Nonclassically causal correlations without backwards-in-time signaling

We investigate the relationship between no-backwards-in-time signaling and classically causal correlations. We discover that, unlike the case for two parties, the no-backwards-in-time signaling paradigm for three parties is not enough to ensure that correlations can be reproduced with a classical causal ordering. We demonstrate this with an explicit example. We also generalize some existing results for linear two-time states to multiparty scenarios.

Figure 1

A laboratory which obeys the NBTS paradigm. Experimenters in this laboratory always perform measurements before transformations.

Figure 2

Pictorial representation of the setup that $\eta$ models. The black lines connecting laboratories represent channels with a $z$-basis measurement. The gates labeled $X$ are flip gates. Note that in the frame of each laboratory the output is produced before the input is received.