The violation of a Bell inequality demonstrates that the outcomes of an experiment have contradicted a set of well defined classical intuitions. Quantum mechanics allows correlations between space-like separated parties that have no explanation in terms of a hidden variable model, i.e. they cannot be repro- duced with the help of classical computers running pre-agreed algorithms. However, when correlations are generated in a temporal scenario, by a sequence of time-like separated measurements, it is more difficult to demonstrate their non-classical nature. The causal structure of physics implies only one-way no-signalling, namely the impossibility of sending communication backwards in time. The only bound on forward signalling is the information capacity of the physical system.

We analyse a single quantum system measured at n points in time and consider to what extent one can prove that the correlations between these measurement outcomes could not be generated by a classical system.

**Non-classicality of temporal correlations**

S Brierley, A Kosowski, M Markiewicz, T Paterek, A Przysiezna

Phys. Rev. Lett. 115, 120404 (2015)

**Genuinely multi-point temporal quantum correlations and universal measurement-based quantum computing**

M Markiewicz, A Przysiezna, S Brierley, T Paterek

Phys. Rev. A 89, 062319 (2014)

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