toqito.states.singlet
=====================

.. py:module:: toqito.states.singlet

.. autoapi-nested-parse::

   Generalized singlet state is a singlet state of `n` qubits in the invariant space of alternating representation.





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

.. py:function:: singlet(dim)

   Produce a generalized singlet state acting on two n-dimensional systems [@Cabello_2002_NParticle].

   .. rubric:: Examples

   For \(n = 2\) this generates the following matrix

   \[
       S = \frac{1}{2} \begin{pmatrix}
                       0 & 0 & 0 & 0 \\
                       0 & 1 & -1 & 0 \\
                       0 & -1 & 1 & 0 \\
                       0 & 0 & 0 & 0
                   \end{pmatrix}
   \]

   which is equivalent to \(|\phi_s \rangle \langle \phi_s |\) where

   \[
       |\phi_s\rangle = \frac{1}{\sqrt{2}} \left( |01 \rangle - |10 \rangle \right)
   \]

   is the singlet state. This can be computed via `|toqito⟩` as follows:

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


   It is possible for us to consider higher dimensional singlet states. For instance, we can consider the
   \(3\)-dimensional Singlet state as follows:

   ```python exec="1" source="above"
   from toqito.states import singlet
   dim = 3
   print(singlet(dim))
   ```

   :param dim: The dimension of the generalized singlet state.

   :returns: The singlet state of dimension `dim`.