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arXiv:quant-ph/9910095 · Physical Review A

Quantum cryptography using larger alphabets

Helle Bechmann-Pasquinucci, Wolfgang Tittel

Published May 16, 2000• 477 citations
arXivHTMLPDF

Abstract

Like all of quantum information theory, quantum cryptography is traditionally based on two-level quantum systems. In this paper, a protocol for quantum key distribution based on higher-dimensional systems is presented. An experimental realization using an interferometric setup is also proposed. Analyzing this protocol from the practical side, one finds an increased key creation rate while keeping the initial laser pulse rate constant. Analyzing it for the case of intercept/resend eavesdropping strategy, an increased error rate is found compared to two-dimensional systems, hence an advantage for the legitimate users to detect an eavesdropper.

DOI
10.1103/physreva.61.062308

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Like all of quantum information theory, quantum cryptography is traditionally based on two-level quantum systems. In this paper, a protocol for quantum key distribution based on higher-dimensional systems is presented. An experimental realization using an interferometric setup is also proposed. Analyzing this protocol from the practical side, one finds an increased key creation rate while keeping the initial laser pulse rate constant. Analyzing it for the case of intercept/resend eavesdropping strategy, an increased error rate is found compared to two-dimensional systems, hence an advantage for the legitimate users to detect an eavesdropper.
We introduce a new quantum key distribution protocol that uses d-level quantum systems to encode an alphabet with c letters. It has the property that the error rate introduced by an intercept-and-resend attack tends to one as the numbers c and d increase. In dimension d=2, when the legitimate parties use a complete set of three mutually unbiased bases, the protocol achieves a quantum bit error rate of 57.1%. This represents a significant improvement over the 25% quantum bit error rate achieved in the BB84 protocol or 33% in the six-state protocol.
Employing the fundamental laws of quantum physics, Quantum Key Distribution (QKD) promises the unconditionally secure distribution of cryptographic keys. However, in practical realisations, a QKD protocol is only secure, when the quantum bit error rate introduced by an eavesdropper unavoidably exceeds the system error rate. This condition guarantees that an eavesdropper cannot disguise his presence by simply replacing the original transmission line with a less faulty one. Unfortunately, this condition also limits the possible distance between the communicating parties, Alice and Bob, to a few hundred kilometers. To overcome this problem, we design a QKD protocol which allows Alice and Bob to distinguish system errors from eavesdropping errors. If they are able to identify the origin of their errors, they can detect eavesdropping even when the system error rate exceeds the eavesdropping error rate. To achieve this, the proposed protocol employs an alternative encoding of information in two-dimensional photon states. Errors manifest themselves as quantum bit and as index transmission errors with a distinct correlation between them in case of intercept-resend eavesdropping. As a result, Alice and Bob can tolerate lower eavesdropping and higher system error rates without compromising their privacy.
The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a new system, based on a symbiosis of two existing ones, and for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible 1 experimental implementation.
The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a system, based on a symbiosis of two existing systems, for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible experimental implementation.
In this article, protocols for quantum key distribution based on encoding in higher dimensional systems in N-dimensional Hilbert space are proposed. We extend the original Bennett-Brassard protocol using two complementary bases and two-dimensional states to M mutually complementary bases and N orthogonal vectors in each base. We study the mutual information between the legitimate parties and the eavesdropper and the error rate by considering various incoherent eavesdropping attacks as a function of the dimension of the Hilbert space.
Quantum cryptography cannot prevent eavesdropping, but any eavesdropping attempt can be detected by the legitimate users of the communication channel. This is because eavesdropping affects the quantum state of the information carriers and results in an abnormal error rate. In this paper, we analyze various eavesdropping techniques, which may be either translucent or opaque to the transmitted photons, and we estimate the error rate above which the key distribution is deemed unsafe and should be abandoned.