  Conditional von Neumann entropy is an intriguing concept in quantum
information theory. In the present work, we examine the effect of global
unitary operations on the conditional entropy of the system. We start with the
set containing states with non-negative conditional entropy and find that some
states preserve the non-negativity under unitary operations on the composite
system. We call this class of states as Absolute Conditional von Neumann
entropy Non Negative class (\textbf{ACVENN}). We are able to characterize such
states for $2\otimes 2$ dimensional systems. On a different perspective the
characterization accentuates the detection of states whose conditional entropy
becomes negative after the global unitary action. Interestingly, we are able to
show that this \textbf{ACVENN} class of states forms a set which is convex and
compact. This feature enables for the existence of hermitian witness operators
the measurement of which could distinguish unknown states which will have
negative conditional entropy after the global unitary operation. This has
immediate application in super dense coding and state merging as negativity of
conditional entropy plays a key role in both these information processing
tasks. Some illustrations are also provided to probe the connection of such
states with Absolute separable (AS) states and Absolute local (AL) states.
