Two-way protocols for quantum cryptography with a nonmaximally entangled qubit pair

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This paper proposes a scheme for quantum cryptography with a nonmaximally entangled qubit pair. In a two-way configuration similar to quantum super dense coding, a two-bit key can be distributed by a round trip of one particle of the qubit pair and received by an appropriate joint measurement with the other. The security of our scheme is based on the quantum-mechanical impossibility of local unitary transformation between certain nonmaximally entangled states. Although an eavesdropper, Eve, can always identify the quantum state and intercept the key, it is impossible for her to resend the state with a unity probability and the legitimate parties inevitably detect her. Our protocol is also capable to quantum secure direct communication.