Characterizing generalized axisymmetric quantum states in $d\times d$ systems

Abstract

We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability problem for a subspace of these states and show that a sizable part of the family is bound entangled. We also calculate some of the Schmidt numbers for the family in $d=3$, thereby characterizing the dimensionality of entanglement. Our results allow us to estimate entanglement properties of arbitrary states, as general states can be symmetrized to the considered family by local operations.

15 pages, 5 figures. Comments are welcome!

References in corpus (15)

• Entanglement detection
• Multi-party entanglement in graph states
• Bloch vectors for qudits
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• The state space for two qutrits has a phase space structure in its core
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Evaluation of convex roof entanglement measures
• Geometric entanglement witnesses and bound entanglement
• Entanglement witnesses and geometry of entanglement of two--qutrit states
• Bound entanglement in the magic simplex of two--qutrits
• Entanglement criteria and full separability of multi-qubit quantum states
• Partial transpose as a direct link between concurrence and negativity
• How often is a random quantum state k-entangled?
• Arboreal Bound Entanglement
• Quantitative bound entanglement in two-qutrit states

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