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tools/tests.py ​

class Space ​

Linear-algebra helpers for vector spaces and bipartite decompositions.

gramSchmidt ​

Gram-Schmidt orthonormalization.

Given vectors {vi}, constructs an orthonormal set {ui} spanning the same subspace (dropping near-zero residuals).

py
def gramSchmidt(vectors: np.ndarray) -> np.ndarray [static]
Implementation
python
def gramSchmidt(vectors: np.ndarray) -> np.ndarray:
    ortho = []
    for v in vectors:
        w = v - sum((np.dot(v, np.conj(u)) * u for u in ortho))
        if LA.norm(w) > 1e-08:
            ortho.append(w / LA.norm(w))
    return np.array(ortho)

schmidtDecompose ​

Schmidt decomposition via SVD.

Treats state as a bipartite coefficient matrix Ψ and returns singular triplets (λk,|uk⟩,|vk⟩) with Ψ=∑kλk|uk⟩⟨vk|.

py
def schmidtDecompose(state: np.ndarray) -> list [static]
Implementation
python
def schmidtDecompose(state: np.ndarray) -> list:
    U, D, V = LA.svd(state)
    dims = int(np.min(state.shape))
    return sorted([(D[k], U[:, k], V.T[:, k]) for k in range(dims)], key=lambda dec: dec[0], reverse=True)

schmidtRank ​

Schmidt rank (matrix rank) of a bipartite coefficient matrix.

py
def schmidtRank(mat: np.ndarray) -> int [static]
Implementation
python
def schmidtRank(mat: np.ndarray) -> int:
    return int(LA.matrix_rank(mat))

PPT ​

Peres–Horodecki (PPT) separability test for a bipartite density matrix.

Performs a blockwise partial transpose on subsystem blocks of size sub and checks positivity: ρTB⪰0.

Note: current implementation overrides sub to 3.

py
def PPT(rho: np.ndarray, sub: int) -> bool
Implementation
python
def PPT(rho: np.ndarray, sub: int) -> bool:
    side = rho.shape[0]
    sub = 3
    if side % sub != 0:
        raise ValueError(f'Matrix side ({side}) not divisible by sub ({sub})')
    mat0 = rho.copy()
    for i in range(0, mat0.shape[0], sub):
        for j in range(0, mat0.shape[1], sub):
            mat0[i:i + sub, j:j + sub] = mat0[i:i + sub, j:j + sub].T
    return bool(np.all(np.linalg.eigvals(mat0) >= 0))