FA-91113 / Quantum circuit simulation / Member archive

Reduced density matrix is not trace-normalized · case 03

An unnormalized GHZ input yields a reduced matrix with trace 8.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [n, amps, keep]; trace out every qubit except keep (0 = LSB) from the pure state and return {"rho": 2x2 matrix of [re, im] entries with rho[r][c] = sum psi_r psi_c^*, trace-normalized, "purity": sum |rho_rc|^2}, all rounded to 6 decimals.

Why this case matters

Reduced states quantify entanglement and are used in debugging subsystem behavior; index or conjugation slips give non-physical matrices.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression: random reduction 4	`{"purity": 12.376083, "rho": [[[2.243891, 0.0], [0.136737, 1.267171]], [[0.136737, -1.267171], [2.022918, 0.0]]]}`	`{"purity": 0.679793, "rho": [[[0.525894, 0.0], [0.032047, 0.296983]], [[0.032047, -0.296983], [0.474106, 0.0]]]}`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.