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Journal of Modern Optics

Security aspects of quantum cryptography with D-dimensional systems

Chiara Macchiavello, D. Bruss

Published Jan 1, 2003• 2 citations
Publisher

Abstract

We analyse the security of quantum key distribution with three-dimensional systems, and show that this scheme is more advantageous against symmetric attacks than protocols using two-dimensional states. We generalize the resulting optimal eavesdropping transformation to cryptographic systems with arbitrary dimensions.
DOI
10.1080/0950034021000057996

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The promise of secure cryptographic quantum key distribution schemes is based on the use of quantum effects in the spin space. We point out that in fact in many current quantum cryptography protocols the space part of the wave function is neglected. However exactly the space part of the wave function describes the behaviour of particles in ordinary real three-dimensional space. As a result such schemes can be secure against eavesdropping attacks in the abstract spin space but could be insecure in the real three-dimensional space. We discuss an approach to the security of quantum key distribution in space by using Bell's inequality and a special preparation of the space part of the wave function.
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Quantum cryptography promises secure communication protocols that surpass the limitations of classical cryptography. By leveraging the principles of quantum mechanics, particularly the phenomenon of quantum entanglement and the uncertainty principle, quantum cryptography protocols offer provable security guarantees against eavesdropping attacks. In this paper, we provide an overview of quantum cryptography, discussing its theoretical foundations, key protocols such as quantum key distribution (QKD), and experimental implementations. We highlight the advantages of quantum cryptography over classical cryptographic techniques and explore its potential applications in secure communication networks, financial transactions, and data privacy. Furthermore, we discuss ongoing research efforts and challenges in the practical deployment of quantum cryptography systems, including the development of robust quantum hardware and the integration of quantum cryptographic protocols into existing communication infrastructures. Overall, quantum cryptography holds great promise for enabling secure communication channels that are resilient to quantum attacks, paving the way for a new era of ultra-secure information exchange.
We study a general quantum key distribution protocol in higher dimension. In this protocol, quantum states in arbitrary g+1g+1g+1 ($1\ensuremath{\le}g\ensuremath{\le}d$) out of all d+1d+1d+1 mutually unbiased bases in a ddd-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=1g=1g=1 and ddd. In our investigation, we study Eve's attack by two slightly different approaches. One is considering the optimal cloner of 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 $g=d\ensuremath{-}1$ quantum key distribution.