Witnessing network steerability of every bipartite entangled state without inputs
Phys. Rev. A 113, 032212 – Published 16 March, 2026
DOI: https://doi.org/10.1103/wtt8-fdj6
Abstract
Quantum steering is an asymmetric form of quantum nonlocality where one can detect whether a measurement on one system can steer or change another distant system. It is well known that there are quantum states that are entangled but unsteerable in the standard quantum steering scenario. Consequently, a long-standing open problem in this regard is whether the steerability of every entangled state can be activated in some way. In this work, we consider quantum networks and focus on the swap-steering scenario without inputs and find linear witnesses of network steerability corresponding to any negative partial transpose bipartite state and a large class of bipartite states that violate the computable cross-norm criterion. Interestingly, one of the inequalities shows an arbitrarily large gap between network steerable and unsteerable models. This is the only example in literature where such an unbounded gap could be established between any form of network local and nonlocal correlations, and notably, it arises in the case of no inputs from either party. Furthermore, by considering that the trusted party can perform tomography of the incoming subsystems, we construct linear inequalities to witness swap steerability of every bipartite entangled state. Consequently, for every bipartite entangled state one can now observe a form of quantum steering.
