Partial transposition of state operator is a well-known tool to detect quantum correlations between two parts of a composite system. In this paper, the global partial transpose (GPT) is linked to conceptually multipartite underlying structures in a state—the negativity fonts. If $K$-way negativity fonts with nonzero determinants exist, then selective partial transposition of a pure state, involving $K$ of the $N$ qubits ($K⩽N$), yields an operator with negative eigenvalues, identifying $K$-body correlations in the state. Expansion of GPT in terms of $K$-way partially transposed (KPT) operators reveals the nature of intricate intrinsic correlations in the state. Classification criteria for multipartite entangled states based on the underlying structure of global partial transpose of canonical state are proposed. The number of $N$-partite entanglement types for an $N$-qubit system is found to be $2^{N-1}-N+2$, while the number of major entanglement classes is $2^{N-1}-1$. Major classes for three- and four-qubit states are listed. Subclasses are determined by the number and type of negativity fonts in canonical states.

• Received 4 February 2012

DOI:https://doi.org/10.1103/PhysRevA.85.042315