Entanglement properties of quantum grid states

Abstract

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way. With these ideas we find bound entangled grid states for two-particle systems of any dimension and multiparticle grid states that provide examples for the different aspects of genuine multiparticle entanglement. Our findings suggest that entanglement theory for grid states, although being a discrete set, has already a complexity similar to the one for general states.

6 pages, 4 figures, v2: small changes, final version

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• Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts
• Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits
• Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states
• Bound entangled Bell diagonal states of unequal local dimensions, and their witnesses
• Multiparticle singlet states cannot be maximally entangled for the bipartitions
• Quantum Grid States and Hybrid Graphs
• Detection of $d_1\otimes d_2$ Dimensional Bipartite Entangled State: A Graph Theoretical Approach