Direct Purification of Bell and Multipartite GHZ States via Weak Measurement

Abstract

Maximally entangled states are crucial for various quantum information processing, yet their quality suffers from entanglement loss due to decoherence. In this paper, a direct purification technique that utilizes weak measurement and requires only two copies of the entangled state is proposed. The method involves transforming the damped entangled state with weak measurements and then applying a direct purification process. This approach yields a maximally entangled state with a certain probability. In the context of Bell state purification, two weak measurement-based operations designed to convert amplitude-damped Bell states into the desired state for direct purification method are presented. The first operation is applied prior to the noisy channel, while the second is employed after the noisy channel. Through comprehensive analysis, the performances of these two schemes are evaluated and compared and benchmarked them against a pioneering weak measurement-based scheme. The findings demonstrate that the proposed methods exhibit superior performance in terms of both fidelity and probability. Additionally, a novel technique for purifying multipartite amplitude-damped Greenberger–Horne–Zeilinger (GHZ) states is introduced, which existing methods cannot address. By employing only two copies of the entangled states and harnessing the unique advantages of weak measurement operations, the method achieves both resource efficiency and effectiveness.