Entanglement Equivalence of $N$-qubit Symmetric States

Abstract

We study the interconversion of multipartite symmetric $N$-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local operation (ILO), then they belong necessarily to the separable, W, or GHZ entanglement class, establishing a practical method of discriminating subsets of entanglement classes. Furthermore, we prove that there always exists a symmetric ILO connecting any pair of symmetric $N$-qubit states equivalent under SLOCC, simplifying the requirements for experimental implementations of local interconversion of those states.

Minor corrections

References in corpus (10)

• Entanglement detection
• Constructing N-qubit entanglement monotones from anti-linear operators
• Entanglement and permutational symmetry
• Inductive Entanglement Classification of Four Qubits under SLOCC
• Sequential Generation of Matrix-Product States in Cavity QED
• Experimental observation of an entire family of four-photon entangled states
• Entanglement monotones and maximally entangled states in multipartite qubit systems
• Inductive classification of multipartite entanglement under SLOCC
• Multi-qubit entanglement engineering via projective measurements
• Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements

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