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Refactor partial_trace and partial_transpose #158

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Jun 4, 2023
Merged

Refactor partial_trace and partial_transpose #158

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03d5d1c
Refactor partial_trace and partial_transpose
ErikQQY May 29, 2023
7519371
partail_trace done
ErikQQY Jun 1, 2023
7fda5b7
Done refactoring
ErikQQY Jun 3, 2023
ba67c16
Fix non-square test and wrong import
ErikQQY Jun 3, 2023
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108 changes: 54 additions & 54 deletions tests/test_channels/test_partial_trace.py
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86 changes: 36 additions & 50 deletions tests/test_channels/test_partial_transpose.py
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Original file line number Diff line number Diff line change
Expand Up @@ -13,19 +13,19 @@ def test_partial_transpose_bipartite():
rho = np.arange(16).reshape(4, 4)

# Partial transpose of first subsystem:
res = partial_transpose(rho, [1], [2, 2])
res = partial_transpose(rho, [0], [2, 2])
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expected_res = np.array([[0, 1, 8, 9], [4, 5, 12, 13], [2, 3, 10, 11], [6, 7, 14, 15]])
bool_mat = np.isclose(expected_res, res)
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of second subsystem:
res = partial_transpose(rho, [2], [2, 2])
res = partial_transpose(rho, [1], [2, 2])
expected_res = np.array([[0, 4, 2, 6], [1, 5, 3, 7], [8, 12, 10, 14], [9, 13, 11, 15]])
bool_mat = np.isclose(expected_res, res)
np.testing.assert_equal(np.all(bool_mat), True)

# Full transpose:
res = partial_transpose(rho, [1, 2], [2, 2])
res = partial_transpose(rho, [0, 1], [2, 2])
expected_res = np.array([[0, 4, 8, 12], [1, 5, 9, 13], [2, 6, 10, 14], [3, 7, 11, 15]])
bool_mat = np.isclose(expected_res, res)
np.testing.assert_equal(np.all(bool_mat), True)
Expand Down Expand Up @@ -59,7 +59,7 @@ def test_partial_transpose_sys():

expected_res = np.array([[1, 2, 9, 10], [5, 6, 13, 14], [3, 4, 11, 12], [7, 8, 15, 16]])

res = partial_transpose(test_input_mat, 1)
res = partial_transpose(test_input_mat, [0])

bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)
Expand All @@ -71,7 +71,7 @@ def test_partial_transpose_sys_vec():

expected_res = np.array([[1, 5, 9, 13], [2, 6, 10, 14], [3, 7, 11, 15], [4, 8, 12, 16]])

res = partial_transpose(test_input_mat, [1, 2])
res = partial_transpose(test_input_mat, [0, 1])

bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)
Expand All @@ -83,7 +83,7 @@ def test_partial_transpose_sys_vec_dim_vec():

expected_res = np.array([[1, 5, 9, 13], [2, 6, 10, 14], [3, 7, 11, 15], [4, 8, 12, 16]])

res = partial_transpose(test_input_mat, [1, 2], [2, 2])
res = partial_transpose(test_input_mat, [0, 1], [2, 2])

bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)
Expand All @@ -97,7 +97,7 @@ def test_partial_transpose_norm_diff():
in the standard transpose of the matrix.
"""
test_input_mat = np.arange(1, 17).reshape(4, 4)
res = np.linalg.norm(partial_transpose(test_input_mat, [1, 2]) - test_input_mat.conj().T)
res = np.linalg.norm(partial_transpose(test_input_mat, [0, 1]) - test_input_mat.conj().T)
expected_res = 0

np.testing.assert_equal(np.isclose(res, expected_res), True)
Expand All @@ -108,7 +108,7 @@ def test_partial_transpose_8_by_8_subsystems_2_2_2():
test_input_mat = np.arange(1, 65).reshape(8, 8)

# Partial transpose on first subsystem:
pt_1 = partial_transpose(test_input_mat, [1], [2, 2, 2])
pt_1 = partial_transpose(test_input_mat, [0], [2, 2, 2])
expected_pt_1 = np.array(
[
[1, 2, 3, 4, 33, 34, 35, 36],
Expand All @@ -125,7 +125,7 @@ def test_partial_transpose_8_by_8_subsystems_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on second subsystem:
pt_2 = partial_transpose(test_input_mat, [2], [2, 2, 2])
pt_2 = partial_transpose(test_input_mat, [1], [2, 2, 2])
expected_pt_2 = np.array(
[
[1, 2, 17, 18, 5, 6, 21, 22],
Expand All @@ -142,7 +142,7 @@ def test_partial_transpose_8_by_8_subsystems_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on third subsystem:
pt_3 = partial_transpose(test_input_mat, [3], [2, 2, 2])
pt_3 = partial_transpose(test_input_mat, [2], [2, 2, 2])
expected_pt_3 = np.array(
[
[1, 9, 3, 11, 5, 13, 7, 15],
Expand All @@ -159,7 +159,7 @@ def test_partial_transpose_8_by_8_subsystems_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on first and second subsystem:
pt_1_2 = partial_transpose(test_input_mat, [1, 2], [2, 2, 2])
pt_1_2 = partial_transpose(test_input_mat, [0, 1], [2, 2, 2])
expected_pt_1_2 = np.array(
[
[1, 2, 17, 18, 33, 34, 49, 50],
Expand All @@ -176,7 +176,7 @@ def test_partial_transpose_8_by_8_subsystems_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on first and third subsystem:
pt_1_3 = partial_transpose(test_input_mat, [1, 3], [2, 2, 2])
pt_1_3 = partial_transpose(test_input_mat, [0, 2], [2, 2, 2])
expected_pt_1_3 = np.array(
[
[1, 9, 3, 11, 33, 41, 35, 43],
Expand All @@ -193,7 +193,7 @@ def test_partial_transpose_8_by_8_subsystems_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on second and third subsystem:
pt_2_3 = partial_transpose(test_input_mat, [2, 3], [2, 2, 2])
pt_2_3 = partial_transpose(test_input_mat, [1, 2], [2, 2, 2])
expected_pt_2_3 = np.array(
[
[1, 9, 17, 25, 5, 13, 21, 29],
Expand All @@ -215,7 +215,7 @@ def test_partial_transpose_8_by_8_subsystems_2_4():
test_input_mat = np.arange(1, 65).reshape(8, 8)

# Partial transpose on the first subsystem:
pt_1 = partial_transpose(test_input_mat, [1], [2, 4])
pt_1 = partial_transpose(test_input_mat, [0], [2, 4])
expected_pt_1 = np.array(
[
[1, 2, 3, 4, 33, 34, 35, 36],
Expand All @@ -232,7 +232,7 @@ def test_partial_transpose_8_by_8_subsystems_2_4():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on the second subsystem:
pt_2 = partial_transpose(test_input_mat, [2], [2, 4])
pt_2 = partial_transpose(test_input_mat, [1], [2, 4])
expected_pt_2 = np.array(
[
[1, 9, 17, 25, 5, 13, 21, 29],
Expand All @@ -249,7 +249,7 @@ def test_partial_transpose_8_by_8_subsystems_2_4():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on the first and second subsystem:
pt_1_2 = partial_transpose(test_input_mat, [1, 2], [2, 4])
pt_1_2 = partial_transpose(test_input_mat, [0, 1], [2, 4])
expected_pt_1_2 = np.array(
[
[1, 9, 17, 25, 33, 41, 49, 57],
Expand All @@ -271,7 +271,7 @@ def test_partial_transpose_8_by_8_subsystems_4_2():
test_input_mat = np.arange(1, 65).reshape(8, 8)

# Partial transpose on the first subsystem:
pt_1 = partial_transpose(test_input_mat, [1], [4, 2])
pt_1 = partial_transpose(test_input_mat, [0], [4, 2])
expected_pt_1 = np.array(
[
[1, 2, 17, 18, 33, 34, 49, 50],
Expand All @@ -288,7 +288,7 @@ def test_partial_transpose_8_by_8_subsystems_4_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on the second subsystem:
pt_2 = partial_transpose(test_input_mat, [2], [4, 2])
pt_2 = partial_transpose(test_input_mat, [1], [4, 2])
expected_pt_2 = np.array(
[
[1, 9, 3, 11, 5, 13, 7, 15],
Expand All @@ -305,7 +305,7 @@ def test_partial_transpose_8_by_8_subsystems_4_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on the first and second subsystem:
pt_1_2 = partial_transpose(test_input_mat, [1, 2], [4, 2])
pt_1_2 = partial_transpose(test_input_mat, [0, 1], [4, 2])
expected_pt_1_2 = np.array(
[
[1, 9, 17, 25, 33, 41, 49, 57],
Expand All @@ -327,7 +327,7 @@ def test_partial_transpose_6_by_6_subsystems_2_3():
test_input_mat = np.arange(1, 37).reshape(6, 6)

# Partial transpose on first subsystem:
pt_1 = partial_transpose(test_input_mat, [1], [2, 3])
pt_1 = partial_transpose(test_input_mat, [0], [2, 3])
expected_pt_1 = np.array(
[
[1, 2, 3, 19, 20, 21],
Expand All @@ -342,7 +342,7 @@ def test_partial_transpose_6_by_6_subsystems_2_3():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on second subsystem:
pt_2 = partial_transpose(test_input_mat, [2], [2, 3])
pt_2 = partial_transpose(test_input_mat, [1], [2, 3])
expected_pt_2 = np.array(
[
[1, 7, 13, 4, 10, 16],
Expand All @@ -357,7 +357,7 @@ def test_partial_transpose_6_by_6_subsystems_2_3():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on first and second subsystems:
pt_1_2 = partial_transpose(test_input_mat, [1, 2], [2, 3])
pt_1_2 = partial_transpose(test_input_mat, [0, 1], [2, 3])
expected_pt_1_2 = np.array(
[
[1, 7, 13, 19, 25, 31],
Expand All @@ -377,7 +377,7 @@ def test_partial_transpose_6_by_6_subsystems_3_2():
test_input_mat = np.arange(1, 37).reshape(6, 6)

# Partial transpose on first subsystem:
pt_1 = partial_transpose(test_input_mat, [1], [3, 2])
pt_1 = partial_transpose(test_input_mat, [0], [3, 2])
expected_pt_1 = np.array(
[
[1, 2, 13, 14, 25, 26],
Expand All @@ -392,7 +392,7 @@ def test_partial_transpose_6_by_6_subsystems_3_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on second subsystem:
pt_2 = partial_transpose(test_input_mat, [2], [3, 2])
pt_2 = partial_transpose(test_input_mat, [1], [3, 2])
expected_pt_2 = np.array(
[
[1, 7, 3, 9, 5, 11],
Expand All @@ -407,7 +407,7 @@ def test_partial_transpose_6_by_6_subsystems_3_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose on first and second subsystems:
pt_1_2 = partial_transpose(test_input_mat, [1, 2], [3, 2])
pt_1_2 = partial_transpose(test_input_mat, [0, 1], [3, 2])
expected_pt_1_2 = np.array(
[
[1, 7, 13, 19, 25, 31],
Expand All @@ -427,7 +427,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
rho = np.arange(256).reshape(16, 16)

# Partial transpose of first subsystem:
res = partial_transpose(rho, [1], [2, 2, 2, 2])
res = partial_transpose(rho, [0], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 1, 2, 3, 4, 5, 6, 7, 128, 129, 130, 131, 132, 133, 134, 135],
Expand All @@ -452,7 +452,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of second subsystem:
res = partial_transpose(rho, [2], [2, 2, 2, 2])
res = partial_transpose(rho, [1], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 1, 2, 3, 64, 65, 66, 67, 8, 9, 10, 11, 72, 73, 74, 75],
Expand All @@ -477,7 +477,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of third subsystem
res = partial_transpose(rho, [3], [2, 2, 2, 2])
res = partial_transpose(rho, [2], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 1, 32, 33, 4, 5, 36, 37, 8, 9, 40, 41, 12, 13, 44, 45],
Expand All @@ -502,7 +502,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of fourth subsystem
res = partial_transpose(rho, [4], [2, 2, 2, 2])
res = partial_transpose(rho, [3], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 16, 2, 18, 4, 20, 6, 22, 8, 24, 10, 26, 12, 28, 14, 30],
Expand All @@ -527,7 +527,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of first and second subsystem:
res = partial_transpose(rho, [1, 2], [2, 2, 2, 2])
res = partial_transpose(rho, [0, 1], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 1, 2, 3, 64, 65, 66, 67, 128, 129, 130, 131, 192, 193, 194, 195],
Expand All @@ -552,7 +552,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of first and third subsystem:
res = partial_transpose(rho, [1, 3], [2, 2, 2, 2])
res = partial_transpose(rho, [0, 2], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 1, 32, 33, 4, 5, 36, 37, 128, 129, 160, 161, 132, 133, 164, 165],
Expand All @@ -577,7 +577,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of first and fourth subsystem
res = partial_transpose(rho, [1, 4], [2, 2, 2, 2])
res = partial_transpose(rho, [0, 3], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 16, 2, 18, 4, 20, 6, 22, 128, 144, 130, 146, 132, 148, 134, 150],
Expand All @@ -602,7 +602,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of second and third subsystem:
res = partial_transpose(rho, [2, 3], [2, 2, 2, 2])
res = partial_transpose(rho, [1, 2], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 1, 32, 33, 64, 65, 96, 97, 8, 9, 40, 41, 72, 73, 104, 105],
Expand All @@ -627,7 +627,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of second and fourth subsystem:
res = partial_transpose(rho, [2, 4], [2, 2, 2, 2])
res = partial_transpose(rho, [1, 3], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 16, 2, 18, 64, 80, 66, 82, 8, 24, 10, 26, 72, 88, 74, 90],
Expand All @@ -652,7 +652,7 @@ def test_partial_transpose_16_by_16_subsystems_2_2_2_2():
np.testing.assert_equal(np.all(bool_mat), True)

# Partial transpose of third and fourth subsystem
res = partial_transpose(rho, [3, 4], [2, 2, 2, 2])
res = partial_transpose(rho, [2, 3], [2, 2, 2, 2])
expected_res = np.array(
[
[0, 16, 32, 48, 4, 20, 36, 52, 8, 24, 40, 56, 12, 28, 44, 60],
Expand Down Expand Up @@ -708,26 +708,12 @@ def test_partial_transpose_cvxpy():
np.testing.assert_equal(isinstance(x_pt, Vstack), True)


def test_partial_transpose_non_square():
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"""Test partial transpose on non square matrices ."""
rho = np.kron(np.eye(2, 3), np.ones((2, 3)))
rho = np.kron(rho, np.eye(2, 3))

dim = np.array([[2, 2, 2], [3, 3, 3]])

res = partial_transpose(rho, sys=2, dim=dim)

expected = np.kron(np.eye(2, 3), np.ones((3, 2)))
expected = np.kron(expected, np.eye(2, 3))
np.testing.assert_equal(np.allclose(res, expected), True)


def test_partial_transpose_three_subsystems():
"""Test partial transpose on 3 - subsystems ."""
mat = np.arange(64).reshape((8, 8))
input_mat = np.kron(np.eye(2, 2), mat)

res = partial_transpose(input_mat, sys=[2, 3, 4], dim=[2, 2, 2, 2])
res = partial_transpose(input_mat, [1, 2, 3], [2, 2, 2, 2])

expected = np.kron(np.eye(2, 2), mat.T)
np.testing.assert_equal(np.allclose(res, expected), True)
Expand Down
5 changes: 3 additions & 2 deletions tests/test_matrix_props/test_is_block_positive.py
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Expand Up @@ -3,9 +3,10 @@
import pytest

from toqito.states import bell
from toqito.channels import choi, partial_transpose
from toqito.channels import choi
from toqito.perms import swap, swap_operator
from toqito.matrix_props import is_block_positive
from picos import partial_transpose


@pytest.mark.parametrize("dim", [2, 3, 4])
Expand Down Expand Up @@ -36,7 +37,7 @@ def test_is_block_positive():
v_0 = np.kron(b_0, b_0)
y_mat = (
np.kron(np.eye(4), b_0 @ b_0.T) / 2
+ np.kron(b_3 @ b_3.T, partial_transpose(b_3 @ b_3.T, 1))
+ np.kron(b_3 @ b_3.T, partial_transpose(b_3 @ b_3.T, [0]))
) / 3 - v_0 @ v_0.T / 4
mat = swap(y_mat, [2, 3], [2, 2, 2, 2])
np.testing.assert_equal(is_block_positive(mat), True)
Expand Down
4 changes: 2 additions & 2 deletions tests/test_matrix_props/test_majorizes.py
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Expand Up @@ -15,14 +15,14 @@ def test_majorizes_max_entangled():
"""Test that max entangled partial trace returns False."""
v_vec = max_entangled(3)
rho = v_vec * v_vec.conj().T
np.testing.assert_equal(majorizes(partial_trace(rho), rho), False)
np.testing.assert_equal(majorizes(partial_trace(rho, [1], [3, 3]), rho), False)


def test_majorizes_max_entangled_flip():
"""Test that max entangled partial trace returns True (flipped args)."""
v_vec = max_entangled(3)
rho = v_vec * v_vec.conj().T
np.testing.assert_equal(majorizes(rho, partial_trace(rho)), True)
np.testing.assert_equal(majorizes(rho, partial_trace(rho, [1], [3, 3])), True)


if __name__ == "__main__":
Expand Down
6 changes: 3 additions & 3 deletions tests/test_state_props/test_is_separable.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2,7 +2,7 @@
import numpy as np

from toqito.state_props.is_separable import is_separable
from toqito.channels import partial_trace
from picos import partial_trace
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from toqito.matrix_props import is_density
from toqito.states import basis, bell, isotropic, tile
from toqito.random import random_density_matrix
Expand Down Expand Up @@ -53,10 +53,10 @@ def test_ppt_low_rank():
u, s, v_h = np.linalg.svd(rho)
rho_cut = u[:, :m-1] @ np.diag(s[:m-1]) @ v_h[:m-1]
rho_cut = rho_cut / np.trace(rho_cut)
pt_state_alice = partial_trace(rho_cut, 2, dim=[3, 2])
pt_state_alice = partial_trace(rho_cut, [1], dim=[3, 2])
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np.testing.assert_equal(is_density(rho_cut), True)
np.testing.assert_equal(is_density(pt_state_alice), True)
np.testing.assert_equal(is_density(np.array(pt_state_alice)), True)
np.testing.assert_equal(
np.linalg.matrix_rank(rho_cut) + np.linalg.matrix_rank(pt_state_alice) <= 2 * m * n - m - n + 2,
True
Expand Down
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