states.breuer

Breuer states represent the Breuer bound entangled states.

These states are based on the Breuer-Hall criterion.

Functions

breuer(dim, lam)

Produce a Breuer state [1].

Module Contents

states.breuer.breuer(dim, lam)

Produce a Breuer state [1].

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 [1].

This function was adapted from the QETLAB package.

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.

>>> from toqito.states import breuer
>>> breuer(2, 0.1)
array([[0.3, 0. , 0. , 0. ],
       [0. , 0.2, 0.1, 0. ],
       [0. , 0.1, 0.2, 0. ],
       [0. , 0. , 0. , 0.3]])

References

[1] (1,2,3)

Heinz-Peter Breuer. Optimal entanglement criterion for mixed quantum states. Physical Review Letters, Aug 2006. URL: http://dx.doi.org/10.1103/PhysRevLett.97.080501, doi:10.1103/physrevlett.97.080501.

Raises:

ValueError – Dimension must be greater than or equal to 1.

Parameters:

  • dim (int) – Dimension of the Breuer state.

  • lam (float) – The weight of the singlet component.

Returns:

Breuer state of dimension dim with weight lam.

Return type:

numpy.ndarray