Abstract: 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) 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 $\frac{1}{2}$. 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.
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移动互联网商规28条
王吉斌、彭盾、程成 / 机械工业出版社 / 2014-6 / 49.00
每一次信息技术革命都会颠覆很多行业现有的商业模式和市场规则，当前这场移动互联网变革的波及面之广和蔓延速度之快，完全超出我们的想象。行业的边界被打破并互相融合，在此之前，我们只面临来自同行业的竞争，但是今天，我们不知道竞争对手会来自哪里。也许今天我们还是行业的巨人，但是明天就会被踩在脚下，当我们的体温犹热时，新的巨人已经崛起。诺基亚等传统科技巨头的衰退告诉我们，企业在一个时代的优势，到了另外一个新时......一起来看看 《移动互联网商规28条》 这本书的介绍吧!
