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Reduced density matrix matches on the kept qubit instead of the environment · case 05

A Bell state reduces to a matrix with coherences instead of the maximally mixed I/2.

Member previewVariant 5 · 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 11	`{"purity": 0.51492, "rho": [[[0.586371, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.413629, 0.0]]]}`	`{"purity": 0.955018, "rho": [[[0.497404, 0.0], [0.079671, 0.470271]], [[0.079671, -0.470271], [0.502596, 0.0]]]}`	Failed

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