Local Density Matrices of Many-Body States in the Constant Weight Subspaces. Issue 3 (June 2019)

• Record Type: Journal Article
• Authors: Chen, Jianxin; Han, Muxin; Li, Youning; Zeng, Bei; Zhou, Jie
• Is Part Of: Reports on mathematical physics. Volume 83:Issue 3(2019)
• Page Start: 273
• Page End: 292
• Publication Date: 2019-06
• Subjects: constant weight subspace -- reduced density matrix -- perfect invariant tensors; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(19)30049-7
• Languages: English
• ISSNs: 0034-4877

Abstract

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.