toqito.states.pusey_barrett_rudolph
===================================

.. py:module:: toqito.states.pusey_barrett_rudolph

.. autoapi-nested-parse::

   Construct a set of mutually unbiased bases.





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

.. py:function:: pusey_barrett_rudolph(n, theta)

   Produce set of Pusey-Barrett-Rudolph (PBR) states [@Pusey_2012_On].

   Let \(\theta \in [0, \pi/2]\) be an angle. Define the states

   \[
       |\psi_0\rangle = \cos(\frac{\theta}{2})|0\rangle +
                        \sin(\frac{\theta}{2})|1\rangle
       \quad \text{and} \quad
       |\psi_1\rangle = \cos(\frac{\theta}{2})|0\rangle -
                        \sin(\frac{\theta}{2})|1\rangle.
   \]

   For some \(n \geq 1\), define a basis of \(2^n\) states where

   \[
       |\Psi_i\rangle = |\psi_{x_i}\rangle \otimes \cdots \otimes |\psi_{x_n}\rangle.
   \]

   These PBR states are defined in Equation (A6) from [@Pusey_2012_On].

   .. rubric:: Examples

   Generating the PBR states can be done by simply invoking the function with a given choice of `n` and
   `theta`:

   ```python exec="1" source="above"
   from toqito.states import pusey_barrett_rudolph
   print(pusey_barrett_rudolph(n=1, theta=0.5))
   ```

   :param n: The number of states in the set.
   :param theta: Angle parameter that defines the states.

   :returns: Vector of trine states.