toqito.state_props.is_product

Checks if a quantum state is product state.

Module Contents

toqito.state_props.is_product.is_product(rho, dim=None)

Determine if a given vector is a product state [@WikiSepSt].

If the input is deemed to be product, then the product decomposition is also returned.

Examples

Consider the following Bell state

[

u = frac{1}{sqrt{2}} left( |00 rangle + |11 rangle right) in mathcal{X}.

]

The corresponding density matrix of (u) may be calculated by:

[

rho = u u^* = frac{1}{2} begin{pmatrix}

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

end{pmatrix} in text{D}(mathcal{X}).

]

We can provide the input as either the vector (u) or the denisty matrix (rho). In either case, this represents an entangled state (and hence a non-product state).

`python exec="1" source="above" session="is_product_example" from toqito.state_props import is_product from toqito.states import bell rho = bell(0) @ bell(0).conj().T u_vec = bell(0) print(is_product(rho)) `

`python exec="1" source="above" session="is_product_example" print(is_product(u_vec)) `

Parameters:

• rho (numpy.ndarray) – The vector or matrix to check.

• dim (int | list[int] | numpy.ndarray | None) – The dimension of the input.

Returns:

True if rho is a product vector and False otherwise.

Return type:

tuple