Quantifying entanglement is an important task by which the resourcefulness of a 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. Our first 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 our second separability test that is better suited for the capabilities of quantum computers available today. This VQSA has an additional interpretation as a distributed variational quantum algorithm (VQA) that can be executed over a quantum network, in which each node is equipped with classical and quantum computers capable of executing VQA. 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. Finally, the whole framework generalizes to the case of multipartite states and entanglement.

翻译：量化纠缠是衡量量子态资源性的重要任务。本文利用量子转向效应，开发了一种检测并量化一般两体态可分离性的量子算法。我们提出的首个可分离性测试涉及两方参与的分布式量子计算：计算能力受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试图将约化系统引导到纯积态的概率系综。为设计实用算法，我们通过参数化酉电路与经典优化技术的组合替代服务器角色，从而完成必要计算。由此产生的变分量子转向算法（VQSA）作为第二个可分离性测试，更适应于当前量子计算机的能力。该VQSA还可被解读为可在量子网络上执行的分布式变分量子算法（VQA），其中每个节点配备能执行VQA的经典计算机与量子计算机。我们在含噪声量子模拟器上模拟VQSA，并在测试实例中观察到良好的收敛特性。同时，我们开发了可在经典计算机上执行的半定规划程序，用于验证VQSA的结果。本研究因而建立了转向、纠缠、量子算法与量子计算复杂度理论之间的深刻联系，展示了参数化中间电路测量在VQSA中的价值，并代表了分布式VQA领域首个此类应用。最后，该框架可推广至多体态与多体纠缠情形。