论文标题
康纳斯暗示着Tsirelson：一个简单的证明
Connes implies Tsirelson: a simple proof
论文作者
论文摘要
更准确地说，我们给出了一个简单而简短的证明“ connes嵌入问题意味着同步的tsirelson猜想”，它仅依赖于两种基本成分：1）众所周知的同步相关性描述，将同步相关性描述为每个播放器代数的痕迹$ c^*（\ mathrm {player}）= c^*（\ mathrm {inputs} | \ mathrm {outputs}）$和2）Kim，Paulsen和Schafhauser的基本提升结果。此外，这绕过了基尔奇伯格（Kirchberg）以及任何其他隐式重新印象的深刻结果，因为微骨者的猜想和thelike。同时，我们还提供了Connes的代数$ \ Mathcal {r}^ω$出现在Connes嵌入问题中的不同结构，该问题更适合于量子信息理论的目的，并且在没有任何经营者代数的任何先前知识的情况下更容易理解读者。 但是，最重要的是，我们出于以下原因提供了此证明：由于最近通过MIP*= re对同步Tsirelson的驳斥，存在一个非局部游戏，违反了同步Tsirelson的猜想，并且通过MIP*= = RE的证明甚至是同步的这样的游戏。但是，该方法是基于与停止问题的不可证明性矛盾的基础，因此仍然是隐式的。因此，现在的任务已经开始给出一个同步游戏的明确示例，该游戏违反了同步的tsirelson猜想以及直接论证失败，而当前文章则是直接翻译到相应的操作员代数及其tracial状态，违反了Connes嵌入问题。
More precisely, we give a simple and very short proof of "the Connes embedding problem implies the synchronous Tsirelson conjecture" that relies on only two elementary ingredients: 1) the well-known description of synchronous correlations as traces on the algebra per player $C^*(\mathrm{player})=C^*(\mathrm{inputs}|\mathrm{outputs})$ and 2) an elementary lifting result by Kim, Paulsen and Schafhauser. Moreover, this bypasses every of the deep results by Kirchberg as well as any other implicit reformulation as the microstates conjecture and thelike. Meanwhile, we also give a different construction of Connes' algebra $\mathcal{R}^ω$ appearing in the Connes embedding problem, which is more suitable for the purposes of quantum information theory and much easier to comprehend for the reader without any prior knowledge in operator algebras. Most importantly, however, we present this proof for the following reason: Since the recent refutation of the synchronous Tsirelson conjecture by MIP*=RE, there exists a nonlocal game which violates the synchronous Tsirelson conjecture, and by the proof of MIP*=RE even a synchronous such game. The approach however is based on contradiction with the undecidability of the Halting problem, and so remains implicit. As such the quest now has started to give an explicit example of a synchronous game violating the synchronous Tsirelson conjecture together with a direct argument for the failure, and the current article serves as a direct translation to the corresponding operator algebra and its tracial state violating the Connes embedding problem.
