Classification of Generaln-Qubit States under Stochastic Local Operations and Classical Communication in Terms of the Rank of Coefficient Matrix

2011/06/30 by Xiangrong Li, Dafa Li · 4 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physrevlett.108.180502

published as Phys. Rev. Lett. 108, 180502 (2012)

openalex publication_date 2012/05/03 · arxiv created 2012/05/04 · arxiv updated 2012/05/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient matrices associated with the states. The rank of the coefficient matrix is preserved under SLOCC and gives rise to a simple way of partitioning all the pure states of n qubits into different families of entanglement classes, as exemplified here. When applied to the symmetric states, this approach reveals that all the Dicke states |ℓ,n> with ℓ=1,…,[n/2] are inequivalent under SLOCC.

Citations

• Three qubits can be entangled in two inequivalent ways
• Characterizing the entanglement of symmetric many-particle spin-12systems

Cited by

• Entanglement classification of four-partite states under the SLOCC
• A generalization of Schmidt number for multipartite states
• Deterministic generation of arbitrary symmetric states and entanglement classes
• Detecting genuine multipartite correlations in terms of the rank of coefficient matrix