Quantum key distribution(QKD) is one of the most significant areas in quantum information theory. For nearly four decades, substantial QKD protocols and cryptographic methods are developed. In early years, the security of QKD protocols is depend on switching different bases, which, in fact, is based on non-orthogonal states. The most famous example is the BB84 protocol. Later, other techniques were developed for orthogonal states cryptography. Representations of such protocols include the GV protocol and order-rearrangement protocols. It might be harder to implement protocols based on orthogonal states since they require extra techniques to obtain the security. In this paper, we present two QKD protocols based on orthogonal states. One of them needs not to employ order-rearrangement techniques while the other needs. We give analyses of their security and efficiency. Also, anti-noisy discussions would be given, namely, we modify the protocols such that they could be implemented in noisy channels as in noiseless ones without errors. Our protocols are highly efficient when considering consumptions of both qubits and classical bits while they are robust over several noisy channels. Moveover, the requirement of maximally entangled states could be less than previous protocols and so the efficiency of measurements could be increased. Keywords: Quantum key distribution; Order-rearrangement; Orthogonal states; Noise; Qubit.
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