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arXiv:quant-ph/0305018 · Physical Review A

Tomographic quantum cryptography

Yeong-Cherng Liang, Dagomir Kaszlikowski, Berthold‐Georg Englert, L. C. Kwek, C. H. Oh

Published Aug 29, 2003• 43 citations
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Abstract

We present a protocol for quantum cryptography in which the data obtained for mismatched bases are used in full for the purpose of quantum state tomography. Eavesdropping on the quantum channel is seriously impeded by requiring that the outcome of the tomography is consistent with unbiased noise in the channel. We study the incoherent eavesdropping attacks that are still permissible and establish under which conditions a secure cryptographic key can be generated. The whole analysis is carried out for channels that transmit quantum systems of any finite dimension.

DOI
10.1103/physreva.68.022324

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We present a protocol for quantum cryptography in which the data obtained for mismatched bases are used in full for the purpose of quantum state tomography. Eavesdropping on the quantum channel is seriously impeded by requiring that the outcome of the tomography is consistent with unbiased noise in the channel. We study the incoherent eavesdropping attacks that are still permissible and establish under which conditions a secure cryptographic key can be generated. The whole analysis is carried out for channels that transmit quantum systems of any finite dimension.
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. We show that---for protocols that use quantum channels of any dimension and completely characterize them by state tomography---the noise threshold for classical advantage distillation of a specific kind is substantially lower than the threshold for quantum entanglement distillation if the eavesdropper can perform powerful coherent attacks. In marked contrast, earlier investigations had shown that the thresholds are identical for incoherent attacks on the same classical distillation scheme. It remains an open question whether other schemes for classical advantage distillation have higher thresholds for coherent eavesdropping attacks.
We consider a variant of the BB84 protocol for quantum cryptography, the prototype of tomographically incomplete protocols, where the key is generated by one-way communication rather than the usual two-way communication. Our analysis, backed by numerical evidence, establishes thresholds for eavesdropping attacks on the raw data and on the generated key at quantum bit error rates of 10% and 6.15%, respectively. Both thresholds are lower than the threshold for unconditional security in the standard BB84 protocol.
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.
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.
The characterization of quantum processes, e.g. communication channels, is an essential ingredient for establishing quantum information systems. For quantum key distribution protocols, the amount of overall noise in the channel determines the rate at which secret bits are distributed between authorized partners. In particular, tomographic protocols allow for the full reconstruction, and thus characterization, of the channel. Here, we perform quantum process tomography of high-dimensional quantum communication channels with dimensions ranging from 2 to 5. We can thus explicitly demonstrate the effect of an eavesdropper performing an optimal cloning attack or an intercept-resend attack during a quantum cryptographic protocol. Moreover, our study shows that quantum process tomography enables a more detailed understanding of the channel conditions compared to a coarse-grained measure, such as quantum bit error rates. This full characterization technique allows us to optimize the performance of quantum key distribution under asymmetric experimental conditions, which is particularly useful when considering high-dimensional encoding schemes.