FA-91112 / Quantum circuit simulation / Member archive

Reduced density matrix is not trace-normalized · case 02

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

Member previewVariant 2 · 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 1	`{"purity": 948.869857, "rho": [[[21.328122, 0.0], [9.389617, 2.449342]], [[9.389617, -2.449342], [17.482926, 0.0]]]}`	`{"purity": 0.629935, "rho": [[[0.549537, 0.0], [0.241932, 0.063109]], [[0.241932, -0.063109], [0.450463, 0.0]]]}`	Failed

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