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arXiv:1603.02370 · Physical Review A

Experimentally feasible quantum-key-distribution scheme using qubit-like qudits and its comparison with existing qubit- and qudit-based protocols

H. F. Chau, Qinan Wang, Cardythy Wong

Published Feb 7, 2017• 7 citations
arXivHTMLPDF

Abstract

Recently, Chau [Phys. Rev. A 92, 062324 (2015)] introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a ${2}^{n}$-dimensional Hilbert space in the form $(|i\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|j\ensuremath{\rangle})/\sqrt{2}$ with $n\ensuremath{\ge}2$. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate $n$ bits of raw key for each qudit prepared and measured in the same basis in the noiseless situation. The reason is that in addition to the phase information, each qudit also carries information on the Hilbert subspace used. The additional $(n\ensuremath{-}1)$ bits of raw key comes from a clever utilization of this extra piece of information. We prove the unconditional security of this modified protocol and compare its performance with other existing provably secure qubit- and qudit-based protocols on market in the one-way classical communication setting. Interestingly, we find that for the case of $n=2$, the secret key rate of this modified protocol using nondegenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.

DOI
10.1103/physreva.95.022311

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Recently, Chau [Phys. Rev. A 92, 062324 (2015)] introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a 2n{2}^{n}2n-dimensional Hilbert space in the form (∣i\ensuremath⟩\ifmmode±\else\textpm\fi∣j\ensuremath⟩)/2(|i\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|j\ensuremath{\rangle})/\sqrt{2}(∣i\ensuremath⟩\ifmmode±\else\textpm\fi∣j\ensuremath⟩)/2​ with n\ensuremath≥2n\ensuremath{\ge}2n\ensuremath≥2. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate nnn bits of raw key for each qudit prepared and measured in the same basis in the noiseless situation. The reason is that in addition to the phase information, each qudit also carries information on the Hilbert subspace used. The additional (n\ensuremath−1)(n\ensuremath{-}1)(n\ensuremath−1) bits of raw key comes from a clever utilization of this extra piece of information. We prove the unconditional security of this modified protocol and compare its performance with other existing provably secure qubit- and qudit-based protocols on market in the one-way classical communication setting. Interestingly, we find that for the case of n=2n=2n=2, the secret key rate of this modified protocol using nondegenerate random quantum code to perform one-way entanglement distillation is equal to that of the six-state scheme.
All known qudit-based prepare-and-measure quantum key distribution (PMQKD) schemes are more error resilient than their qubit-based counterparts. Their high error resiliency comes partly from the careful encoding of multiple bits of signals used to generate the raw key in each transmitted qudit so that the same eavesdropping attempt causes a higher bit error rate (BER) in the raw key. Here I show that highly-error-tolerant PMQKD schemes can be constructed simply by encoding one bit of classical information in each transmitted qudit in the form $(|i\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|j\ensuremath{\rangle})/\sqrt{2}$, where $|i\ensuremath{\rangle}$'s form an orthonormal basis of the 2n{2}^{n}2n-dimensional Hilbert space. Moreover, I prove that these schemes can tolerate up to the theoretical maximum of a 50% BER for $n\ensuremath{\ge}2$ provided the raw key is generated under a certain technical condition, making them extremely-error-tolerant PMQKD schemes involving the transmission of unentangled finite-dimensional qudits. This shows the potential of processing quantum information using lower-dimensional quantum signals encoded in a higher-dimensional quantum state.
In comparison to qubit-based protocols, qudit-based quantum key distribution ones generally allow two cooperative parties to share unconditionally secure keys under a higher channel noise. However, it is very hard to prepare and measure the required quantum states in qudit-based protocols in general. One exception is the recently proposed highly error tolerant qudit-based protocol known as the Chau15 (Chau 2015 Phys. Rev. A 92 062324). Remarkably, the state preparation and measurement in this protocol can be done relatively easily since the required states are phase encoded almost like the diagonal basis states of a qubit. Here we report the first proof-of-principle demonstration of the Chau15 protocol. One highlight of our experiment is that its post-processing is based on practical one-way manner, while the original proposal in Chau (2015 Phys. Rev. A 92 062324) relies on complicated two-way post-processing, which is a great challenge in experiment. In addition, by manipulating time-bin qudit and measurement with a variable delay interferometer, our realization is extensible to qudit with high-dimensionality and confirms the experimental feasibility of the Chau15 protocol.
Abstract High-dimensional quantum key distribution (QKD) based on entangled qudits has emerged as a promising route for advancing the performance and practicality of quantum communication. By extending beyond the qubit framework, qudit entanglement enables the encoding of multiple bits per particle and offers greater robustness against noise, loss, and eavesdropping. In this review, we present qudit-based entanglement QKD protocols and their experimental demonstrations. We first introduce the basic concepts of qudits and provide an overview of foundational qubit-based entanglement QKD schemes, such as Ekert '91 (E91) and Bennett–Brassard–Mermin '92 (BBM92), which establish the core principles of entanglement-based secure key generation. Subsequently, we examine the generalization of these protocols to entangled qudits, highlighting how higher dimensionality enhances secure key rates and noise tolerance. Finally, we survey experimental demonstrations of qudit-based entanglement QKD across photonic platforms and outline prospects, showing that high-dimensional entanglement can be reliably generated, distributed, and measured for QKD with high stability and scalability. Remarkably, these achievements not only verify the feasibility of practical high-dimensional QKD, but also demonstrate clear advantages over qubit-based systems. Overall, theoretical frameworks and experimental realizations reviewed here position photonic qudit-based entanglement QKD as a promising resource for scalable, high-speed, and secure quantum communication networks, unveiling its potential as a central component in the future of quantum information technologies.
Quantum key distribution (QKD) protocols most often use two conjugate bases in order to verify the security of the quantum channel. In the majority of protocols, these bases are mutually unbiased to one another, which is to say they are formed from balanced superpositions of the entire set of states in the opposing basis. Here, we introduce a high-dimensional QKD protocol using qubit-like states, referred to as Fourier-qubits (or F-qubits). In our scheme, each F-qubit is a superposition of only two computational basis states with a relative phase that can take d distinct values, where d is the dimension of the computational basis. This non-mutually-unbiased approach allows us to bound the information leaked to an eavesdropper, maintaining security in high-dimensional quantum systems despite the states’ seemingly two-dimensional nature. By simplifying state preparation and measurement, our protocol offers a practical alternative for secure high-dimensional quantum communications. We experimentally demonstrate this protocol for a noisy high-dimensional QKD channel using the orbital angular momentum degree of freedom of light and discuss the potential benefits for encoding in other degrees of freedom. High dimensional quantum key distribution (QKD) systems will allow for higher key generation rate, but with added complexity for creating and detecting high dimensional quantum states. The authors demonstrate a QKD protocol using “qubit-like” qudit states, “F-qubits”, with simpler generation and detection, maintaining the benefits of high dimensional QKD protocols.
Abstract Since the 80 s when it was first proposed, Quantum Key Distribution (QKD) elicited great interest in the field of cryptography as a unique procedure for key generation that could in principle guarantee unconditionally secure communication “by the laws of Physics”. In the last fifteen years commercial solutions have started appearing on the market, showing that practical implementations of the protocol were not only possible but also competitive in terms of security and achievable secret-key rate. In this work we describe a simulation of the historical QKD protocol E91 on the IBM Quantum platform, making use of the qubit formalism to represent the quantum states received by two communicating nodes. Having implemented also the post-processing steps for the error correction and the privacy amplification, this model can represent a simple stand-alone tool to study the performance not only of one-to-one communication but of more complex systems that rely on QKD for security, one above all QKD networks.