General Quantum Key Distribution in Higher Dimension

Abstract

We study a general quantum key distribution protocol in higher dimension. In this protocol, quantum states in arbitrary $g+1$ ($1\le g\le d$) out of all $d+1$ mutually unbiased bases in a d-dimensional system can be used for the key encoding. This provides a natural generalization of the quantum key distribution in higher dimension and recovers the previously known results for $g=1$ and $d$. In our investigation, we study Eve's attack by two slightly different approaches. One is considering the optimal cloner for Eve, and the other, defined as the optimal attack, is maximizing Eve's information. We derive results for both approaches and show the deviation of the optimal cloner from the optimal attack. With our systematic investigation of the quantum key distribution protocols in higher dimension, one may balance the security gain and the implementation cost by changing the number of bases in the key encoding. As a side product, we also prove the equivalency between the optimal phase covariant quantum cloning machine and the optimal cloner for the $g=d-1$ quantum key distribution.

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Cited by in corpus (10)

• Entropic uncertainty relations for multiple measurements
• Rate-loss analysis of an efficient quantum repeater architecture
• Quantum key distribution session with 16-dimensional photonic states
• Quantum Cloning Machines and the Applications
• Distribution of quantum Fisher information in asymmetric cloning machines
• Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis
• The general fine-grained uncertainty relation and the second law of thermodynamics
• Minimal sets determining universal and phase-covariant quantum cloning
• Structure of the sets of mutually unbiased bases with cyclic symmetry
• Asymmetric quantum multicast network coding: asymmetric optimal cloning over quantum networks