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Journal of the Optical Society of America B

Security analysis for a mutually partially unbiased bases–based protocol

Zehong Chang, Fumin Wang, Junliang Jia, Xiaoli Wang, Yi Lv, Pei Zhang

Published Sep 13, 2022• 4 citations
Publisher

Abstract

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.

DOI
10.1364/josab.466304

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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.
Abstract 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 d = 2 , 4 , 5 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.
We propose a practical high-dimensional quantum key distribution protocol based on mutually partially unbiased bases utilizing transverse modes of light. In contrast to conventional protocols using mutually unbiased bases, our protocol uses Laguerre-Gaussian and Hermite-Gaussian modes of the same mode order as two mutually partially unbiased bases for encoding, which leads to a scheme free from mode-dependent diffraction in long-distance channels. Since only linear and passive optical elements are needed, our experimental implementation significantly simplifies qudit generation and state measurement. Since this protocol differs from conventional protocols using mutually unbiased bases, we provide a security analysis of our protocol.
Practical quantum key distribution (QKD) modulators inevitably introduce correlations, causing the state emitted in a given round to depend on the setting choices made in previous rounds. These correlations break the round-by-round independence structure on which many widely used security proof techniques rely, leaving a significant gap between available theoretical guarantees and the reality of practical implementations. In this work, we develop a fully analytical finite-key security proof for decoy-state BB84 against general coherent attacks that rigorously incorporates correlations introduced by Alice's bit-and-basis encoder, while requiring only partial characterization of such correlations. Crucially, it does so without requiring the round partitioning of the data used for phase-error estimation introduced in previous works, showing that this technique is not indispensable for dealing with correlated encoders, and resulting in improved finite-key performance. Moreover, we also analyze the case of ideal single-photon sources, and our results reveal a counterintuitive effect: in the presence of strong encoding correlations, decoy-state BB84 can outperform single-photon implementations.
Standard protocols for quantum key distribution (QKD) require that the sender be able to transmit in two or more mutually unbiased bases. Here, we analyze the extent to which the performance of QKD is degraded by diffraction effects that become relevant for long propagation distances and limited sizes of apertures. In such a scenario, different states experience different amounts of diffraction, leading to state-dependent loss and phase acquisition, causing an increased error rate and security loophole at the receiver. To solve this problem, we propose a precompensation protocol based on preshaping the transverse structure of quantum states. We demonstrate, both theoretically and experimentally, that when performing QKD over a link with known, state-dependent loss and phase shift, the performance of QKD will be better if we intentionally increase the loss of certain states to make the loss and phase shift of all states equal. Our results show that the precompensated protocol can significantly reduce the error rate induced by state-dependent diffraction and thereby improve the secure key rate of QKD systems without sacrificing the security.
Abstract The performance of quantum key distribution (QKD) is severely limited by multiphoton emissions, due to the photon-number-splitting attack. The most efficient solution, the decoy-state method, requires that the phases of all transmitted pulses are independent and uniformly random. In practice, however, these phases are often correlated, especially in high-speed systems, which opens a security loophole. Here, we address this pressing problem by providing a security proof for decoy-state QKD with correlated phases that offers key rates close to the ideal scenario. Our work paves the way towards high-performance secure QKD with practical laser sources, and may have applications beyond QKD.
Secure exchange of cryptographic keys is extremely important for any communication system where security and privacy of data is desirable. Although classical cryptographic algorithms provide computationally secure methods for secret key exchange, quantum key distribution (QKD) provides an extraordinary means to this end by guaranteeing unconditional security. Any malicious interception of communication by a man-in-the-middle on a QKD link immediately alerts sender and receiver by introducing an unavoidable error-rate. Higher-dimensional QKD protocols such as KMB09 exhibit higher eavesdropping error-rates with improved intrusion detection but their practical implementation is still awaited. In this paper, we present the design and implementation of KMB09 protocol using Laguerre–Gaussian orbital angular momentum to demonstrate and highlight the advantages of using dynamic spatial modes in QKD system. A complete error-rate analysis of KMB09 protocol implementation is presented with two different types of eavesdropping error-rates. Furthermore, we also demonstrate the decoy state method to show the robustness of the protocol against photon-number-splitting attack.