Abstract
A recent framework of quantum theory with no global causal order predicts the existence of ‘causally nonseparable’ processes. Some of these processes produce correlations incompatible with any causal order (they violate so-called ‘causal inequalities’ analogous to Bell inequalities) while others do not (they admit a ‘causal model’ analogous to a local model). Here we show for the first time that bipartite causally nonseparable processes with a causal model exist, and give evidence that they have no clear physical interpretation. We also provide an algorithm to generate processes of this kind and show that they have nonzero measure in the set of all processes. We demonstrate the existence of processes which stop violating causal inequalities but are still causally nonseparable when mixed with a certain amount of ‘white noise’. This is reminiscent of the behavior of Werner states in the context of entanglement and nonlocality. Finally, we provide numerical evidence for the existence of causally nonseparable processes which have a causal model even when extended with an entangled state shared among the parties.
Highlights
It is well-known that quantum mechanics is at odds with naive notions of reality and locality as predicted by Bell’s celebrated theorem [1, 2]
Using a random sample generated by a ‘hit-and-run’ Markov chain [11, 12], we show that nonseparable processes with a causal model have nonzero measure in the space of all processes
We studied the classification of causally nonseparable process matrices for two parties and found that composing a class of causally separable processes with a transpose map on one party’s side results in nonseparable processes with causal models, i.e., that cannot violate causal inequalities
Summary
Original content from this Abstract work may be used under A recent framework of quantum theory with no global causal order predicts the existence of ‘causally the terms of the Creative Commons Attribution 3.0 nonseparable’ processes. Some of these processes produce correlations incompatible with any causal licence. We demonstrate the existence of processes which stop violating causal inequalities but are still causally nonseparable when mixed with a certain amount of ‘white noise’ This is reminiscent of the behavior of Werner states in the context of entanglement and nonlocality. We provide numerical evidence for the existence of causally nonseparable processes which have a causal model even when extended with an entangled state shared among the parties
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