Causal Influence in Quantum Theory
Talkat Quantum Physics and Statistical Causal Models (Simons Institute workshop, 2022) · 2022-04-27..04-29
summary
Proposes a formal account of causality in quantum theory that defines causal influence by unitary evolution and uses Choi-Jamiołkowski operators to prove an Uber Theorem: the unitary’s Choi operator factorizes into commuting channels from each output’s parent inputs. Deduces causal atomicity and causal reversibility, represents processes as stretched unitaries with quantum nodes giving a DAG, and develops direct-sum/tensor circuit decompositions that make direct causes explicit. Gives examples, proves existence for up to three inputs or outputs, leaves general existence open, and sketches ontic interpretations via index-valued facts.
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chapters (17)
- 0:00Introduction
- 2:50Outline
- 3:32Causal Influence
- 7:23Summary
- 9:17Notation
- 10:27Definition
- 12:58Uber Theorem
- 15:43Uber Theorem Consequences
- 18:40Causal Reversibility
- 20:25Quantum Processes
- 34:11unitary transformations
- 35:21extended circuit diagram
- 36:20unitary circuit diagram
- 39:38hidden variable theory
- 40:45Questions
- 49:19Defining causal influence
- 51:31Unitaries with multiple inputs