Absolutely entangled set of pure states

• URL: http://arxiv.org/abs/2011.04903v1
• Date: Tue, 10 Nov 2020 05:15:41 GMT
• Title: Absolutely entangled set of pure states
• Authors: Mao-Sheng Li, and Man-Hong Yung
• Abstract summary: Cai et al. [arXiv:2006.07165v1] proposed a new concept "absolutely entangled set" for bipartite quantum systems. We derive two necessity conditions for a set of states to be an absolutely entangled set. We obtain another construction of absolutely entangled set with $2n+1 elements in $mathbbC2otimes mathbbCn$.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Quite recently, Cai et al. [arXiv:2006.07165v1] proposed a new concept "absolutely entangled set" for bipartite quantum systems: for any possible choice of global basis, at least one state of the set is entangled. There they presented a minimum example with a set of four states in two qubit systems and they proposed a quantitative measure for the absolute set entanglement. In this work, we derive two necessity conditions for a set of states to be an absolutely entangled set. In addition, we give a series constructions of absolutely entangled bases on $\mathbb{C}^{d_1}\otimes \mathbb{C}^{d_2}$ for any nonprime dimension $d=d_1\times d_2$. Moreover, based on the structure of the orthogonal product basis in $\mathbb{C}^2\otimes \mathbb{C}^n$, we obtain another construction of absolutely entangled set with $2n+1$ elements in $\mathbb{C}^2\otimes \mathbb{C}^n$.

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