  Environmental interactions are ubiquitous in any real-world application of a
quantum information processing protocol. Such interactions result in depletion
of quantum resources. Two important figure of merits in the context of quantum
information are the fully entangled fraction (FEF) and conditional entropy of a
composite quantum system. FEF has a key role to play in tasks like
teleportation. Conditional entropy on the other hand can be negative for
certain quantum states and thus the negativity remains a resource for tasks
like dense coding and state merging. FEF $ > 1/d $ for a $ d \otimes d $
quantum system is a significant threshold, however for some quantum states it
remains less than the threshold even with global unitary operations,
consequently being known as states having absolute fully entangled fraction
(AFEF). Pertaining to conditional von Neumann entropy, there are some states
which retains the nonnegativity of the conditional entropy under global unitary
action, to be called as states with absolute conditional von Neumann entropy
nonnegative (ACVENN) property. In the present submission, we probe the action
of some quantum channels in two qubits and two qudits and find that some
quantum states move from the non-absolute regime to the absolute regime under
the action. Since, global unitary operations are unable to retrieve them back
to the non-absolute regime, we provide a prescription for the retrieval using
an entanglement swapping network. Furthermore, we extend the notion of
absoluteness to conditional R\'enyi entropies and find the required condition
for a state to have absolute conditional R\'enyi entropy non-negative (ACRENN)
property. We then extend the work to include the marginals of a tripartite
system and provide for their characterization with respect to the
aforementioned absolute properties.
