Quantifying entanglement is an important task by which the resourcefulness of a quantum state can be measured. Here we develop a quantum algorithm that tests for and quantifies the separability of a general bipartite state, by making use of the quantum steering effect, the latter originally discovered by Schr\"odinger. Our separability test consists of a distributed quantum computation involving two parties: a computationally limited client, who prepares a purification of the state of interest, and a computationally unbounded server, who tries to steer the reduced systems to a probabilistic ensemble of pure product states. To design a practical algorithm, we replace the role of the server by a combination of parameterized unitary circuits and classical optimization techniques to perform the necessary computation. The result is a variational quantum steering algorithm (VQSA), which is a modified separability test that is better suited for the capabilities of quantum computers available today. We then simulate our VQSA on noisy quantum simulators and find favorable convergence properties on the examples tested. We also develop semidefinite programs, executable on classical computers, that benchmark the results obtained from our VQSA. Our findings here thus provide a meaningful connection between steering, entanglement, quantum algorithms, and quantum computational complexity theory. They also demonstrate the value of a parameterized mid-circuit measurement in a VQSA and represent a first-of-its-kind application for a distributed VQA.

翻译：量化纠缠是衡量量子态资源价值的重要任务。本文利用薛定谔最初发现的量子导引效应，发展了一种能够检测和量化一般二分态可分离性的量子算法。我们的可分离性测试涉及两个参与方的分布式量子计算：计算能力有限的客户端制备目标态的纯化态，而计算能力无限的服务器则尝试将约化系统导引至纯乘积态的概率系综。为设计实用算法，我们用参数化酉电路与经典优化技术的组合替代服务器角色来执行必要计算，最终得到变分量子导引算法（VQSA）——这是一种更适合当前量子计算机能力的改进型可分离性测试。我们在含噪量子模拟器上对VQSA进行仿真，在测试案例中观察到良好的收敛特性。同时开发了可在经典计算机上执行半定规划程序，用于基准测试VQSA的结果。本文的研究成果为导引、纠缠、量子算法与量子计算复杂度理论建立了有意义的联系，同时展示了参数化中间电路测量在VQSA中的价值，标志着分布式变分量子算法的首次实际应用。