论文标题
mip*= re
MIP*=RE
论文作者
论文摘要
我们表明，可以通过与多个全能量量子抛弃共享纠缠纠缠的经典验证者来决定的语言类MIP*等于递归枚举的语言的类别。我们的证明是基于对（Natarajan和Vidick，Focs，2018年）的量子低度测试以及经典的低个体学位测试（Ji等，2020），通过整合（Natarajan and Wright，focs 2019）的最新发展，并将它们与递归的压缩框架结合在一起，并将其与Fitzsimons et al Al fitzsimons等（Fitzsimons et al and fitzsimons et and comply of Fitzsimons et and。 我们结果的直接副产品是，从停止问题到确定两个玩家的非局部游戏是纠缠$ 1 $还是最多$ 1/2 $的问题。使用已知的连接，纠缠值的不可证明性意味着对Tsirelson的问题有负面答案：我们通过提供一个明确的示例来表明，一组量子张量产品相关性的封闭$ C_ {QA} $严格包含在集合$ C_ {QC} $的量子通勤相关的集合中。在（Fritz，Rev。Math。Phys。2012）和（Junge等人，J。Math。Phys。2011）的工作之后，我们的结果提供了Connes嵌入的猜想的反驳。
We show that the class MIP* of languages that can be decided by a classical verifier interacting with multiple all-powerful quantum provers sharing entanglement is equal to the class RE of recursively enumerable languages. Our proof builds upon the quantum low-degree test of (Natarajan and Vidick, FOCS 2018) and the classical low-individual degree test of (Ji, et al., 2020) by integrating recent developments from (Natarajan and Wright, FOCS 2019) and combining them with the recursive compression framework of (Fitzsimons et al., STOC 2019). An immediate byproduct of our result is that there is an efficient reduction from the Halting Problem to the problem of deciding whether a two-player nonlocal game has entangled value $1$ or at most $1/2$. Using a known connection, undecidability of the entangled value implies a negative answer to Tsirelson's problem: we show, by providing an explicit example, that the closure $C_{qa}$ of the set of quantum tensor product correlations is strictly included in the set $C_{qc}$ of quantum commuting correlations. Following work of (Fritz, Rev. Math. Phys. 2012) and (Junge et al., J. Math. Phys. 2011) our results provide a refutation of Connes' embedding conjecture from the theory of von Neumann algebras.
