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L6-10 · Design a quantum causal experiment

Specify an identifiable, testable causal comparison.

Level 6 icon Level 6 · Graduate
Objective. Specify an identifiable, testable causal comparison.
Before this lesson. L6-05, L6-07, L6-09
Hands-on lab. Noise and quantum channels

Learn

Start with a precise question and a list of candidate mechanisms. State which systems enter and leave each laboratory. Separate a direct channel from a common source where the question requires that distinction. List the operations and observations actually available to the experimenter.

Calculate predictions before collecting data. Find settings where the candidates differ, then allocate trials with a declared rule. Include calibration, drift controls, and a method for uncertainty. Reserve independent data for checking a fitted model. Report failures as evidence against the model assumptions.

A good design can return an inconclusive result. Two mechanisms may remain equivalent under restricted operations. In that case, report the equivalence or a bound rather than forcing a single graph. A larger model family needs its own identifiability and statistical analysis.

Practice

Solution

Identity predicts outcome - with probability one. Complete Z dephasing predicts one half. Calibrate the X measurement or verify preparation stability so apparatus error is not mistaken for channel dephasing.

Check your understanding

What is the correct result when all allowed predictions match?

Show the answer

A. Report an unresolved equivalence under the stated design

Matching predictions imply no identifying evidence within that design. A preference for simplicity can be stated, but it cannot be reported as experimental identification.

Sources

This lesson draws on Costa & Shrapnel, 2016Barrett et al., 2019Watrous, 2018.

Next: L7-01 · Define the learning task

References
  1. Costa, F., & Shrapnel, S. (2016). Quantum causal modelling. New Journal of Physics, 18(6), 063032. 10.1088/1367-2630/18/6/063032
  2. Barrett, J., Lorenz, R., & Oreshkov, O. (2019). Quantum Causal Models. https://arxiv.org/abs/1906.10726
  3. Watrous, J. (2018). The Theory of Quantum Information. https://cs.uwaterloo.ca/~watrous/TQI/