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/
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 and trotter, the
other two modules promoted alongside this one from a real traversable-
wormhole-inspired quantum teleportation reproduction (arXiv:2604.10090)
— see Dense-Evolution-Discovery
for the real experiments, including a control run confirming
mutual_information correctly returns exactly 0 when two subsystems
are structurally disconnected.