FA-91115 / Quantum circuit simulation / Member archive

Reduced density matrix is not trace-normalized · case 05

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

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 10	`{"purity": 102.876055, "rho": [[[3.824042, 0.0], [-3.202463, -3.042622]], [[-3.202463, 3.042622], [7.016133, 0.0]]]}`	`{"purity": 0.875471, "rho": [[[0.352766, 0.0], [-0.295425, -0.28068]], [[-0.295425, 0.28068], [0.647234, 0.0]]]}`	Failed

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