There exist infinitely many kinds of partial separability/entanglement
arXiv:2112.05338 · doi:10.1063/5.0084613
Abstract
In tri-partite systems, there are three basic biseparability, -, - and - biseparability according to bipartitions of local systems. We begin with three convex sets consisting of these basic biseparable states in the three qubit system, and consider arbitrary iterations of intersections and/or convex hulls of them to get convex cones. One natural way to classify tri-partite states is to consider those convex sets to which they belong or do not belong. This is especially useful to classify partial entanglement of mixed states. We show that the lattice generated by those three basic convex sets with respect to convex hull and intersection has infinitely many mutually distinct members, to see that there are infinitely many kinds of three qubit partial entanglement. To do this, we consider an increasing chain of convex sets in the lattice and exhibit three qubit Greenberger-Horne-Zeilinger diagonal states distinguishing those convex sets in the chain.
arXiv comment9 pages, more detailed calculations was added. Accepted to Journal of Mathematical Physics
References in corpus (24)
- Quantum entanglement
- Three qubits can be entangled in two inequivalent ways
- Entanglement detection
- Bell Inequalities and the Separability Criterion
- Unextendible Product Bases and Bound Entanglement
- Classification of mixed three-qubit states
- Exact and Asymptotic Measures of Multipartite Pure State Entanglement
- Separability criteria for genuine multiparticle entanglement
- Classification of multi-qubit mixed states: separability and distillability properties
- Separability and distillability of multiparticle quantum systems
- Genuinely Multipartite Concurrence of N-qubit X-matrices
- Multipartite entanglement measures
- Partial separability and entanglement criteria for multiqubit quantum states
- Partial separability revisited: Necessary and sufficient criteria
- k-stretchability of entanglement, and the duality of k-separability and k-producibility
- A study of separability criteria for mixed three-qubit states
- Construction of multi-qubit optimal genuine entanglement witnesses
- Three-qubit entanglement witnesses with the full spanning properties
- The classification of multipartite quantum correlation
- Various notions of positivity for bi-linear maps and applications to tri-partite entanglement
- Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification
- Multipartite entanglement
- On the convex cones arising from classifications of partial entanglement in the three qubit system
- Polytope structures for Greenberger-Horne-Zeilinger diagonal states