| # Entropy (partial trace, von Neumann entropy, mutual information) | |
| Multi-qubit partial trace, von Neumann entropy, and quantum mutual | |
| information — nothing like this existed anywhere in the package before | |
| these functions were promoted. The only prior partial trace | |
| (`dashboard_core/state_visuals.py`'s private `_reduced_density_matrix`) | |
| is single-qubit-only and uses the *opposite*, little-endian convention | |
| (qubit 0 = least significant bit). This module uses the package's own | |
| convention instead, matching [`observables`](observables.md)/ | |
| `pauli_hamiltonian_to_matrix`: qubit 0 is the *most* significant bit of | |
| the basis-state index — do not mix the two, reusing the dashboard's | |
| helper here would silently transpose which qubits get traced out. | |
| `mutual_information` exists because a qubit entangled in a Bell pair (or | |
| more generally, maximally mixed on its own) has a marginal `<Z>` of | |
| exactly 0 regardless of what operation was applied to its partner — the | |
| no-signaling theorem, not a measurement limitation. Mutual information | |
| *can* reveal correlations a marginal expectation value structurally | |
| cannot, since it depends on the joint state of two subsystems, not | |
| either one alone. Verified against the exact textbook value for a Bell | |
| pair (`I = 2*ln(2)`, maximal) and a GHZ state. | |
| ::: dense_evolution.physics.entropy | |
| --- | |
| **See also**: [`fermions`](fermions.md) and [`trotter`](trotter.md), the | |
| other two modules promoted alongside this one from a real traversable- | |
| wormhole-inspired quantum teleportation reproduction (arXiv:2604.10090) | |
| — see [Dense-Evolution-Discovery](https://tatopenn-cell.github.io/Dense-Evolution-Discovery/wormhole_syk_teleportation/) | |
| for the real experiments, including a control run confirming | |
| `mutual_information` correctly returns exactly `0` when two subsystems | |
| are structurally disconnected. | |