Quantum Key Distribution Using Qudits Each Encoding One Bit Of Raw Key

Abstract

All known qudit-based prepare-and-measure quantum key distribution (PM-QKD) 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 PM-QKD schemes can be constructed simply by encoding one bit of classical information in each transmitted qudit in the form $(|i⟩\pm |j⟩)/\sqrt{2}$, where $|i⟩$'s form an orthonormal basis of the $2^n$-dimensional Hilbert space. Moreover, I prove that these schemes can tolerate up to the theoretical maximum of 50\% BER for $n\ge 2$ provided that the raw key is generated under a certain technical condition, making them the most error-tolerant PM-QKD schemes involving the transmission of unentangled finite-dimensional qudits to date. This shows the potential of processing quantum information using lower-dimensional quantum signals encoded in a higher-dimensional quantum state.

minor revision, 5 pages, to appear in PRA

References in corpus (5)

• Quantum cryptography: Public key distribution and coin tossing
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• Experimental Passive Round-Robin Differential Phase-Shift Quantum Key Distribution
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• Proof-of-principle experimental realization of a qubit-like qudit-based quantum key distribution scheme
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• Round-Robin Differential Phase-Shift Quantum Key Distribution with Twisted Photons
• The future of secure communications: device independence in quantum key distribution
• Experimentally Feasible Quantum-Key-Distribution Scheme Using Qubit-Like Qudits And Its Comparison With Existing Qubit- and Qudit-Based Protocols
• Implementing positive-operator-valued-measurement elements in photonic circuits for performing minimum quantum state tomography of path qudits
• Optimal quantum state identification with qudit-encoded unknown states
• Differential-phase-shift QKD with practical Mach-Zehnder interferometer
• High-Dimensional Quantum Key Distribution with Qubit-like States
• Equiangular quantum key distribution in more than two dimensions