Universal observable detecting all two-qubit entanglement and determinant-based separability tests

Abstract

We construct a single observable, measurement of whose mean value on four copies of an unknown two-qubit state is sufficient to determine unambiguously whether the state is separable or entangled. In other words, there exists a universal collective entanglement witness detecting all two-qubit entanglement. The test is directly linked to a function that characterizes the entanglement quantitatively to some extent. This function is an entanglement monotone under so-called local pure operations and classical communication which preserve local dimensions. Moreover, it provides tight upper and lower bounds for negativity and concurrence. An elementary quantum computing device estimating unknown two-qubit entanglement is designed.