toqito.states.isotropic

Isotropic state is a bipartite quantum state.

These states are separable for α ≤ 1/(d+1), but are otherwise entangled.

Module Contents

toqito.states.isotropic.isotropic(dim, alpha)

Produce a isotropic state [@Horodecki_1998_Reduction].

Returns the isotropic state with parameter alpha acting on (dim-by-dim)-dimensional space. The isotropic state has the following form

[

begin{equation}

rho_{alpha} = frac{1 - alpha}{d^2} mathbb{I} otimes mathbb{I} + alpha |psi_+ rangle langle psi_+ | in mathbb{C}^d otimes mathbb{C}^2

end{equation}

]

where (|psi_+ rangle = frac{1}{sqrt{d}} sum_j |j rangle otimes |j rangle) is the maximally entangled state.

Examples

To generate the isotropic state with parameter (alpha=1/2), we can make the following call to |toqito⟩ as

`python exec="1" source="above" from toqito.states import isotropic print(isotropic(3, 1 / 2)) `

Parameters:

• dim (int) – The local dimension.

• alpha (float) – The parameter of the isotropic state.

Returns:

Isotropic state of dimension dim.

Return type:

numpy.ndarray