Maximum entanglement of mixed symmetric states under unitary transformations
arXiv:2112.05102 · doi:10.21468/SciPostPhys.15.3.120
Abstract
We study the maximum entanglement that can be produced by a global unitary transformation for systems of two and three qubits constrained to the fully symmetric states. This restriction to the symmetric subspace appears naturally in the context of bosonic or collective spin systems. We also study the symmetric states that remain separable after any global unitary transformation, called symmetric absolutely separable states (SAS), or absolutely classical for spin states. The results for the two-qubit system are deduced analytically. In particular, we determine the maximal radius of a ball of SAS states around the maximally mixed state in the symmetric sector, and the minimal radius of a ball that contains the set of SAS states. As an application of our results, we also analyse the temperature dependence of the maximum entanglement that can be obtained from the thermal state of a spin-1 system with a spin-squeezing Hamiltonian. For the symmetric three-qubit case, our results are mostly numerical, and we conjecture a 3-parameter family of states that achieves the maximum negativity in the unitary orbit of any mixed state. In addition, we derive upper bounds, apparently tight, on the radii of balls containing only/all SAS states.
The updated version contains new material (9 pages approx.), including the study of the three-qubit system
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- Platonic dynamical decoupling sequences for interacting spin systems
- Nonequivalence between absolute separability and positive partial transposition in the symmetric subspace
- Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses
- Polytopes of Absolutely Wigner Bounded Spin States