Necessary Condition for Steerability of Arbitrary Two-Qubit States with Loss

Einstein–Podolsky–Rosen steering refers to the quantum phenomenon whereby the state of a system held by one party can be ‘steered’ into different states at the will of another, distant, party by performing different local measurements. Although steering has been demonstrated in a number of experiments involving qubits, the question of which two-qubit states are steerable remains an open theoretical problem. Here, we derive a necessary condition for any two-qubit state to be steerable when the steering party suffers from a given probability of qubit loss. Our main result finds application in one-way steering demonstrations that rely upon loss. Specifically, we apply it to a recent experiment on one-way steering with projective measurements and POVMs, reported by Wollmann et al (2016 Phys. Rev. Lett. 116 160403).