We investigate the first-order theory of closed subspaces of complex Hilbert spaces in the signature \((\vee ,\perp ,0,1)\), where ‘\(\perp \)’ is the orthogonality relation. Our main result is that already its quasi-identities are undecidable: there is no algorithm to decide whether an implication between equations and orthogonality relations implies another equation. This is a corollary of a recent result of Slofstra in combinatorial group theory. It follows upon reinterpreting that result in terms of the hypergraph approach to quantum contextuality, for which it constitutes a proof of the inverse sandwich conjecture. It can also be interpreted as stating that a certain quantum satisfiability problem is undecidable.

我们研究签名\（（\ vee，\ perp，0,1）\）中复杂Hilbert空间的封闭子空间的一阶理论，其中' \（\ perp \） '是正交关系。我们的主要结果是，它的准恒性已经不可确定：没有算法可以确定方程式和正交关系之间的含意是否暗示着另一个方程式。这是Slofstra最近在组合群论中得出的结果。因此，根据超图论方法对量子语境进行了重新解释，从而构成了反三明治猜想的证明。也可以解释为说明某个量子可满足性问题是不确定的。