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

.. py:module:: states.singlet

.. autoapi-nested-parse::

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



Functions
---------

.. autoapisummary::

   states.singlet.singlet


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

.. py:function:: singlet(dim)

   Produce a generalized singlet state acting on two n-dimensional systems :cite:`Cabello_2002_NParticle`.

   .. rubric:: Examples

   For :math:`n = 2` this generates the following matrix

   .. math::
       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 :math:`|\phi_s \rangle \langle \phi_s |` where

   .. math::
       |\phi_s\rangle = \frac{1}{\sqrt{2}} \left( |01 \rangle - |10 \rangle \right)

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

   .. jupyter-execute::

     from toqito.states import singlet
     dim = 2
     singlet(dim)

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

   .. jupyter-execute::

     from toqito.states import singlet
     dim = 3
     singlet(dim)



   .. rubric:: References

   .. bibliography::
       :filter: docname in docnames

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