2023/03/23 by Griffiths, Robert B.
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2303.13617
Developing a quantum analog of the modern classical theory of causation, as formulated by Pearl and others using directed acyclic graphs, requires a theory of random or stochastic time development at the microscopic level, where the noncommutation of Hilbert-space projectors cannot be ignored. The Consistent Histories approach provides such a theory. How it works is shown by applying it to simple examples involving beam splitters and a Mach-Zehnder interferometer. It justifies the usual laboratory intuition that properly tested apparatus can reveal the earlier microscopic cause (e.g., as in radioactive decay) of a later macroscopic meassurement outcome. This approach is further illustrated by how it resolves the Bell inequalities paradox. The use of quantum circuits in discussions of quantum information in a time-irreversible manner can prevent the proper identification of earlier causes; this is illustrated using a specific circuit in the case of Bell inequalities. The approach to quantum causes known as Quantum Causal Models fails becuase it is not based upon a satisfactory theory of quantum random processes.