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Journal of Experimental and Theoretical Physics Letters

Quantum key distribution in a single-photon regime with nonorthogonal basis states

Dmitry Anatolevich Kronberg, S. N. Molotkov

Published Jun 1, 2009• 1 citation
Publisher

Abstract

A quantum key distribution protocol with nonorthogonal basis states is a generalization of the known BB84 key distribution protocol. The critical error and length of a secure key have been determined for the protocol with nonorthogonal basis states for an arbitrary angle between information states. An explicit optimal attack on the distributed key has been constructed; this attack maximizes eavesdropper information at a given error on the receiver side.

DOI
10.1134/s0021364009070133

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A quantum key distribution protocol with nonorthogonal basis states is a generalization of the known BB84 key distribution protocol. The critical error and length of a secure key have been determined for the protocol with nonorthogonal basis states for an arbitrary angle between information states. An explicit optimal attack on the distributed key has been constructed; this attack maximizes eavesdropper information at a given error on the receiver side.
A quantum key distribution (QKD) protocol based on constructed nonorthogonal states is proposed. By transmitting the photons from Bell states in random order the sender constructs nonorthogonal states, which can prevent an eavesdropper from extracting the key information. At the destination, the receiver performs Bell measurements and then obtains secure key. Different from previous nonorthogonal-states-based QKD protocols, our protocol exhibits a new feature, that is, the users can also obtain some key bits even when they choose different "bases"! Thus it can reach a higher efficiency in theory. Besides, we present a trade-off between the information that an eavesdropper can elicit and the corresponding error rate he/she would introduce, which shows that our protocol is secure.
Quantum key distribution(QKD) could be the most significant application of quantum information theory. In nearly four decades, although substantial QKD protocols are developed, the BB84 protocol and its variants are still the most researched ones. It is well-known that the secure bound of qubit error rate(QBER) of BB84 protocol is about 11%\%% while it can be increased to 12.6%\%% by six-state protocol. It would not be surprising that employing more basis could increase the bound. However, what is the optimal one? In this paper, investigations of asymptotically optimal QKD protocols are proposed. Precisely, We present an abstraction of prepare-measure QKD protocols and investigate two special cases which are optimal among all protocols coding by the same states. Our analyses demonstrate that the asymptotically optimal QBER bounds coding by orthogonal qubits are about 22.17%\%% for both general and memoryless attacks while the bounds coding by non-orthogonal states in two mutually unbiased basis are about 25.30%\%% for general attacks and 27.00%\%% for memoryless attacks. The significant improvement indicates the huge space for previous protocols to improve their security while the optimality of our protocols demonstrates the ultimate potential of their security.
We present and analyze a quantum key distribution protocol based on sending entangled NNN-qubit states instead of single-qubit ones as in the trail-blazing scheme by Bennett and Brassard 1984 (BB84). Since the qubits are sent and acknowledged individually, an eavesdropper is limited to accessing them one by one. In an intercept-resend attack, this fundamental restriction allows one to make the eavesdropper's information on the transmitted key vanish if even one of the qubits is not intercepted. The implied upper bound 1∕(2N)1∕(2N)1∕(2N) for this information is further shown not to be the lowest, as the information can be reduced to less than 30% of that in the BB84 scheme in the case N=2N=2N=2. In general, the protocol is at least as secure as BB84.
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.