Adding check for linear independence.

docs/_autosummary/toqito.matrix_props.is_linearly_independent.rst

@@ -0,0 +1,6 @@
+toqito.matrix\_props.is\_linearly\_independent
+==============================================
+
+.. currentmodule:: toqito.matrix_props
+
+.. autofunction:: is_linearly_independent

docs/_autosummary/toqito.matrix_props.is_totally_positive.rst

@@ -0,0 +1,6 @@
+toqito.matrix\_props.is\_totally\_positive
+==========================================
+
+.. currentmodule:: toqito.matrix_props
+
+.. autofunction:: is_totally_positive

docs/_autosummary/toqito.states.bb84.rst

@@ -0,0 +1,6 @@
+toqito.states.bb84
+==================
+
+.. currentmodule:: toqito.states
+
+.. autofunction:: bb84

docs/_autosummary/toqito.states.mutually_unbiased_basis.rst

@@ -0,0 +1,6 @@
+toqito.states.mutually\_unbiased\_basis
+=======================================
+
+.. currentmodule:: toqito.states
+
+.. autofunction:: mutually_unbiased_basis

docs/_autosummary/toqito.states.trine.rst

@@ -0,0 +1,6 @@
+toqito.states.trine
+===================
+
+.. currentmodule:: toqito.states
+
+.. autofunction:: trine

docs/articles.bib

@@ -933,6 +933,15 @@ @misc{WikiInnerProd
 
 }
 
+
+@misc{WikiLinearIndependence,
+  author  = "Wikipedia",
+  title   = "Linear independence",
+  howpublished = {https://en.wikipedia.org/wiki/Linear_independence}
+
+}
+
+
 @misc{WikiNeg,
   author  = "Wikipedia",
   title   = "Negativity",

docs/matrices.rst

@@ -55,6 +55,7 @@ Properties of Matrices and Vectors
     toqito.matrix_props.is_hermitian
     toqito.matrix_props.is_idempotent
     toqito.matrix_props.is_identity
+    toqito.matrix_props.is_linearly_independent
     toqito.matrix_props.is_normal
     toqito.matrix_props.is_orthonormal
     toqito.matrix_props.is_permutation
@@ -63,6 +64,7 @@ Properties of Matrices and Vectors
     toqito.matrix_props.is_projection
     toqito.matrix_props.is_square
     toqito.matrix_props.is_symmetric
+    toqito.matrix_props.is_totally_positive
     toqito.matrix_props.is_unitary
     toqito.matrix_props.kp_norm
     toqito.matrix_props.majorizes

docs/states.rst

@@ -67,6 +67,7 @@ Properties of Quantum States
     toqito.state_props.entanglement_of_formation
     toqito.state_props.has_symmetric_extension
     toqito.state_props.in_separable_ball
+    toqito.state_props.is_antidistinguishable
     toqito.state_props.is_ensemble
     toqito.state_props.is_mixed
     toqito.state_props.is_mutually_orthogonal
@@ -93,6 +94,7 @@ Quantum States
    :toctree: _autosummary
 
     toqito.states.basis
+    toqito.states.bb84
     toqito.states.bell
     toqito.states.brauer
     toqito.states.breuer
@@ -105,7 +107,9 @@ Quantum States
     toqito.states.isotropic
     toqito.states.max_entangled
     toqito.states.max_mixed
+    toqito.states.mutually_unbiased_basis
     toqito.states.singlet
     toqito.states.tile
+    toqito.states.trine
     toqito.states.w_state
     toqito.states.werner

toqito/matrix_ops/vectors_to_gram_matrix.py

@@ -10,14 +10,14 @@ def vectors_to_gram_matrix(vectors: list[np.ndarray]) -> np.ndarray:
 
     Examples
     ========
-    # Example with real vectors:
+    >>> # Example with real vectors:
     >>> vectors = [np.array([1, 2]), np.array([3, 4])]
     >>> gram_matrix = vectors_to_gram_matrix(vectors)
     >>> gram_matrix
     array([[ 5., 11.],
            [11., 25.]])
 
-    # Example with complex vectors:
+    >>> # Example with complex vectors:
     >>> vectors = [np.array([1+1j, 2+2j]), np.array([3+3j, 4+4j])]
     >>> gram_matrix = vectors_to_gram_matrix(vectors)
     >>> gram_matrix

toqito/matrix_props/__init__.py

@@ -22,3 +22,4 @@
 from toqito.matrix_props.trace_norm import trace_norm
 from toqito.matrix_props.is_diagonally_dominant import is_diagonally_dominant
 from toqito.matrix_props.is_totally_positive import is_totally_positive
+from toqito.matrix_props.is_linearly_independent import is_linearly_independent

toqito/matrix_props/is_linearly_independent.py

@@ -0,0 +1,44 @@
+"""Is linearly independent."""
+import numpy as np
+
+
+def is_linearly_independent(vectors: list[np.ndarray]) -> bool:
+    r"""Check if set of vectors are linearly independent :cite:`WikiLinearIndependence`.
+
+    Examples
+    ==========
+
+    The following vectors are an example of a linearly independent set of vectors in :math:`\mathbb{R}^3`.
+
+    .. math::
+        \begin{pmatrix}
+            1 \\ 0 \\ 1
+        \end{pmatrix}, \quad
+        \begin{pmatrix}
+            1 \\ 1 \\ 0
+        \end{pmatrix}, \quad \text{and} \quad
+        \begin{pmatrix}
+            0 \\ 0 \\ 1
+        \end{pmatrix}
+
+    We can see that these are linearly independent:
+
+    >>> import numpy as np
+    >>> from toqito.matrix_props import is_linearly_independent
+    >>>
+    >>> v_1 = np.array([[1], [0], [1]])
+    >>> v_2 = np.array([[1], [1], [0]])
+    >>> v_3 = np.array([[0], [0], [1]])
+    >>> is_linearly_independent([v_1, v_2, v_3])
+    True
+
+    References
+    ==========
+    .. bibliography::
+        :filter: docname in docnames
+
+    :param vectors: Vectors to check the linear independence of.
+    :return: Return :code:`True` if vectors are linearly independent :code:`False` otherwise.
+    """
+    # Check if the rank of the matrix equals the number of vectors.
+    return np.linalg.matrix_rank(np.column_stack(vectors)) == len(vectors)

toqito/matrix_props/is_totally_positive.py

@@ -12,14 +12,14 @@ def is_totally_positive(mat: np.ndarray, tol: float = 1e-6, sub_sizes: list | No
 
     Examples
     ========
-
     Consider the matrix
 
     .. math::
         \begin{pmatrix}
             1 & 2 \\
             3 & 4
         \end{pmatrix}
+
     To determine if this matrix is totally positive, we need to check the positivity of all of its minors. The 1x1
     minors are simply the individual entries of the matrix. For :math:`X`, these are
 

toqito/matrix_props/tests/test_is_linearly_independent.py

@@ -0,0 +1,14 @@
+"""Test is_linearly_independent."""
+import numpy as np
+import pytest
+
+from toqito.matrix_props import is_linearly_independent
+
+
+@pytest.mark.parametrize("vectors, expected_result", [
+    ([np.array([[1], [0], [1]]), np.array([[1], [1], [0]]), np.array([[0], [0], [1]])], True),
+    ([np.array([[0], [1], [2]]), np.array([[1], [2], [3]]), np.array([[3], [5], [7]])], False),
+])
+def test_is_linearly_independent(vectors, expected_result):
+    """Test for linear independence/dependence of vectors."""
+    np.testing.assert_equal(is_linearly_independent(vectors), expected_result)

toqito/state_opt/tests/test_ppt_distinguishability.py

@@ -171,7 +171,7 @@ def test_ppt_distinguishability_four_bell_states():
 
     The resource state is defined by
 
-    ..math::
+    .. math::
         |\tau_{\epsilon} \rangle = \sqrt{\frac{1+\epsilon}{2}} +
         |0\rangle | 0\rangle +
         \sqrt{\frac{1-\epsilon}{2}} |1 \rangle |1 \rangle

toqito/states/mutually_unbiased_basis.py

@@ -23,8 +23,8 @@ def mutually_unbiased_basis(dim: int) -> list[np.ndarray]:
 
     References
     ==========
-    .. [WikiMUB] Wikipedia: Mutually unbiased bases
-        https://en.wikipedia.org/wiki/Mutually_unbiased_bases
+    .. bibliography::
+        :filter: docname in docnames
 
     :param dim: The dimension of the mutually unbiased bases to produce.
     :return: The set of mutually unbiased bases of dimension :code:`dim` (if known).