1 Introduction
2 Quantum conditional operators
3 Inferring acausal structures
-
\(\mathbb {G}=(\mathbf{X}, \mathbf{E})\) is a directed acyclic graph, where each vertex \(X_i\in \mathbf{X}\) is associated to a quantum system with space \(\mathcal {L}(\mathcal {H}_{i})\).
-
\(\mathbb {D}=\{\rho _{{X_i}|\Pi _{X_i}}:1\le i \le N\}\) is the set of the conditional operators between node \(X_i\) and its parents \(\Pi _{X_i}\).
4 Acausal structure in Monty Hall game
4.1 Classical case
Host | ||||||
---|---|---|---|---|---|---|
No. 0 | No. 1 | No.2 | ||||
Prize | No. 0 | Player | No. 0 | 0 |
\(\frac{1}{2}\)
|
\(\frac{1}{2}\)
|
No. 1 | 0 | 0 | 1 | |||
No. 2 | 0 | 1 | 0 | |||
No. 1 | Player | No. 0 | 0 | 0 | 1 | |
No. 1 |
\(\frac{1}{2}\)
| 0 |
\(\frac{1}{2}\)
| |||
No. 2 | 1 | 0 | 0 | |||
No. 2 | Player | No. 0 | 0 | 1 | 0 | |
No. 1 | 1 | 0 | 0 | |||
No. 2 |
\(\frac{1}{2}\)
|
\(\frac{1}{2}\)
| 0 |