Classification of four-qubit entangled states via machine learning

Abstract

We apply the support vector machine (SVM) algorithm to derive a set of entanglement witnesses (EW) to identify entanglement patterns in families of four-qubit states. The effectiveness of SVM for practical EW implementations stems from the coarse-grained description of families of equivalent entangled quantum states. The equivalence criteria in our work is based on the stochastic local operations and classical communication (SLOCC) classification and the description of the fourqubit entangled Werner states. We numerically verify that the SVM approach provides an effective tool to address the entanglement witness problem when the coarse-grained description of a given family state is available. We also discuss and demonstrate the efficiency of nonlinear kernel SVM methods as applied to four-qubit entangled state classification.

Non-unital channel can sometimes enhance faithfulness of two-qubit entanglement

“…The states with f ≤ 1/d are used to define the robustness of teleportability [10]. Similar to fidelity-based entanglement witnesses for bipartite states, this method was also extended to multipartite systems [11], coherence witness [12], and Schmidt number witnesses [5,[13][14][15][16]. A link between rank-constrained optimization and the theory of quantum entanglement was established.…”