  We propose the resource theory of a special antiunitary asymmetry in quantum
theory. The notion of antiunitary asymmetry, in particular, ${\cal
PT}$-asymmetry is different from the usual resource theory for asymmetry about
unitary representation of a symmetry group, as the ${\cal PT}$ operator is an
antiunitary operator with ${\cal P}$ being any self-inverse unitary and ${\cal
T}$ being the time-reversal operations. Here, we introduce the ${\cal
PT}$-symmetric states, ${\cal PT}$-covariant operations and ${\cal
PT}$-asymmetry measures. For single qubit system, we find duality relations
between the ${\cal PT}$-asymmetry measures and the coherence. Moreover, for
two-qubit states we prove the duality relations between the ${\cal
PT}$-asymmetry measures and entanglement measure such as the concurrence. This
gives a resource theoretic interpretation to the concurrence which is lacking
till today. Thus, the ${\cal PT}$-asymmetry measure and entanglement can be
viewed as two sides of an underlying resource. Finally, the ${\cal
PT}$-symmetric dynamics is discussed and some open questions are addressed.
