Elimination of quantum causal confusion in the presence of dual states

Abstract

There is a rich class of bipartite quantum correlations between qubits which are consistent both with measurements performed in parallel and measurements performed in sequence. This phenomenon has recently been termed \emph{quantum causal confusion}, which is made mathematically precise by the notion of a dual state---a bipartite density operator whose associated correlations are causally ambiguous. A natural question is then whether or not the spatial and temporal scenarios associated with a dual state are fundamentally indistinguishable from a causal perspective. Here we show that as long as the reduced density operator of a dual state is oblique---meaning that all coefficients in its Pauli expansion are non-zero---then the underlying joint probabilities giving rise to such causally ambiguous correlations will differ in the spatial and temporal scenarios. Specifically, the temporal joint probabilities will inherently violate the no-signalling condition, thus eliminating quantum causal confusion. Moreover, as oblique states form an open dense subset of the Bloch ball, the elimination of quantum causal confusion is the norm rather than an exception.