Abstract
Fully entangled fraction (FEF) is a significant figure of merit for density matrices. In bipartite d ⊗ d quantum systems, the threshold value FEF > 1/d, dictates prominent implications for tasks like teleportation and entanglement distillation. Like separability, the value of FEF is also related to the choice of global basis of the underlying Hilbert space. A state having its FEF ≤ 1/d, might give a value > 1/d in another global basis. A change in the global basis corresponds to a global unitary action on the quantum state. In the present work, we find that there are quantum states whose FEF remains less than 1/d, under the action of any global unitary i.e., any choice of global basis. Based on the fixed spectrum of density matrices, we provide necessary and sufficient criteria in two qubit systems which also prove to be sufficient in any d⊗d dimensions, to identify such states. Further, we prove that states having their FEF bounded by 1/d under any global unitary, form a convex and compact set. This entails the distinction of states whose FEF can be increased beyond 1/d, through unitary action. The demarcation is of paramount importance as it provides for the identification of states which can prove to be useful in teleportation and entanglement distillation after the action of global unitary operators, as underpinned by illustrations in our work.
