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L6-05 · Discovery and informational access

Identify the assumptions needed to infer a quantum causal structure.

Level 6 icon Level 6 · Graduate
Objective. Identify the assumptions needed to infer a quantum causal structure.
Before this lesson. L6-03, L6-04, L4-08
Hands-on lab. Qubits and the Bloch sphere

Learn

Causal discovery infers a graph or an equivalence class from data and assumptions. A quantum discovery procedure also needs a specified set of preparations and instruments. Restricted operations can hide distinctions between candidate processes. More samples cannot resolve a distinction absent from the measurement design.

Informationally complete operations span the operator space needed for reconstruction. Their availability is a strong experimental condition. Reconstructed operators also carry statistical error and calibration error. A discovery result should distinguish algebraic identifiability from stable estimation at the available sample size.

Faithfulness rules out certain exact cancellations between mechanisms and observed independences. It is an assumption about the data-generating model. It is not guaranteed by quantum mechanics. Report hidden-system assumptions, dimensional bounds, trusted instruments, and candidate graph restrictions beside the recovered structure.

Practice

Solution

They cannot be distinguished with that restricted design because the phase is global for |1>. Prepare |+> and measure X. Identity gives +, while Z gives -.

Check your understanding

What can repair a lack of informational access?

Show the answer

B. A suitable additional preparation or measurement

A new informative operation can separate previously identical predictions. Extra repetitions reduce uncertainty but cannot separate exactly equal predictions for the original design.

Sources

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

Next: L6-06 · Bell inequalities and causal inequalities

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