L6-01 · Quantum common causes
Explain why a quantum common cause differs from a classical hidden variable.
Level 6 · Graduate
Objective. Explain why a quantum common cause differs from a classical hidden variable.
Before this lesson. L5-08, L4-01
Hands-on lab. Entanglement and Bell tests
Learn¶
A classical common cause can explain correlations through a shared variable. Given its complete value, the local response probabilities factorize in a local hidden-variable model. Bell correlations show that this classical explanation is insufficient under the Bell test assumptions.
A quantum common cause can distribute an entangled state to two laboratories. Each laboratory applies a local measurement. The joint probabilities follow the Born rule on the joint state. They need not admit a factorization over a measurement-independent classical common variable.
This does not require a direct influence between the laboratories. The preparation can be in their shared past. A quantum causal model describes allowed physical systems and transformations along causal connections. It changes the model class rather than granting permission to ignore experimental causal assumptions.
Practice¶
Solution
No. The stated mixture already produces perfect Z correlation without entanglement. One correlation table is insufficient. Use additional settings and a valid entanglement or Bell criterion.
Check your understanding¶
What changes in a quantum common-cause explanation?
A. The model permits a shared quantum state
B. Probabilities can be negative
C. Every correlation becomes signalling
Show the answer
A. The model permits a shared quantum state
The shared cause can be a quantum system in an entangled state. Outcome probabilities remain ordinary nonnegative normalized probabilities.
Sources¶
This lesson draws on Allen et al., 2017Bell, 1964.
Next: L6-02 · Channels in the Choi representation
- Allen, J.-M. A., Barrett, J., Horsman, D. C., Lee, C. M., & Spekkens, R. W. (2017). Quantum common causes and quantum causal models. Physical Review X, 7(3). 10.1103/PhysRevX.7.031021
- Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics Physique Fizika, 1(3), 195–200. 10.1103/physicsphysiquefizika.1.195