toqito.states.breuer
====================

.. py:module:: toqito.states.breuer

.. autoapi-nested-parse::

   Breuer states represent the Breuer bound entangled states.

   These states are based on the Breuer-Hall criterion.





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

.. py:function:: breuer(dim, lam)

   Produce a Breuer state [@Breuer_2006_Optimal].

   Gives a Breuer bound entangled state for two qudits of local dimension `dim`, with the
   `lam` parameter describing the weight of the singlet component as described in
   [@Breuer_2006_Optimal].

   This function was adapted from the QETLAB package.

   .. rubric:: Examples

   We can generate a Breuer state of dimension \(4\) with weight \(0.1\). For any weight above \(0\), the
   state will be bound entangled, that is, it will satisfy the PPT criterion, but it will be entangled.

   ```python exec="1" source="above"
   from toqito.states import breuer
   print(breuer(2, 0.1))
   ```

   :raises ValueError: Dimension must be greater than or equal to 1.

   :param dim: Dimension of the Breuer state.
   :param lam: The weight of the singlet component.

   :returns: Breuer state of dimension `dim` with weight `lam`.