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arXiv:0901.3909 · New Journal of Physics

High error-rate quantum key distribution for long-distance communication

Muhammad Mubashir Khan, Michael Murphy, Almut Beige

Published Jun 22, 2009• 57 citations
arXivHTMLPDF

Abstract

In the original BB84 protocol by Bennett and Brassard, an eavesdropper is detected because his attempts to intercept information result in a quantum bit error rate (QBER) of at least 25%. Here we design an alternative quantum key distribution protocol, where Alice and Bob use two mutually unbiased bases with one of them encoding a '0' and the other one encoding a '1'. The security of the scheme is due to a minimum index transmission error rate (ITER) introduced by an eavesdropper that increases significantly for higher-dimensional photon states. This allows for more noise in the transmission line, thereby increasing the possible distance between Alice and Bob without the need for intermediate nodes.

DOI
10.1088/1367-2630/11/6/063043

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In the original BB84 protocol by Bennett and Brassard, an eavesdropper is detected because his attempts to intercept information result in a quantum bit error rate (QBER) of at least 25%. Here we design an alternative quantum key distribution protocol, where Alice and Bob use two mutually unbiased bases with one of them encoding a '0' and the other one encoding a '1'. The security of the scheme is due to a minimum index transmission error rate (ITER) introduced by an eavesdropper that increases significantly for higher-dimensional photon states. This allows for more noise in the transmission line, thereby increasing the possible distance between Alice and Bob without the need for intermediate nodes.
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.
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.
We present the scheme of compatible quantum information analysis of the quantum key distribution (QKD) protocols, which give answers to the following questions: is it possible to improve the quantum bit error rate (QBER) of the 6-state protocol by employing more states, up to infinity, and can we essentially improve the QBER if the multidimensional Hilbert space with dimensionality more than 3 is used? Also, a novel quantum key distribution (QKD) protocol, based on all unselected states of a quantum system, which set the alphabet with continuous set of letters, is proposed. Employing all states of the Hilbert space leads to the maximal quantum uncertainty of transmitted states and therefore an eavesdropper receives the minimal amount of information. For the case of two-dimensional Hilbert space, our protocol allows secure transmission at the error rate higher than that one for the BB84-protocol and comparable with the characteristics of the best known QKD-protocols. However, with increasing the dimensionality of the Hilbert space the critical error rate for our protocol increases and in the limit of infinite-dimensional space the protocol becomes non-threshold.
Quantum key distribution (QKD) enables information-theoretic secure communication, yet its ultimate tolerance to noise and achievable transmission distance remain fundamentally constrained. We establish the maximum quantum bit error rate (QBER) compatible with secure QKD and derive corresponding upper bounds on communication distance. Our results follow from a fundamental capacity threshold for qubit Pauli channels and apply to protocols based on two or more mutually unbiased bases, using either single-photon or weak coherent sources. By connecting information-theoretic limits to realistic physical noise models, we obtain universal bounds on achievable distances in fiber and free-space links, including diffraction-limited constraints relevant to deep-space quantum communications. These findings clarify the ultimate noise robustness of QKD and delineate the fundamental boundaries of secure quantum communication.
Quantum Key Distribution (QKD) provides a secure way of generating shared cryptographic keys between a sender (Alice) and a receiver (Bob). The original BB84 protocol uses a two-dimensional polarization basis, limiting the information content of a single photon to 1 bit. Using the transverse position of single photons as one basis and the Fourier space as a second basis, one can construct a pair of mutually unbiased higher-dimensional bases. This improves not only the security of the protocol, but also the key generation rate. We present experimental results with a Spatial-Light-Modulator-based encoding scheme employing two nearly orthogonal alphabets with on the order of 103symbols each and an information content of about 10 bit.
Quantum key distribution (QKD) allows two spatially separated parties to securely generate a cryptographic key. The first QKD protocol, published by C. H. Bennett and G. Brassard in 1984 (BB84), describes how this is achieved by transmitting individual qubits and exchanging classical authenticated information. Any attempt to eavesdrop on the protocol introduces errors detectable by the legitimate parties. This Licentiate Thesis studies the recently introduced EEQKD protocol which builds on BB84. In EEQKD, the qubits sent individually in BB84 are entangled and thus not directly available to an eavesdropper who is, in this protocol, provided only one-by-one access to the transmission. The maximal information an eavesdropper can gain using a straightforward intercept-resend (IR) attack, is obtained for a given error rate. The secure key generation rate of EEQKD is estimated in practical scenarios including qubit loss and quantum channel noise. In addition, an exquisite vulnerability is exposed: For a particular setting of qubit entanglement, paradoxically proving most useful in the face of an IR attack, EEQKD reduces to BB84. Part of this research has been published in O. Ahonen et al., Physical Review A 78, 032314 (2008).