Quantum Grid States and Hybrid Graphs
arXiv:2207.09826 · doi:10.1103/PhysRevA.107.042425
Abstract
Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement properties of grid states are adapted to these interpretations. These additional classes of grid states are shown to exhibit rich entanglement properties, including bound entanglement. Further, we introduce graphical techniques to construct bound entangled states in a modular fashion. We also extend the grid states model to hypergraphs. Our work, on one hand, opens up possibilities for constructing additional families of mixed quantum states in the grid state model. On the other hand, it can serve as an instrument for investigating entanglement problems from a graph theory perspective.
arXiv comment12 pages, 8 figures
References in corpus (11)
- Separability of Mixed States: Necessary and Sufficient Conditions
- Separability criterion and inseparable mixed states with positive partial transposition
- Bound entanglement can be activated
- Secure key from bound entanglement
- Reflections upon separability and distillability
- Quantum states with a positive partial transpose are useful for metrology
- Measurement-free preparation of grid states
- Some families of density matrices for which separability is easily tested
- Bound entangled singlet-like states for quantum metrology
- Entanglement properties of quantum grid states
- Activation of nonlocality in bound entanglement