Implementing direct three-tangle measurement of tripartite GHZ states on IBM quantum platforms

Abstract

Among the various quantum phenomena that contribute to the efficiency of quantum computation compared to classical computation, entanglement plays a pivotal role. To witness and measure entanglement, various approaches such as concurrence for bipartite systems and tangle for three-qubit entangled systems have been developed. In this regard, researchers have endeavored to design algorithms capable of directly measuring these parameters to enhance efficiency and feasibility in computation. This topic has garnered significant attention due to its importance in the experimental implementation of desired quantum computations. While theoretical proposals are respected and have generated many unique ideas, experimental implementation can provide invaluable insights. To achieve this goal, IBM quantum platforms, available in cloud form, serve as unique testbeds for scrutinizing theoretical algorithms performed on these devices, which simulate artificial atoms using different technologies like low-capacitance Josephson junctions. In this paper, we propose a new algorithm capable of directly measuring the three-tangle in tripartite GHZ states. To assess the reliability of our algorithm, we ran experiments by executing the circuit on three IBM backends featuring 127 qubits, deliberately selecting qubits with the lowest readout error. Despite the NISQ nature of the IBM quantum platforms, the results indicate the precision of our proposed protocol. This research introduces a valuable protocol, alongside its experimental proof, to measure three-tangle without using tomography and intensive numerical optimization methods to calculate three-tangle.