Abstract
The concept of causal nonseparability has been recently introduced, in opposition to that of causal separability, to qualify physical processes that locally abide by the laws of quantum theory, but cannot be embedded in a well-defined global causal structure. While the definition is unambiguous in the bipartite case, its generalisation to the multipartite case is not so straightforward. Two seemingly different generalisations have been proposed, one for a restricted tripartite scenario and one for the general multipartite case. Here we compare the two, showing that they are in fact inequivalent. We propose our own definition of causal (non)separability for the general case, which—although a priori subtly different—turns out to be equivalent to the concept of ‘extensible causal (non)separability’ introduced before, and which we argue is a more natural definition for general multipartite scenarios. We then derive necessary, as well as sufficient conditions to characterise causally (non)separable processes in practice. These allow one to devise practical tests, by generalising the tool of witnesses of causal nonseparability.
Highlights
The notion of a causal order between events is an essential ingredient in our understanding of the world
We provide a characterisation of multipartite causallyseparable processes via necessary as well as sufficient conditions (Propositions 3, 4 and 5), allowing us to generalise the tool of witnesses of causal nonseparability
The formalism of process matrices was introduced in Ref. [2] to study correlations between events that locally obey the laws of quantum theory, but which are not a priori embedded into any global causal order
Summary
The notion of a causal order between events is an essential ingredient in our understanding of the world. A particular model describing causal relations between quantum events is the so-called process matrix formalism [2]. The physical resource relating the local events is described by a process matrix, which, broadly speaking, is a generalisation of a multipartite density matrix allowing for the description of signalling scenarios, such as quantum channels. As it turns out, some scenarios arising within this formalism are incompatible with any definite causal order. We provide a characterisation of multipartite causally (non)separable processes via necessary as well as sufficient conditions (Propositions 3, 4 and 5), allowing us to generalise the tool of witnesses of causal nonseparability
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