Partial transpose criteria for symmetric states

Abstract

We express the positive partial transpose (PPT) separability criterion for symmetric states of multi-qubit systems in terms of matrix inequalities based on the recently introduced tensor representation for spin states. We construct a matrix from the tensor representation of the state and show that it is similar to the partial transpose of the density matrix written in the computational basis. Furthermore, the positivity of this matrix is equivalent to the positivity of a correlation matrix constructed from tensor products of Pauli operators. This allows for a more transparent experimental interpretation of the PPT criteria for an arbitrary spin-j state. The unitary matrices connecting our matrix to the partial transpose of the state generalize the so-called magic basis that plays a central role in Wootters' explicit formula for the concurrence of a 2-qubit system and the Bell bases used for the teleportation of a one or two-qubit state.

8 pages

References in corpus (6)

• Entanglement and permutational symmetry
• Multiqubit symmetric states with high geometric entanglement
• All Maximally Entangled Four Qubits States
• Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Tensor Representation of Spin States

Cited by in corpus (5)

• Absolutely classical spin states
• Separability criteria based on Heisenberg-Weyl representation of density matrices
• Genuinely entangled symmetric states with no $N$-partite correlations
• Geometric Multiaxial Representation of N-qubit Mixed Symmetric Separable States
• Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement