  The task of device independent secure key distribution requires preparation
and subsequently distribution of nonlocal resources. For secured practical
implementation, one needs to take two initially uncorrelated quantum systems
and perform a unitary on the composite system to generate the nonlocal
resource, which is supposed to violate a Bell inequality (say, Bell-CHSH).
States which do not violate Bell-CHSH inequality, but violate it when
transformed by a global unitary, can be deemed useful for the preparation of
nonlocal resource. One may then start from a state which is Bell-CHSH local
(take for example, a pure product state) and apply an appropriate global
unitary on it which results in a Bell-CHSH non-local state. However, an
intriguing fact is the existence of useless states from which no Bell-CHSH
non-local resource can be generated with a global unitary. This is due to the
purity preserving nature of unitary operators which bound the amount of
correlation in the set of final states depending on the purity of the initial
(possibly uncorrelated) states. The present work confirms the existence of such
a set, pertaining to two qubit systems. The set exhibits counter intuitive
features by containing within it some entangled states which remain Bell-CHSH
local on the action of any unitary. From practical perspective, this work draws
a line between useful and useless states for the task of preparing nonlocal
resource using global unitary transformations. Furthermore through an analytic
characterization of the set we lay down a generic prescription through which
one can operationally identify the useful states. It has also been shown that
our prescription remains valid for any linear Bell inequality.
