Thread by @fgrosshans

Now seated for a seminar by Zizhu Wang (王子竹) on
Entanglement and Nonlocality in Infinite 1D Systems (joint work with Sukhwinder Singh, and Miguel Navascués)
arXiv:1608.03485 arxiv.org/abs/1608.03485 / Phys. Rev. Lett. 118, 230401 (2017)
doi.org/10.1103/PhysRe…

Zizhu Wang looks at symmetrisation techniques to move between condense-matter n-body systems with no symmetry and infinite translation invariant systems. This procedure works when one only has access to local information
#LTQI

Zizhu Wang now look at the classical marginal problem: Does a finite distribution P(A₁, A₂, …, A_n) come from a translation invariant distribution ? Yes iff P_{A₁…A_{n-1}}(a₁,…,a_{n-1}) = P_{A₂…A_{n}}(a₁,…,a_{n-1})
#LTQI

Zizhu Wang: Now moves on to quantum problems, characterizing translation invariant (TI) and separable states. He ahs a characterization of TI and separable extention of a state, but it is neither simple (one needs to find the correct decomposition) nor intuitive.
#LTQI

Zizhu Wang: Looks for simpler characterization, but find many counter examples along the way and deos not find one. But he finds a way to estimate the size at which the extension becomes entangled. #LTQI

Zizhu Wang now moces on to characterize TI and local classical black boxes P(a_i|x_i). Its TI extension is the well known classical problem. It leads to a polytope.
#LTQI

Zizhu then find TI Bell’s inequalities with access to neighbours and nearest neighbours, the 3-2-2 Inequalities. To find states violating the inequality, he turns it into a 3-local 2-body Hamiltonian, then minimize the H oc infinit matrix product states [iMPS) #LTQI

Zizhu Wang: One of the intwi inequalities only detect tripartite non-locality (even if TI), the other detects genuinely TI nonlocality (even if the state is made tripartite local) #LTQI

Zizhu Wang moves on to 2D. Characterizing the marginals in 2D is more difficult. Actually, computing the nearest neighbour in general in undecidable in generl. For small number of values per site, the marginals are a polytope. For 3000 values, the set is no-longer algebraic #LTQI

Zizhu Wang’s paper on 2D is arXiv:1703.05640 arxiv.org/abs/1703.05640 #LTQI