  Entanglement witnesses (EWs) are a versatile tool in the verification of
entangled states. The framework of mirrored EW doubles the power of a given EW
by introducing its twin -- a mirrored EW -- whereby two EWs related by
mirroring can bound the set of separable states more efficiently. In this work,
we investigate the relation between the EWs and its mirrored ones, and present
a conjecture which claims that the mirrored operator obtained from an optimal
EW is either a positive operator or a decomposable EW, which implies that
positive-partial-transpose entangled states, also known as the bound entangled
states, cannot be detected. This conjecture is reached by studying numerous
known examples of optimal EWs. However, the mirrored EWs obtained from the
non-optimal ones can be non-decomposable as well. We also show that mirrored
operators obtained from the extremal decomposable witnesses are positive
semi-definite. Interestingly, the witnesses that violate the well known
conjecture of Structural Physical Approximation, do satisfy our conjecture. The
intricate relation between these two conjectures is discussed and it reveals a
novel structure of the separability problem.
