toqito.state_props.is_distinguishable
=====================================

.. py:module:: toqito.state_props.is_distinguishable

.. autoapi-nested-parse::

   Checks if a set of quantum states are distinguishable.





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

.. py:function:: is_distinguishable(states, probs = None)

   Check whether a collection of vectors are (perfectly) distinguishable or not.

   The ability to determine whether a set of quantum states are distinguishable can be obtained via the state
   distinguishability SDP as defined in `state_distinguishability`

   .. rubric:: Examples

   The set of Bell states are an example of distinguishable states. Recall that the Bell states are defined as:

   \[
   \begin{aligned}
   u_1 &= \frac{1}{\sqrt{2}} \left(|00\rangle + |11\rangle\right), \quad
   u_2 = \frac{1}{\sqrt{2}} \left(|00\rangle - |11\rangle\right), \\
   u_3 &= \frac{1}{\sqrt{2}} \left(|01\rangle + |10\rangle\right), \quad
   u_4 = \frac{1}{\sqrt{2}} \left(|01\rangle - |10\rangle\right).
   \end{aligned}
   \]

   It can be checked in `toqito` that the Bell states are distinguishable:

   ```python exec="1" source="above"
   from toqito.states import bell
   from toqito.state_props import is_distinguishable
   bell_states = [bell(0), bell(1), bell(2), bell(3)]
   print(is_distinguishable(bell_states))
   ```

   :param states: A set of vectors consisting of quantum states to determine the distinguishability of.
   :param probs: Respective list of probabilities each state is selected. If no probabilities are provided, a uniform
   :param probability distribution is assumed.:

   :returns: `True` if the vectors are distinguishable; `False` otherwise.