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arXiv · 1704.08564

Local density matrices of many-body states in the constant weight subspaces

Jianxin Chen·Muxin Han·Youning Li·Bei Zeng·Jie Zhou
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Abstract

Let $V=\bigotimes_{k=1}^{N} V_{k}$ be the $N$ spin-$j$ Hilbert space with $d=2j+1$-dimensional single particle space. We fix an orthonormal basis $\{|m_i\rangle\}$ for each $V_{k}$, with weight $m_i\in \{-j,\ldots j\}$. Let $V_{(w)}$ be the subspace of $V$ with a constant weight $w$, with an orthonormal basis $\{|m_1,\ldots,m_N\rangle\}$ subject to $\sum_k m_k=w$. We show that the combinatorial properties of the constant weight condition imposes strong constraints on the reduced density matrices for any vector $|\psi\rangle$ in the constant weight subspace, which limits the possible entanglement structures of $|\psi\rangle$. Our results find applications in the overlapping quantum marginal problems, quantum error-correcting codes, and the spin-network structures in quantum gravity.

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Jianxin Chen, Muxin Han, Youning Li, Bei Zeng, Jie Zhou. 2017-04-27. Local density matrices of many-body states in the constant weight subspaces. https://doi.org/10.1016/s0034-4877(19)30049-7

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