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 ($K\ensuremath{\leqslant}N$), 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 ${2}^{N\ensuremath{-}1}\ensuremath{-}N+2$, while the number of major entanglement classes is ${2}^{N\ensuremath{-}1}\ensuremath{-}1$. Major classes for three- and four-qubit states are listed. Subclasses are determined by the number and type of negativity fonts in canonical states.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 ($K\ensuremath{\leqslant}N$), 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 ${2}^{N\ensuremath{-}1}\ensuremath{-}N+2$, while the number of major entanglement classes is ${2}^{N\ensuremath{-}1}\ensuremath{-}1$. Major classes for three- and four-qubit states are listed. Subclasses are determined by the number and type of negativity fonts in canonical states.

arXiv:1204.0376Physical Review AApr 13, 201214 citations

Complementary quantum correlations among multipartite systems

Zhi‐Xiang Jin, Shao-Ming Fei, Cong‐Feng Qiao

arXiv:2002.04456Quantum Information ProcessingFeb 4, 202017 citations

Scalable Test of Genuine Multipartite Entanglement via Partially Randomized Measurements

Jan Wojcik, Pawel Chrabkowski, Wieslaw Laskowski

Certifying genuine multipartite entanglement in quantum systems can require a number of measurements that grows exponentially with the system size. Here we introduce a criterion based on correlation-tensor subsector lengths restricted to local measurement planes and show that it can be evaluated using partially randomized measurements without an explicit exponential dependence on the number of qubits. We derive the corresponding bounds for $k$ -separable states and illustrate the criterion using representative families of multipartite entangled states. Finally, we demonstrate the practical applicability of the method on an ion-trap quantum computer by certifying genuine five-partite entanglement.Certifying genuine multipartite entanglement in quantum systems can require a number of measurements that grows exponentially with the system size. Here we introduce a criterion based on correlation-tensor subsector lengths restricted to local measurement planes and show that it can be evaluated using partially randomized measurements without an explicit exponential dependence on the number of qubits. We derive the corresponding bounds for $k$-separable states and illustrate the criterion using representative families of multipartite entangled states. Finally, we demonstrate the practical applicability of the method on an ion-trap quantum computer by certifying genuine five-partite entanglement.

quant-pharXiv:2608.13725Aug 17, 20260 citations

Generalized approach to quantify correlations in bipartite quantum systems

Diego G. Bussandri, A. P. Majtey, Pedro W. Lamberti +1 more

Feb 1, 20197 citations

K

-way negativity fonts with nonzero determinants exist, then selective partial transposition of a pure state, involving

K

of the

N

qubits ($K\ensuremath{\leqslant}N$), 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 ${2}^{N\ensuremath{-}1}\ensuremath{-}N+2$, while the number of major entanglement classes is ${2}^{N\ensuremath{-}1}\ensuremath{-}1$. Major classes for three- and four-qubit states are listed. Subclasses are determined by the number and type of negativity fonts in canonical states.

k

-separable states and illustrate the criterion using representative families of multipartite entangled states. Finally, we demonstrate the practical applicability of the method on an ion-trap quantum computer by certifying genuine five-partite entanglement.