toqito.state_props.log_negativity
=================================

.. py:module:: toqito.state_props.log_negativity

.. autoapi-nested-parse::

   Calculates the logarithmic negativity property of a quantum state.





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

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

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

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

   \[
       E_\mathcal{N}(\rho) \equiv \text{log}_2\left( ||\rho^{\Gamma_A}||_1 \right).
   \]

   Calculate the log-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).

   .. rubric:: Examples

   Example of the log-negativity of density matrix of Bell state.

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

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

   :raises ValueError: If the input matrix is not a density matrix.

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

   :returns: A positive value that corresponds to the logarithmic negativity of \(\rho\).