# state_infidelity

`Graph.state_infidelity(x, y, *, name=None)`

Calculate the infidelity of two pure states.

### Parameters

**x**(*np.ndarray**or**Tensor*) – A pure state, $|\psi\rangle$, with shape`(..., D)`

. Note that the last dimension must be the same as y, and the batch dimension, if any, must be broadcastable with y.**y**(*np.ndarray**or**Tensor*) – A pure state, $|\phi\rangle$, with shape`(..., D)`

. Note that the last dimension must be the same as x, and the batch dimension, if any, must be broadcastable with x.**name**(*str**or**None**,**optional*) – The name of the node.

### Returns

The infidelity of two pure states, with shape `(...)`

.

### Return type

### SEE ALSO

`Graph.density_matrix_infidelity`

: Infidelity between two density matrices.

`Graph.inner_product`

: Inner product of two vectors.

`Graph.unitary_infidelity`

: Infidelity between a unitary and target operators.

## Notes

The infidelity of two pure states $|\psi\rangle$ and $|\phi\rangle$ is defined as $1 - | \langle \psi | \phi \rangle |^2$.

For more information about the state fidelity, see fidelity of quantum states on Wikipedia.

## Examples

```
>>> graph.state_infidelity(
... np.array([0, 1]), np.array([[1, 0], [0, 1]]), name="infidelity"
... )
<Tensor: name="infidelity", operation_name="state_infidelity", shape=(2,)>
>>> result = bo.execute_graph(graph=graph, output_node_names="infidelity")
>>> result["output"]["infidelity"]["value"]
array([1., 0.])
```