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Asymptotically Optimal Quantum Key Distribution Protocols.

Hao Shu

Published Oct 5, 2021• 2 citations
OpenAlex

Abstract

Quantum key distribution(QKD) could be the most significant application of quantum information theory. In nearly four decades, although substantial QKD protocols are developed, the BB84 protocol and its variants are still the most researched ones. It is well-known that the secure bound of qubit error rate(QBER) of BB84 protocol is about 11$\%$ while it can be increased to 12.6$\%$ by six-state protocol. It would not be surprising that employing more basis could increase the bound. However, what is the optimal one? In this paper, investigations of asymptotically optimal QKD protocols are proposed. Precisely, We present an abstraction of prepare-measure QKD protocols and investigate two special cases which are optimal among all protocols coding by the same states. Our analyses demonstrate that the asymptotically optimal QBER bounds coding by orthogonal qubits are about 22.17$\%$ for both general and memoryless attacks while the bounds coding by non-orthogonal states in two mutually unbiased basis are about 25.30$\%$ for general attacks and 27.00$\%$ for memoryless attacks. The significant improvement indicates the huge space for previous protocols to improve their security while the optimality of our protocols demonstrates the ultimate potential of their security.

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Quantum key distribution(QKD) could be the most significant application of quantum information theory. In nearly four decades, although substantial QKD protocols are developed, the BB84 protocol and its variants are still the most researched ones. It is well-known that the secure bound of qubit error rate(QBER) of BB84 protocol is about 11%\%% while it can be increased to 12.6%\%% by six-state protocol. It would not be surprising that employing more basis could increase the bound. However, what is the optimal one? In this paper, investigations of asymptotically optimal QKD protocols are proposed. Precisely, We present an abstraction of prepare-measure QKD protocols and investigate two special cases which are optimal among all protocols coding by the same states. Our analyses demonstrate that the asymptotically optimal QBER bounds coding by orthogonal qubits are about 22.17%\%% for both general and memoryless attacks while the bounds coding by non-orthogonal states in two mutually unbiased basis are about 25.30%\%% for general attacks and 27.00%\%% for memoryless attacks. The significant improvement indicates the huge space for previous protocols to improve their security while the optimality of our protocols demonstrates the ultimate potential of their security.
Quantum key distribution(QKD) is one of the most significant areas in quantum information theory. For nearly four decades, substantial QKD protocols and cryptographic methods are developed. In early years, the security of protocols are depend on switching different bases, which, in fact, are based on non-orthogonal states. The most famous example is the BB84 protocol. Later, other techniques were developed for orthogonal states cryptography. Representations of such protocols including the GV protocol and order-rearrangement protocols. It might be harder to implement protocols based on orthogonal states since they require extra techniques to obtain security. In this paper, we give two QKD protocols based on orthogonal states. One of them needs not to employ order-rearrangement techniques while the other needs. We give analyses of their security and efficiency. Also, anti-noisy discussions would be given. Our protocols are highly efficient when considering consumptions of both qubits and classical bits while they are robust over several noisy channels. Moveover, the requirements of maximally entangled states maybe less than previous protocols and so the efficiency of measurements may be increased.
Abstract Quantum key distribution (QKD) protocols allow for information theoretically secure distribution of (classical) cryptographic key material. However, due to practical limitations the performance of QKD implementations is somewhat restricted. For this reason, it is crucial to find optimal protocol parameters, while guaranteeing information theoretic security. The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines thekey-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making a number of heuristic assumptions. For instance, the number of decoy states is restricted to only one or two, with one of the decoy intensities set to a fixed value, and vacuum states are ignored as they are assumed to contribute only marginally to the secure key-rate. These assumptions simplify the optimization problem and reduce the size of search space significantly. However, they also cause the security analysis to be non-tight, and thereby result in sub-optimal performance. In this work, we follow a more rigorous approach using both linear and nonlinear programs describing the optimization problem. Our approach, focusing on the decoy-state BB84 protocol, allows heuristic assumptions to be omitted, and therefore results in a tighter security analysis with better protocol parameters. We show an improved performance for the decoy-state BB84 QKD protocol, demonstrating that the heuristic assumptions typically made are too restrictive. Moreover, our improved optimization frameworks shows that the complexity of the performance optimization problem can also be handled without making heuristic assumptions, even with limited computational resources available.
We investigate the resilience to noise of single-qubit quantum key distribution (QKD) protocols in the scenario of security against independent eavesdropping attacks and key distillation based on one-way classical communication. To this end, we introduce a noise-based metric that quantifies the efficiency of QKD protocols. Within this framework, we analyze the maximal noise levels that allow Alice and Bob to asymptotically establish a secure secret key. Using this assumption, we compare the noise tolerance of general single-qubit QKD protocols, in particular the BB84, B92, E91, and six-state protocols. Our main result determines the noise level threshold for QKD allowing one to distill an asymptotically secure secret key. Additionally, we demonstrate that the six-state protocol achieves the greatest resistance to noise while simultaneously yielding a higher post-selection efficiency than the other analyzed single-qubit protocols, confirming its robustness within the considered security model. Finally, we perform an analysis of the proposed noise-based metric and the conventional quantum bit error rate (QBER) metric.
Quantum key distribution protocols have been studied for almost four decades, and have already seen real world applications. Such implementations often operate in naturally noisy environments (e.g., sensor thermal noise, sun radiation, etc.) with known or measurable noise levels. However, existing security proofs implicitly attribute any channel noise to a possible eavesdropper, an overly pessimistic assumption that can adversely effect the guaranteed protocol key-rate. In this paper, we analyze general prepare-and-measure QKD schemes, and show how to improve the bounds on the key-rate under the assumption of an independent state replacement noise at the receiver. Taking BB84 as a concrete example, our results theoretically guarantee a higher key-rate, as a function of the minimal possible replacement probability. In practice, for some parameter-regimes, this guarantees a higher tolerable QBER.
The goal of cryptography is to encode data in such a way that no one can decode it unless they are the intended recipient. With the emergence of quantum computing, classical cryptography is not reliable enough to protect sensitive information. Nevertheless, there are alternatives. Quantum Key Distribution (QKD) is a method to secure communication based on the laws of quantum physics. Due to being impossible to measure the quantum state of a system without disturbing it, QKD provides a way to communicate between two parties while being, in theory, immune to eavesdropping. In this work, a free-space high-speed QKD setup is proposed, with the objective of implementing the polarization three-state one-decoy variant of the BB84 protocol. An assessment of the best type of laser diode to use for free-space QKD is made between several options. The system’s performance was assessed, incorporating a quantitative analysis of system losses and an estimation of the number of photons traversing the quantum channel. The system achieved a Quantum Bit Error Rate (QBER) of 1.58% for the Z basis and 1.46% for the X basis, for an average reception of two photons per pulse. Preliminary QBER measurements were also undertaken in the context of Quantum Keyless Private Communication protocols, focusing on the average number of photons per pulse.
In this paper we consider a three-state variant of the BB84 quantum key distribution (QKD) protocol. We derive a new lower-bound on the key rate of this protocol in the asymptotic scenario and use mismatched measurement outcomes to improve the channel estimation. Our new key rate bound remains positive up to an error rate of 11%11\%11%, exactly that achieved by the four-state BB84 protocol.