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 (SAS) states, 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.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 (SAS) states, 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.

arXiv:2112.05102SciPost PhysicsSep 28, 20236 citations

Absolutely classical spin states

Fabian Bohnet-Waldraff, O. Giraud, Daniel Braun

We introduce the concept of ``absolutely classical'' spin states, in analogy to absolutely separable states of bipartite quantum systems. Absolutely classical states are states that remain classical (i.e., a convex sum of projectors on coherent states of a spin $j$ ) under any unitary transformation applied to them. We investigate the maximal size of the ball of absolutely classical states centered on the maximally mixed state and derive a lower bound for its radius as a function of the total spin quantum number. We also obtain a numerical estimate of this maximal radius and compare it to the case of absolutely separable states.We introduce the concept of ``absolutely classical'' spin states, in analogy to absolutely separable states of bipartite quantum systems. Absolutely classical states are states that remain classical (i.e., a convex sum of projectors on coherent states of a spin $j$) under any unitary transformation applied to them. We investigate the maximal size of the ball of absolutely classical states centered on the maximally mixed state and derive a lower bound for its radius as a function of the total spin quantum number. We also obtain a numerical estimate of this maximal radius and compare it to the case of absolutely separable states.

arXiv:1611.06064Physical Review AJan 19, 201715 citations

Quantum Systems with Variables in ${\mathbb Z}(d)$ Quantum Systems with Variables in $${\mathbb Z}(d)$$

Apostol Vourdas

Quantum science and technologyJan 1, 20170 citations

Constructing Separable States in Infinite-Dimensional Systems by Operator Matrices

Jinchuan Hou, Jinfei Chai

arXiv:1612.01092International Journal of Theoretical PhysicsMar 25, 20172 citations

Constructing a ball of separable and absolutely separable states for

2\otimes d

quantum system

j

) under any unitary transformation applied to them. We investigate the maximal size of the ball of absolutely classical states centered on the maximally mixed state and derive a lower bound for its radius as a function of the total spin quantum number. We also obtain a numerical estimate of this maximal radius and compare it to the case of absolutely separable states.

Quantum Systems with Variables in

{\mathbb Z}(d)