Locally inequivalent four qubit hypergraph states

Abstract

Hypergraph states as real equally weighted pure states are important resources for quantum codes of non-local stabilizer. Using local Pauli equivalence and permutational symmetry, we reduce the 32768 four qubit real equally weighted pure states to 28 locally inequivalent hypergraph states and several graph states. The calculation of geometric entanglement supplemented with entanglement entropy confirms that further reduction is impossible for true hypergraph states.

6 pages,2 figures, Accepted by J. Phys. A

References in corpus (9)

• Quantifying Entanglement
• Multi-party entanglement in graph states
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Robustness of entanglement
• Computing Local Invariants of Qubit Systems
• Quantum Hypergraph States
• Local unitary equivalence of multipartite pure states
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Encoding Hypergraphs into Quantum States

Cited by in corpus (9)

• Verified measurement-based quantum computing with hypergraph states
• Extreme violation of local realism in quantum hypergraph states
• Local unitary symmetries of hypergraph states
• Entanglement of random hypergraph states
• Efficient Entanglement Measure for Graph States
• Qudit hypergraph states and their properties
• A strong-weak coupling duality between two perturbed quantum many-body systems: CSS codes and Ising-like systems
• Multipartite entanglement sudden death and birth in randomized hypergraph states
• Multiple multi-control unitary operations: implementation and applications