Improving Steering and Entanglement by Local Filtering Operation under Noisy Channels

In reality, a quantum system will inevitably interact with the environment around it, and this will lead to decoherence. In this paper, we mainly study quantum entanglement and Einstein–Podolsky–Rosen (EPR) steering of two-qubit system in some typical environments. Exactly, consider the initial two-qubit state to be the Werner-type state, we let one of the qubits pass through some different channels including amplitude damping (AD) channel, phase damping (PD) channel, phase flip (PF) channel, and bit flip (BF) channel. We research entanglement and EPR steering in the progress. Most importantly, we find that entanglement and EPR steering can be improved by local filtering operations with an appropriate k. Besides, we also give an example of the fact that the EPR steering is the proper subset of entanglement. These results will promote the application of the two quantum resources in quantum information tasks.