toqito.state_props.negativity
=============================

.. py:module:: toqito.state_props.negativity

.. autoapi-nested-parse::

   Calculates the negativity property of a quantum state.





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

.. py:function:: negativity(rho, dim = None)

   Compute the negativity of a bipartite quantum state [@WikiNeg].

   The negativity of a subsystem can be defined in terms of a density matrix \(\rho\):

   \[
       \mathcal{N}(\rho) \equiv \frac{||\rho^{\Gamma_A}||_1-1}{2}.
   \]

   Calculate the negativity of the quantum state \(\rho\), assuming that the two subsystems on
   which \(\rho\) acts are of equal dimension (if the local dimensions are unequal, specify
   them in the optional `dim` argument). The negativity of \(\rho\) is the sum of the
   absolute value of the negative eigenvalues of the partial transpose of \(\rho\).

   .. rubric:: Examples

   Example of the negativity of density matrix of Bell state.

   ```python exec="1" source="above"
   from toqito.states import bell
   from toqito.state_props import negativity
   rho = bell(0) @ bell(0).conj().T
   print(negativity(rho))
   ```

   !!!See Also
       [log_negativity()][toqito.state_props.log_negativity.log_negativity]

   :raises ValueError: If dimension of matrix is invalid.

   :param rho: A density matrix of a pure state vector.
   :param dim: The default has both subsystems of equal dimension.

   :returns: A value between 0 and 1 that corresponds to the negativity of \(\rho\).