J ul 2 01 9 Bipartite post-quantum steering in generalised scenarios

ly, we may view the steering scenario as one where Alice has a device that accepts a classical input, x, usually thought of as labelling the choice of measurement, and produces a classical outcome, a, usually thought of as the measurement result, while Bob has a device without an input, that produces a quantum outcome, ρa|x, correlated with the input and outcome of Alice, and usually thought of as the steered state. From this perspective, it becomes natural to ask the question of whether there could be steering beyond quantum theory. That is, could it be possible to find a pair of devices for Alice and Bob which could not be produced by Alice and Bob sharing a quantum state, upon which Alice performs quantum measurements labelled by x and with outcomes a? The only requirements that we wish to impose on the devices is that of relativistic causality – that the devices do not allow for signalling from Alice to Bob. In particular, if we conceive of hypothetical situations where the local structure of quantum theory is maintained, but the global structure is not – for instance having more general states or dynamics globally – a natural question is what observable nonlocal effects this might lead to, in the form of post-quantum steering. A celebrated theorem by Gisin [11] and Hughston, Josza and Wootters [12] (GHJW) shows that in fact, post-quantum steering cannot occur. Namely, any pair of devices that satisfies the no-signalling constraints from Alice and Bob can always be realised by some carefully chosen set of measurements on a carefully chosen quantum state. This traditional bipartite steering scenario is however not the only interesting scenario where one can see the general effect of steering. We can think more generally that steering is about correlations between devices that have only classical inputs and outcomes, and separated devices that produce quantum states. In [13], using this perspective, post-quantum multi-partite steering was demonstrated. In particular, it was shown that in a tri-partite scenario, when Alice and Bob have devices where the inputs and outcomes are classical, and Charlie’s device produces a quantum state, there are correlations that are consistent with relativistic causality, but which provably cannot arise in quantum theory, i.e., it is impossible to find a tripartite entangled states and measurements for Alice and Bob that reproduce the observed correlations. Unified frameworks for the study of quantum and post-quantum steering in the multipartite setting have subsequently been found, providing a playground for exploration of this fascinating effect [14, 15]. A key question that however remained open is whether it is possible to have post-quantum steering in a suitable bipartite generalised scenario. In this work, in order to provide an answer to this question, we explore three natural bipartite generalisations of the traditional steering scenario: (i) One where Alice performs a sequence of measurements on her untrusted black-box device while Bob remains passive; (ii) another in which Alice performs a single measurement, as in the conventional scenario, but where Bob has a random input that is used to prepare a quantum system; (iii) and finally