling.

Bounded quantum storage and data locking concepts are also reviewed. The use of entropic uncertainty relations, locking capacities, and the distinction between strong and weak scenarios (e.g., private and locking capacities) is emphasized, providing theoretical pathways for cryptography under physically realistic assumptions on adversary capabilities.

Experimental Implementations and Hardware Advances

State-of-the-Art QKD Implementations

A thorough account of experimental QKD systems is presented, enumerating decoy-state BB84 realizations (fiber, free-space, GHz clocking, integration with telecom hardware), DPS and COW protocols, MDI-QKD field trials (up to 404 km using ULL fibers and SNSPDs), high-dimensional optical and integrated photonic circuits, and satellite-based QKD (LEO to GEO).

The discussion includes practical advances in detector technology (InGaAs APDs, SNSPDs), signal modulation, synchronisation, and post-processing (rate-adaptive LDPC error reconciliation, composable security analysis, energy-limited modulation). High-dimensional time-energy and OAM-based QKD is analyzed for its impact on key rates, multiplexing, and robustness over metropolitan-scale and cross-city links.

Satellite and Network-Scale Quantum Communication

Progress in satellite QKD is systematically described, encompassing link budget analysis, orbits, daylight and atmospheric effects, synchronization, and integration with terrestrial quantum networks. The first violation of the PLOB bound is examined through the lens of TF-QKD and its family of phase-matching and SNS protocols, offering key rate scaling as $O(\sqrt{\eta})$ rather than $O(\eta)$ and thus outperforming direct transmission limits over long distances.

Ultimate Limits, Repeaters, and Network Topologies

The paper devotes substantial analysis to the ultimate rate-loss trade-offs in point-to-point and repeater-assisted quantum networks. The REE-based upper bounds, PLOB (Pirandola–Laurenza–Ottaviani–Banchi) bound, and the operational significance of teleportation covariance and channel simulation for bounding two-way assisted capacities are meticulously discussed.

Moreover, for distillable channels (pure-loss, erasure, dephasing, quantum-limited amplifier), the secret key capacity is shown to coincide with the corresponding REE bounds, with explicit closed-form expressions. Quantum repeaters are categorized into probabilistic, deterministic, and memoryless classes, with explicit attention given to entanglement swapping, nesting levels, operational rates, hardware requirements for long-distance, fault-tolerant operation, and resource scaling.

The extension to multi-hop network settings is mathematically formalized with graph-theoretic tools (widest path, max-flow min-cut theorems), and fundamentally, practical deployment scenarios are evaluated, including integrated quantum-classical networking.

Security Proofs, Randomness Generation, and Randomness Expansion

The review includes mathematically precise treatments of composable security, entropy accumulation, min-entropy smoothing, and their operational implications for randomness expansion, both in trusted and device-independent scenarios. The equivalence to key generation composability is articulated, and practical realizations are placed in the context of non-signaling constraints and seed randomness amplification.

Conclusion

This review presents an authoritative, technical, and comprehensive survey of the theoretical and experimental landscape in quantum cryptography. By addressing protocol design, rigorous security proofs, hardware constraints, adversarial models, ultimate rate bounds, repeaters, and networking, it synthesizes the multi-disciplinary challenges that must be overcome for quantum cryptography to become ubiquitous in global secure communications. Ongoing open questions include the closing of the rate gaps for noisy bosonic channels and amplitude damping channels, further improvement of hardware for both terrestrial and satellite links, and scalable integration with post-quantum cryptosystems and classical infrastructure. Future research will need to focus on practical repeater architectures, network composability, and robust device-independent cryptographic primitives.