Universal framework for entanglement detection

Abstract

We construct nonlinear multiparty entanglement measures for distinguishable particles, bosons, and fermions. In each case properties of an entanglement measure are related to the decomposition of the suitably chosen representation of the relevant symmetry group onto irreducible components. In the case of distinguishable particles considered entanglement measure reduces to the well-known many-particle concurrence. We prove that our entanglement criterion is sufficient and necessary for pure states living in both finite and infinite dimensional spaces. We generalize our entanglement measures to mixed states by the convex roof extension and give a nontrivial lower bound of thus obtained generalized concurrence.

Symmetry criteria for quantum simulability of effective interactions

“…Moreover, our results on quadratic symmetries distinguishing local properties from global ones can be generalized into an overarching framework that encapsulates concurrence (Example 1) and links naturally to entanglement detection via a quadratic invariant of the quantum system under local transformations in [75][76][77][78].…”

Multipartite concurrence for identical-fermion systems

“…Several efforts have been devoted to the study of the entanglement features in systems of N identical fermions in the last few years [13][14][15][16][17][18][19][20][21][22]. Various bipartite entanglement measures for pure N -fermion states have been discussed, yet these measures are, in general (for N > 2), difficult to implement [5].…”

Geometric entanglement in the Laughlin wave function

“…We note that while the geometric entanglement of spin systems have been extensively studied (e.g., see [17][18][19][20][21][22][23][24][25][26][27][28][29] and references therein), it is much less discussed for identical particles, although some works on symmetric spin states [20,21] can be translated into the bosonic language too. The reason might be that the extra symmetry or antisymmetry constraint makes the optimization problem seemingly more complicated [30][31][32][33]. Despite this difficulty, however, recently some progress has been made on the fermionic case [13,14,34,35].…”