We use an error backpropagation (BP) neural network to determine whether an arbitrary two-qubit quantum state is steerable and optimize the steerability bounds of the generalized Werner state. Results show that, regardless of how we select the features for the quantum states, we can use the BP neural network to construct several models to obtain high-performance quantum steering classifiers compared with the support vector machine. Moreover, we predict the steerability bounds of the generalized Werner states using the classifiers that are newly constructed by the BP neural network; that is, the predicted steerability bounds are closer to the theoretical bounds. In particular, high-performance quantum steering classifiers with partial information about the quantum states that we need to measure in only three fixed measurement directions are obtained.

Wigner–Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity. We present the uncertainty principle for two successive projective measurements in terms of Wigner–Yanase skew information based on a single quantum system. It could capture the incompatibility of the observables, i.e. the lower bound can be nontrivial for the observables that are incompatible with the state of the quantum system. Furthermore, the lower bound is also constrained by the quantum Fisher information. In addition, we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state, respectively.