Quantum correlations with no causal order

Abstract

The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? Here, we address these questions from the standpoint of quantum mechanics in a new framework for multipartite correlations that does not assume a pre-defined global causal structure but only the validity of quantum mechanics locally. All known situations that respect causal order, including space-like and time-like separated experiments, are captured by this framework in a unified way. Surprisingly, we find correlations that cannot be understood in terms of definite causal order. These correlations violate a 'causal inequality' that is satisfied by all space-like and time-like correlations. We further show that in a classical limit causal order always arises, which suggests that space-time may emerge from a more fundamental structure in a quantum-to-classical transition.

Causally nonseparable processes admitting a causal model

“…The Werner processes' causal nonseparability is more resistant to the introduction of 'white noise' than its ability to violate causal inequalities. This shows that the analogy between causal nonseparability and causal inequalities on the one hand, and entanglement and Bell inequalities on the other, extends beyond what was previously known [3,7,8,13].…”

“…They consist of wires, representing quantum systems, which connect boxes, representing quantum operations. While for quantum circuits, the order of the operations is fixed [14], situations where the order of operations is not well-defined are readily represented in the process matrix formalism [3], which can be thought of as a generalization of the quantum circuit formalism. We will briefly introduce the main elements of the formalism; a more detailed introduction to it can be found in [7].…”

“…These causal structures can produce correlations incompatible with any definite causal order, violating so-called 4 'causal inequalities' [3,4].…”

“…One might wonder whether peculiar quantum features could challenge other fundamental notions, like the concept of causality, as well. The process matrix formalism of Oreshkov, Costa and Brukner [3] was developed to explore this question-studying the most general causal structures compatible with local quantum mechanics for two parties A and B.…”

Functional quantum computing: An optical approach

“…This is best illustrated by the N − switch operation [4,5] which coherently permutes the orderings of N black box operators based on the value of control qubits and applies them to a target qubit register. In addition to being an interesting example of the differences between quantum functions and quantum circuits, arbitrary control over causal orderings is a useful mechanism for investigating the fundamental role of causality in quantum systems [10][11][12][13] and enhancing the efficiency of certain quantum information processing tasks [14,15]. A recent experiment has implemented 2−switch using spatial modes to control operator ordering, but to our knowledge there have been no practical proposals for permuting more than 2 operators.…”