Deterministic and Efficient Quantum Key Distribution Using Entanglement Parity Bits and Ancillary Qubits

In this paper, we propose an efficient and deterministic quantum key distribution protocol for establishing a secret key between two untrusted users. In this protocol, a secret key is distributed to a sender and a receiver who share entangled states with a third trusted party but not with each other. This secret key is distributed by the means of special pure quantum states using remote state preparation and controlled gates. In addition, we employ the parity bits of the entangled pairs and the ancillary states to assist in preparing and measuring the secret states. Distributing a state to two users requires two maximally entangled pairs as the quantum channel and a two-particle von Neumann projective measurement. The proposed protocol is exact and deterministic. It distributes a secret key of <inline-formula> <tex-math notation="LaTeX">$ d $ </tex-math></inline-formula> qubits by the means of <inline-formula> <tex-math notation="LaTeX">$ 2d $ </tex-math></inline-formula> entangled pairs and, on average, <inline-formula> <tex-math notation="LaTeX">$ d $ </tex-math></inline-formula> bits of classical communication. We demonstrate the security of this protocol against entanglement attacks and present a method of privacy amplification.

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