[en] The problem studied by Verstraete, Audenaert and De Moor [1] - about the global unitary operations that maximise the entanglement of a bipartite system of qubits - is revisited and solved when we consider the permutation symmetry between the qubits. This condition appears naturally in bosonic or spin-1 systems [2]. Our results also allow us to characterise the set of symmetric absolutely separable states (SAS). For symmetric 3-qubit systems, we present numerical calculations for the maximum entanglement and analytical wirnesses for absolute separability. As an application of our results, we determine the minimum outer ball and the maximum inner ball of the set of SAS states around the maximally mixed state.
[1] F. Verstraete, K. Audenaert, and B. De Moor, Phys. Rev. A, 64, 012316, (2001).
[2] O. Giraud, P. Braun, and D. Braun, Phys. Rev. A, 78, 042112, (2008).
[3] E. Serrano-Ensástiga, and J. Martin, SciPost Phys. 15, 120 (2023).
Disciplines :
Physics
Author, co-author :
Serrano Ensástiga, Eduardo ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM)
Martin, John ; Université de Liège - ULiège > Département de physique ; Université de Liège - ULiège > Département de physique > Optique quantique ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM)
Denis, Jérôme ; Université de Liège - ULiège > Département de physique > Optique quantique ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM) ; Université de Liège - ULiège > Faculté des Sciences > Doct. scienc. (physiques)
Language :
English
Title :
Maximum entanglement and absolute separability of symmetric states under unitary transformations
