Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1801.03202 · Physical Review A

Securing quantum key distribution systems using fewer states

Nurul T. Islam, Charles Ci Wen Lim, Clinton Cahall, Jungsang Kim, Daniel J. Gauthier

Published Apr 30, 2018• 31 citations
arXivHTMLPDF

Abstract

Quantum key distribution (QKD) allows two remote users to establish a secret key in the presence of an eavesdropper. The users share quantum states prepared in two mutually unbiased bases: one to generate the key while the other monitors the presence of the eavesdropper. Here, we show that a general $d$-dimension QKD system can be secured by transmitting only a subset of the monitoring states. In particular, we find that there is no loss in the secure key rate when dropping one of the monitoring states. Furthermore, it is possible to use only a single monitoring state if the quantum bit error rates are low enough. We apply our formalism to an experimental $d=4$ time-phase QKD system, where only one monitoring state is transmitted, and obtain a secret key rate of $17.4\ifmmode\pm\else\textpm\fi{}2.8$ Mbits/s at a 4 dB channel loss and with a quantum bit error rate of $0.045\ifmmode\pm\else\textpm\fi{}0.001$ and $0.037\ifmmode\pm\else\textpm\fi{}0.001$ in time and phase bases, respectively, which is 58.4% of the secret key rate that can be achieved with the full setup. This ratio can be increased, potentially up to 100%, if the error rates in time and phase basis are reduced. Our results demonstrate that it is possible to substantially simplify the design of high-dimensional QKD systems, including those that use the spatial or temporal degrees of freedom of the photon, and still outperform qubit-based ($d=2$) protocols.

DOI
10.1103/physreva.97.042347

Related papers

High-dimensional quantum key distribution with Qubit-like states

Lukas Scarfe, Rojan Abolhassani, Frédéric Bouchard +4 more

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.

arXiv:2504.03893•Communications Physics•Nov 25, 2025•5 citations

Enhancing the secure key rate in a quantum-key-distribution system using discrete-variable, high-dimensional, time-frequency states

Nurul T. Islam, Clinton Cahall, Andrés Aragoneses +6 more

High-dimensional (dimension d > 2) quantum key distribution (QKD) protocols that encode information in the temporal degree of freedom promise to overcome some of the challenges of qubit-based (d = 2) QKD systems. In particular, the long recovery time of single-photon detectors and large channel noise at long distance both limit the rate at which a final secure key can be generated in a low-dimension QKD system. We propose and demonstrate a practical discrete-variable time-frequency protocol with d = 4 at a wavelength of 1550 nm, where the temporal states are secured by transmitting and detecting their dual states under Fourier transformation, known as the frequency-basis states, augmented by a decoy-state protocol. We show that the discrete temporal and frequency states can be generated and detected using commercially-available equipment with high timing and spectral efficiency. In our initial experiments, we only have access to detectors that have low efficiency (1%) at 1550 nm. Together with other component losses, our system is equivalent to a QKD system with ideal components and a 50-km-long optical-fiber quantum channel. We find that our system maintains a spectral visibility of over 99.0% with a quantum bit error rate of 2.3%, which is largely due to the finite extinction ratio of the intensity modulators used in the transmitter. The estimated secure key rate of this system is 7.7×104 KHz, which should improve drastically when we use detectors optimized for 1550 nm.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 24, 2016•1 citation

Simple and secure quantum key distribution with biphotons

I. Bregman, Dorit Aharonov, Michael Ben-Or +1 more

The best qubit one-way quantum-key-distribution (QKD) protocol can tolerate up to 14.6% in the error rate. It has been shown how this rate can be increased by using larger quantum systems. The polarization state of a biphoton can encode a three-level quantum system---a qutrit. The realization of a QKD system with biphotons encounters several problems in generating, manipulating, and detecting such photon states. We define those limitations and find within them a few protocols that perform almost as well as the ideal qutrit protocol. One advantage is that these protocols can be implemented with minor modifications into existing single photon systems. The security of one protocol is proved for the most general coherent attacks and the largest acceptable error rate for this protocol is found to be around 17.7%. For comparison, the security of the best possible qutrit protocol of four mutually unbiased bases was also rigorously analyzed against general attacks, with a proven bound on the acceptable error rate of 21.1%.

arXiv:0709.3804•Physical Review A•May 7, 2008•26 citations

High-rate field demonstration of large-alphabet quantum key distribution

Catherine Lee, Darius Bunandar, Zheshen Zhang +6 more

Quantum key distribution (QKD) exploits the quantum nature of light to share provably secure keys, allowing secure communication in the presence of an eavesdropper. The first QKD schemes used photons encoded in two states, such as polarization. Recently, much effort has turned to large-alphabet QKD schemes, which encode photons in high-dimensional basis states. Compared to binary-encoded QKD, large-alphabet schemes can encode more secure information per detected photon, boosting secure communication rates, and also provide increased resilience to noise and loss. High-dimensional encoding may also improve the efficiency of other quantum information processing tasks, such as performing Bell tests and implementing quantum gates. Here, we demonstrate a large-alphabet QKD protocol based on high-dimensional temporal encoding. We achieve record secret-key rates and perform the first field demonstration of large-alphabet QKD. This demonstrates a new, practical way to optimize secret-key rates and marks an important step towards transmission of high-dimensional quantum states in deployed networks.

arXiv:1611.01139•Nov 3, 2016•12 citations

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

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.

arXiv:1603.02370•Physical Review A•Feb 7, 2017•7 citations

Generalization of Quantum Key Distribution Protocol

Muhammad Mubashir Khan, Jie Xu

Summary Quantum Key Distribution (QKD) is a secure key sharing technology with unconditional security. Certain well-known protocols for QKD have been presented, which claim their security by means of higher eavesdropping error-rates. A generalized quantum key distribution protocol that can be optimized for arbitrary number of bases and dimensions of photon states is presented in this paper. The protocol can provide higher eavesdropping error-rates than the well-known existing QKD protocols like BB-84 [4] and B-92 [5]. The higher error-rate makes it possible for Alice and Bob to share secure keys on relatively large distances.

•Jan 1, 2012•1 citation
Quantum key distribution (QKD) allows two remote users to establish a secret key in the presence of an eavesdropper. The users share quantum states prepared in two mutually unbiased bases: one to generate the key while the other monitors the presence of the eavesdropper. Here, we show that a general ddd-dimension QKD system can be secured by transmitting only a subset of the monitoring states. In particular, we find that there is no loss in the secure key rate when dropping one of the monitoring states. Furthermore, it is possible to use only a single monitoring state if the quantum bit error rates are low enough. We apply our formalism to an experimental d=4d=4d=4 time-phase QKD system, where only one monitoring state is transmitted, and obtain a secret key rate of 17.4\ifmmode±\else\textpm\fi2.817.4\ifmmode\pm\else\textpm\fi{}2.817.4\ifmmode±\else\textpm\fi2.8 Mbits/s at a 4 dB channel loss and with a quantum bit error rate of 0.045\ifmmode±\else\textpm\fi0.0010.045\ifmmode\pm\else\textpm\fi{}0.0010.045\ifmmode±\else\textpm\fi0.001 and 0.037\ifmmode±\else\textpm\fi0.0010.037\ifmmode\pm\else\textpm\fi{}0.0010.037\ifmmode±\else\textpm\fi0.001 in time and phase bases, respectively, which is 58.4% of the secret key rate that can be achieved with the full setup. This ratio can be increased, potentially up to 100%, if the error rates in time and phase basis are reduced. Our results demonstrate that it is possible to substantially simplify the design of high-dimensional QKD systems, including those that use the spatial or temporal degrees of freedom of the photon, and still outperform qubit-based (d=2d=2d=2) protocols.
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.
High-dimensional (dimension d > 2) quantum key distribution (QKD) protocols that encode information in the temporal degree of freedom promise to overcome some of the challenges of qubit-based (d = 2) QKD systems. In particular, the long recovery time of single-photon detectors and large channel noise at long distance both limit the rate at which a final secure key can be generated in a low-dimension QKD system. We propose and demonstrate a practical discrete-variable time-frequency protocol with d = 4 at a wavelength of 1550 nm, where the temporal states are secured by transmitting and detecting their dual states under Fourier transformation, known as the frequency-basis states, augmented by a decoy-state protocol. We show that the discrete temporal and frequency states can be generated and detected using commercially-available equipment with high timing and spectral efficiency. In our initial experiments, we only have access to detectors that have low efficiency (1%) at 1550 nm. Together with other component losses, our system is equivalent to a QKD system with ideal components and a 50-km-long optical-fiber quantum channel. We find that our system maintains a spectral visibility of over 99.0% with a quantum bit error rate of 2.3%, which is largely due to the finite extinction ratio of the intensity modulators used in the transmitter. The estimated secure key rate of this system is 7.7×104 KHz, which should improve drastically when we use detectors optimized for 1550 nm.
The best qubit one-way quantum-key-distribution (QKD) protocol can tolerate up to 14.6% in the error rate. It has been shown how this rate can be increased by using larger quantum systems. The polarization state of a biphoton can encode a three-level quantum system---a qutrit. The realization of a QKD system with biphotons encounters several problems in generating, manipulating, and detecting such photon states. We define those limitations and find within them a few protocols that perform almost as well as the ideal qutrit protocol. One advantage is that these protocols can be implemented with minor modifications into existing single photon systems. The security of one protocol is proved for the most general coherent attacks and the largest acceptable error rate for this protocol is found to be around 17.7%. For comparison, the security of the best possible qutrit protocol of four mutually unbiased bases was also rigorously analyzed against general attacks, with a proven bound on the acceptable error rate of 21.1%.
Quantum key distribution (QKD) exploits the quantum nature of light to share provably secure keys, allowing secure communication in the presence of an eavesdropper. The first QKD schemes used photons encoded in two states, such as polarization. Recently, much effort has turned to large-alphabet QKD schemes, which encode photons in high-dimensional basis states. Compared to binary-encoded QKD, large-alphabet schemes can encode more secure information per detected photon, boosting secure communication rates, and also provide increased resilience to noise and loss. High-dimensional encoding may also improve the efficiency of other quantum information processing tasks, such as performing Bell tests and implementing quantum gates. Here, we demonstrate a large-alphabet QKD protocol based on high-dimensional temporal encoding. We achieve record secret-key rates and perform the first field demonstration of large-alphabet QKD. This demonstrates a new, practical way to optimize secret-key rates and marks an important step towards transmission of high-dimensional quantum states in deployed networks.
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 $(|i\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|j\ensuremath{\rangle})/\sqrt{2}$ 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 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 $(n\ensuremath{-}1)$ 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.
Summary Quantum Key Distribution (QKD) is a secure key sharing technology with unconditional security. Certain well-known protocols for QKD have been presented, which claim their security by means of higher eavesdropping error-rates. A generalized quantum key distribution protocol that can be optimized for arbitrary number of bases and dimensions of photon states is presented in this paper. The protocol can provide higher eavesdropping error-rates than the well-known existing QKD protocols like BB-84 [4] and B-92 [5]. The higher error-rate makes it possible for Alice and Bob to share secure keys on relatively large distances.