toqito.states.singlet

Generalized singlet state is a singlet state of n qubits in the invariant space of alternating representation.

Module Contents

toqito.states.singlet.singlet(dim)

Produce a generalized singlet state acting on two n-dimensional systems [@Cabello_2002_NParticle].

Examples

For (n = 2) this generates the following matrix

[

S = frac{1}{2} begin{pmatrix}

0 & 0 & 0 & 0 \ 0 & 1 & -1 & 0 \ 0 & -1 & 1 & 0 \ 0 & 0 & 0 & 0

end{pmatrix}

]

which is equivalent to (|phi_s rangle langle phi_s |) where

[

|phi_srangle = frac{1}{sqrt{2}} left( |01 rangle - |10 rangle right)

]

is the singlet state. This can be computed via |toqito⟩ as follows:

`python exec="1" source="above" from toqito.states import singlet dim = 2 print(singlet(dim)) `

It is possible for us to consider higher dimensional singlet states. For instance, we can consider the (3)-dimensional Singlet state as follows:

`python exec="1" source="above" from toqito.states import singlet dim = 3 print(singlet(dim)) `

Parameters:

dim (int) – The dimension of the generalized singlet state.

Returns:

The singlet state of dimension dim.

Return type:

numpy.ndarray