Multipartite States under Elementary Local Operations
arXiv:1905.01824 · doi:10.1103/PhysRevA.100.022317
Abstract
Multipartite pure states are equivalent under Stochastic Local Operations and Classical Communication (SLOCC) whenever they can be mapped into one another by Invertible Local Operations. It is shown that this is equivalent to the inter-convertibility through finite sequences of Elementary Local Operations. A multipartite version of the Gauss-Jordan elimination strategy is then obtained, enabling the analytical SLOCC-classification of previously unknown examples. It is argued that the problem of SLOCC-classification is equivalent to the problem of classifying the Multipartite Fully Reduced Forms that the coefficient matrix of a state can assume after being subjected to this Gauss-Jordan elimination procedure. The method is applied to examples of so-called LME and hypergraph states, showing new SLOCC-equivalences. Moreover, possible physical implications for states with a Dicke-like structure are sketched.
arXiv commentPhys. Rev. A 100, 022317 (2019)
References in corpus (33)
- Quantum entanglement
- Three qubits can be entangled in two inequivalent ways
- Entanglement detection
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Quantum Resource Theories
- The role of quantum information in thermodynamics --- a topical review
- Quantum metrology from a quantum information science perspective
- Taming multiparticle entanglement
- Normal forms and entanglement measures for multipartite quantum states
- Classification of multipartite entangled states by multidimensional determinants
- Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states
- Converting Nonclassicality into Entanglement
- Entanglement Theory and the Second Law of Thermodynamics
- Quantum Hypergraph States
- Local unitary equivalence of multipartite pure states
- Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems
- Quasiprobabilities for Multipartite Quantum Correlations of Light
- Inductive classification of multipartite entanglement under SLOCC
- Multipartite Entanglement and Global Information
- Genuinely multipartite entangled quantum states with fully local hidden variable models and hidden multipartite nonlocality
- Entanglement and nonclassical properties of hypergraph states
- Encoding Hypergraphs into Quantum States
- Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
- Converting multilevel nonclassicality into genuine multipartite entanglement
- Characterizing multipartite entanglement classes via higher-dimensional embeddings
- Multiparticle entanglement as an emergent phenomenon
- Of Local Operations and Physical Wires
- Entanglement classification with matrix product states
- Qudit Hypergraph States
- Purification to Locally Maximally Entangleable States
- Characterizing ground and thermal states of few-body Hamiltonians
- Proving genuine multiparticle entanglement from separable nearest-neighbor marginals
- Bipartite bound entanglement in continuous variables through deGaussification