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arXiv:quant-ph/9502020 · Physical Review A

Quantum cryptography with coherent states

B. Hüttner, N. Imoto, Nicolas Gisin, Tal Mor

Published Mar 1, 1995• 611 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.51.1863

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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.
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.
All existing quantum cryptosystems use nonorthogonal states as the carriers of information. Nonorthogonal states cannot be cloned (duplicated) by an eavesdropper. As a result, any eavesdropping attempt must introduce errors in the transmission, and, therefore, can be detected by the legal users of the communication channel. Orthogonal states are not used in quantum cryptography, since they can be faithfully cloned without altering the transmitted data. We present a cryptographic scheme based on orthogonal states, which also assures the detection of any eavesdropper.
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.
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.
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.
The cryptographic communication has a lot of important applications, particularly in the magnificent prospects of private communication. As one knows, the security of cryptographic channel depends crucially on the secrecy of the key. The Vernam cipher is the only cipher system which has guaranteed security. In that system the key must be as long as the message and most be used only once. Quantum cryptography is a method whereby key secrecy can be guaranteed by a physical law. So it is impossible, even in principle, to eavesdrop on such channels. Quantum cryptography has been developed in recent years. Up to now, many schemes of quantum cryptography have been proposed. Now one of the main problems in this field is how to increase transmission distance. In order to use quantum nature of light, up to now proposed schemes all use very dim light pulses. The average photon number is about 0.1. Because of the loss of the optical fiber, it is difficult for the quantum cryptography based on one photon level or on dim light to realize quantum key-distribution over long distance. A quantum key distribution based on coherent state is introduced in this paper. Here we discuss the feasibility and security of this scheme.