  Recently, it has been shown that locally randomized measurements can be
employed to get partial transpose moments of a density matrix [Elben A., {\it
et al.} Phys. Rev. Lett. {\bf 125}, 200501 (2020)]. Consequently, two general
entanglement detection methods were proposed based on partial transpose moments
of a density matrix [Yu X-D., {\it et al.} Phys. Rev. Lett. {\bf 127}, 060504
(2021)]. In this context, a natural question arises that how partial transpose
moments are related with entanglement and with well known idea of principal
minors. In this work, we analytically demonstrate that for qubit-qubit quantum
systems, partial transpose moments can be expressed as simple functions of
principal minors. We expect this relation to exist for every bipartite quantum
systems. In addition, we have extended the idea of PT-moments for tripartite
qubit systems and have shown that PT-moments can only detect the whole range of
being NPT for $GHZ$ and $W$ states mixed with white noise.
