toqito.states.basis
===================

.. py:module:: toqito.states.basis

.. autoapi-nested-parse::

   A basis state represents the standard basis vectors of some n-dimensional Hilbert Space.

   Here, n can be given as a parameter as shown below.





Module Contents
---------------

.. py:function:: basis(dim, pos)

   Obtain the ket of dimension `dim` [@WikiBraKet].

   .. rubric:: Examples

   The standard basis ket vectors given as \(|0 \rangle\) and \(|1 \rangle\) where

   \[
       |0 \rangle = \left[1, 0 \right]^{\text{T}} \quad \text{and} \quad
       |1 \rangle = \left[0, 1 \right]^{\text{T}},
   \]

   can be obtained in `|toqito⟩` as follows.

   Example:  Ket basis vector: \(|0\rangle\).

   ```python exec="1" source="above"
   from toqito.states import basis
   print(basis(2, 0))
   ```

   Example: Ket basis vector: \(|1\rangle\).

   ```python exec="1" source="above"
   from toqito.states import basis
   print(basis(2, 1))
   ```

   :raises ValueError: If the input position is not in the range [0, dim - 1].

   :param dim: The dimension of the column vector.
   :param pos: 0-indexed position of the basis vector where the 1 will be placed.

   :returns: The column vector of dimension `dim` with all entries set to `0` except the entry at `pos` which is set to `1`.