FA-91119 / Quantum circuit simulation / Member archive

Reduced density purity ignores off-diagonal entries · case 04

A pure product qubit such as |+> reports purity 0.5 instead of 1.

Member previewVariant 4 · 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 8	`{"purity": 0.512448, "rho": [[[0.578893, 0.0], [0.238878, -0.116767]], [[0.238878, 0.116767], [0.421107, 0.0]]]}`	`{"purity": 0.653843, "rho": [[[0.578893, 0.0], [0.238878, -0.116767]], [[0.238878, 0.116767], [0.421107, 0.0]]]}`	Failed

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