Comment on “Quantum key agreement protocol”

Abstract

The first two-party Quantum Key Agreement (QKA) protocol, based on quantum teleportation, was proposed by Zhou et al. (Electron. Lett. 40(18) (2004) 1149). In this protocol, to obtain the key bit string, one of the parties uses a device to obtain the inner product of two quantum states, one being unknown, and the other one performs Bell measurement. However, in this paper, we show that it is not possible to obtain a device that would output the inner product of two qubits even when only one of the qubits is unknown. This is so because the existence of such a device would imply perfectly distinguishing among four different states in a two-dimensional vector space. This is not permissible in quantum mechanics. Furthermore, we argue that the existence of such a device would also imply a violation of the “No Signaling Theorem” as well.