Almost all even-particle pure states are determined by their half-body marginals

• URL: http://arxiv.org/abs/2401.07499v1
• Date: Mon, 15 Jan 2024 06:44:22 GMT
• Title: Almost all even-particle pure states are determined by their half-body marginals
• Authors: Wanchen Zhang, Fei Shi and Xiande Zhang
• Abstract summary: We show that almost all generic pure states of even $N$-particle with equal local dimension are uniquely determined among all other pure states (UDP) by four of their half-body marginals. We also give a graphical description of the marginals for determining genuinely multipartite entangled states.
• Score: 12.44437922654023
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Determining whether the original global state is uniquely determined by its local marginals is a prerequisite for some efficient tools for characterizing quantum states. This paper shows that almost all generic pure states of even $N$-particle with equal local dimension are uniquely determined among all other pure states (UDP) by four of their half-body marginals. Furthermore, we give a graphical description of the marginals for determining genuinely multipartite entangled states, which leads to several lower bounds on the number of required marginals. Finally, we present a construction of N-qudit states obtained from certain combinatorial structures that cannot be UDP by its k-body marginals for some k>N/2-1.

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