toqito.states.tile¶

Tile state.

Module Contents¶

toqito.states.tile.tile(idx)[source]¶

Produce a Tile state [@Bennett_1999_UPB].

The Tile states constitute five states on 3-by-3 dimensional space that form a UPB (unextendible product basis).

Returns one of the following five tile states depending on the value of idx:

[

begin{equation}

begin{aligned}: |psi_0 rangle = frac{1}{sqrt{2}} |0 rangle left(|0rangle - |1rangle right), qquad & |psi_1rangle = frac{1}{sqrt{2}} left(|0rangle - |1rangle right) |2rangle, \ |psi_2rangle = frac{1}{sqrt{2}} |2rangle left(|1rangle - |2rangle right), qquad & |psi_3rangle = frac{1}{sqrt{2}} left(|1rangle - |2rangle right) |0rangle, \ qquad & |psi_4rangle = frac{1}{3} left(|0rangle + |1rangle + |2rangle)right) left(|0rangle + |1rangle + |2rangle right).

end{aligned}

end{equation}

]

Examples

When idx = 0, this produces the following tile state

]

Using |toqito⟩, we can see that this yields the proper state.

`python exec="1" source="above" from toqito.states import tile import numpy as np print(tile(0)) `