Entanglement detection via Frank-Wolfe algorithms
Abstract.
Entanglement is the core feature in the quantum world, which plays an important role in many quantum information processes. For low-dimensional and small systems, quantum entanglement can be detected by the positive partial transpose (PPT) criterion sufficiently and necessarily. However, it is tricky to detect entanglement for high-dimensional and/or large multipartite quantum systems, both theoretically and numerically. In this work, with the help of the Frank-Wolfe algorithms, or named conditional gradient algorithms, and their progress in recent years, we develop a high-precision numerical tool that can certify quantum entanglement and quantum separability at the same time. Our method can detect the entanglement of bipartite systems with local dimensions higher than 20. For multipartite systems, our method can characterize entanglement within not only a specific partition, but also the more general k-separability structure, which includes the genuine multipartite entanglement (GME) problem (i.e., 2-separability), up to 10 qubits. Moreover, the overall design of the tool is oriented towards experimentation, which can access the raw data and achieve an operational entanglement witness. Last but not least, our method supports the analysis of noise robustness for arbitrary noise types, not limited to conventional white noise.
