The single-letter characterisation of the entanglement-assisted capacity of a quantum channel is one of the seminal results of quantum information theory. In this paper, we consider a modified communication scenario in which the receiver is allowed an additional, `inconclusive' measurement outcome, and we employ an error metric given by the error probability in decoding the transmitted message conditioned on a conclusive measurement result. We call this setting postselected communication and the ensuing highest achievable rates the postselected capacities. Here, we provide a precise single-letter characterisation of postselected capacities in the setting of entanglement assistance as well as the more general nonsignalling assistance, establishing that they are both equal to the channel's projective mutual information -- a variant of mutual information based on the Hilbert projective metric. We do so by establishing bounds on the one-shot postselected capacities, with a lower bound that makes use of a postselected teleportation protocol and an upper bound in terms of the postselected hypothesis testing relative entropy. As such, we obtain fundamental limits on a channel's ability to communicate even when this strong resource of postselection is allowed, implying limitations on communication even when the receiver has access to postselected closed timelike curves.

翻译：对量子信道纠缠辅助容量的单字符描述是量子信息理论的开创性成果之一。本文考虑一种修正的通信场景，其中允许接收者获得一个额外的“非决定性”测量结果，我们采用由译码条件概率（以决定性测量结果为前提）定义的错误度量标准。我们将这一场景称为后选择通信，并由此定义可达到的最高速率为后选择容量。在纠缠辅助以及更一般的非信号辅助场景下，我们给出了后选择容量的精确单字符描述，证明两者均等于信道的投影互信息——一种基于希尔伯特投影度量的互信息变体。我们通过建立单次后选择容量的上下界实现这一结果：下界利用后选择遥传协议构建，上界则基于后选择假设检验相对熵。由此，即使允许后选择这一强大资源，我们仍获得了信道通信能力的基本极限，这意味着即使接收者能访问后选择封闭类时曲线，通信依然存在固有限制。