Identification of Causal Influences in Quantum Processes
- URL: http://arxiv.org/abs/2311.08882v1
- Date: Wed, 15 Nov 2023 11:41:18 GMT
- Title: Identification of Causal Influences in Quantum Processes
- Authors: Isaac Friend (University of Oxford), Aleks Kissinger (University of
Oxford)
- Abstract summary: A major obstacle to a theory of causal identification in the quantum setting is the question of what should play the role of "observational data"
We present sufficient conditions for quantum causal identification, starting with a quantum analogue of the well-known "front-door criterion"
Results emerge from generalizing the process-theoretic account of classical causal inference due to Jacobs, Kissinger, and Zanasi.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Though the topic of causal inference is typically considered in the context
of classical statistical models, recent years have seen great interest in
extending causal inference techniques to quantum and generalized theories.
Causal identification is a type of causal inference problem concerned with
recovering from observational data and qualitative assumptions the causal
mechanisms generating the data, and hence the effects of hypothetical
interventions. A major obstacle to a theory of causal identification in the
quantum setting is the question of what should play the role of "observational
data," as any means of extracting data at a certain locus will almost certainly
disturb the system. Hence, one might think a priori that quantum measurements
are already too much like interventions, so that the problem of causal
identification trivializes. This is not the case. Fixing a limited class of
quantum instruments (namely the class of all projective measurements) to play
the role of "observations," we note that as in the classical setting, there
exist scenarios for which causal identification is not possible. We then
present sufficient conditions for quantum causal identification, starting with
a quantum analogue of the well-known "front-door criterion" and finishing with
a broader class of scenarios for which the effect of a single intervention is
identifiable. These results emerge from generalizing the process-theoretic
account of classical causal inference due to Jacobs, Kissinger, and Zanasi
beyond the setting of Markov categories, and thereby treating the classical and
quantum problems uniformly.
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