Local Density Matrices of Many-Body States in the Constant Weight Subspaces. Issue 3 (June 2019) - Chen, Jianxin; Han, Muxin; Li, Youning; Zeng, Bei; Zhou, Jie
Abstract : Let V = ⊗ N k =1 V k be an N -particle Hilbert space, whose individual single-particle space is the one with spin j and dimension d = 2 j + 1. Let V ( w ) be the subspace of V with constant weight w, consisting of vectors whose total spins are w . We show that the combinatorial properties of the constant weight condition impose strong constraints on the reduced density matrices for any vector |ψ) in the constant weight subspace V ( w ), which limit the possibility of the entanglement structures of |ψ). Our results find applications in the overlapping quantum marginal problem, quantum error-correcting codes, and the spin-network structures in quantum gravity.