The single-letter characterization 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 non-signalling 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：量子信道的纠缠辅助容量的单字母刻画是量子信息理论的重要奠基性成果之一。本文考虑一种改进的通信场景，允许接收者获得一个额外的"不确定"测量结果，并采用以确定性测量结果条件下解码传输消息的错误概率作为误差度量。我们称这种设置为后选择通信，并称由此得到的最高可达速率为后选择容量。在此，我们给出了纠缠辅助以及更一般的无信号辅助场景下后选择容量的精确单字母刻画，证明二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。我们通过建立后选择容量的单次容量界限来实现这一目标：下界采用后选择隐形传态协议，上界则基于后选择假设检验相对熵。由此，我们获得了即使在允许使用后选择这种强资源时信道通信能力的基本极限，这意味着即使接收者能够访问后选择闭合类时曲线，通信仍存在限制。