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arXiv 1405.7429quant-ph
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$π$ - LME态的纠缠和SAT问题

Entanglement of $π$-LME states and the SAT problem

Adi Makmal, Markus Tiersch, Vedran Dunjko, Shengjun Wu

发表信息：
Phys. Rev. A 90, 042308 (2014)
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摘要：

本文研究了一类$π$ -局域最大可纠缠态（$π$ -LME）的纠缠特性，这类态又被称为“实等权态”或“超图态”. $π$ -LME态包括被充分研究的量子态类（例如图形态），并且表现出很大程度的对称性。受LME态结构的启发，我们证明了（有效地）确定$π$ -LME态是否纠缠的能力意味着布尔可满足性（SAT）问题的有效解决方案。更具体地说，我们表明，这个特殊的纠缠检测问题，措辞作为一个决策问题，是$\mathsf{NP}$ -完成。我们考虑的限制设置产生了一个技术上无关的证明，并说明纠缠检测，即使在考虑的量子态是高度限制，仍然是困难的。

英文摘要：

In this paper we investigate the entanglement properties of the class of $π$-locally maximally entanglable ($π$-LME) states, which are also known as the "real equally weighted states" or the "hypergraph states". The $π$-LME states comprise well-studied classes of quantum states (e.g. graph states) and exhibit a large degree of symmetry. Motivated by the structure of LME states, we show that the capacity to (efficiently) determine if a $π$-LME state is entangled would imply an efficient solution to the boolean satisfiability (SAT) problem. More concretely, we show that this particular problem of entanglement detection, phrased as a decision problem, is $\mathsf{NP}$-complete. The restricted setting we consider yields a technically uninvolved proof, and illustrates that entanglement detection, even when quantum states under consideration are highly restricted, still remains difficult.

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