  Quantum entropy is an important measure for describing the uncertainty of a
quantum state, more uncertainty in subsystems implies stronger quantum
entanglement between subsystems. Our goal in this work is to quantify bipartite
entanglement using both von Neumann entropy and its complementary dual. We
first propose a type of dual entropy from Shannon entropy. We define
$S^{t}$-entropy entanglement based on von Neumann entropy and its complementary
dual. This implies an analytic formula for two-qubit systems. We show that the
monogamy properties of the $S^{t}$-entropy entanglement and the entanglement of
formation are inequivalent for high-dimensional systems. We finally prove a new
type of entanglement polygon inequality in terms of $S^{t}$-entropy
entanglement for quantum entangled networks. These results show new features of
multipartite entanglement in quantum information processing.
