Trading Causal Order for Locality.

Quantum theory admits ensembles of quantum nonlocality without entanglement (QNLWE). These ensembles consist of seemingly classical states (they are perfectly distinguishable and nonentangled) that cannot be perfectly discriminated with local operations and classical communication (LOCC). Here, we analyze QNLWE from a causal perspective, and show how to perfectly discriminate some of these ensembles using local operations and classical communication without definite causal order. Specifically, three parties with access to an instance of indefinite causal order-the Araújo-Feix-Baumeler-Wolf process-can perfectly discriminate the states in a QNLWE ensemble-the SHIFT ensemble-with local operations. Hence, this type of quantum nonlocality disappears at the expense of definite causal order while retaining classical communication. Our results thereby leverage the fact that LOCC is a conjunction of three constraints: local operations, classical communication, and definite causal order. Moreover, we show how multipartite generalizations of the Araújo-Feix-Baumeler-Wolf process are transformed into multiqubit ensembles that exhibit QNLWE. Such ensembles are of independent interest for cryptographic protocols and for the study of separable quantum operations unachievable with LOCC.

Contextuality without Incompatibility.

The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable notion of classicality is the existence of a generalized-noncontextual ontological model. In particular, this notion can imply constraints on the representation of outcomes even within a single nonprojective measurement. We leverage this fact to demonstrate that measurement incompatibility is neither necessary nor sufficient for proofs of the failure of generalized noncontextuality. Furthermore, we show that every proof of the failure of generalized noncontextuality in a quantum prepare-measure scenario can be converted into a proof of the failure of generalized noncontextuality in a corresponding scenario with no incompatible measurements.

From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism.

The Kochen-Specker theorem demonstrates that it is not possible to reproduce the predictions of quantum theory in terms of a hidden variable model where the hidden variables assign a value to every projector deterministically and noncontextually. A noncontextual value assignment to a projector is one that does not depend on which other projectors-the context-are measured together with it. Using a generalization of the notion of noncontextuality that applies to both measurements and preparations, we propose a scheme for deriving inequalities that test whether a given set of experimental statistics is consistent with a noncontextual model. Unlike previous inequalities inspired by the Kochen-Specker theorem, we do not assume that the value assignments are deterministic and therefore in the face of a violation of our inequality, the possibility of salvaging noncontextuality by abandoning determinism is no longer an option. Our approach is operational in the sense that it does not presume quantum theory: a violation of our inequality implies the impossibility of a noncontextual model for any operational theory that can account for the experimental observations, including any successor to quantum theory.

An experimental test of noncontextuality without unphysical idealizations.

To make precise the sense in which nature fails to respect classical physics, one requires a formal notion of classicality. Ideally, such a notion should be defined operationally, so that it can be subject to direct experimental test, and it should be applicable in a wide variety of experimental scenarios so that it can cover the breadth of phenomena thought to defy classical understanding. Bell's notion of local causality fulfils the first criterion but not the second. The notion of noncontextuality fulfils the second criterion, but it is a long-standing question whether it can be made to fulfil the first. Previous attempts to test noncontextuality have all assumed idealizations that real experiments cannot achieve, namely noiseless measurements and exact operational equivalences. Here we show how to devise tests that are free of these idealizations. We perform a photonic implementation of one such test, ruling out noncontextual models with high confidence.