toqito.rand.random_state_vector

Generates a random state vector.

Module Contents

toqito.rand.random_state_vector.random_state_vector(dim, is_real=False, k_param=0, seed=None)[source]

Generate a random pure state vector.

Randomness model

We sample entries independently from the standard normal distribution using numpy’s default_rng. If is_real is False (default), the imaginary part is sampled in the same way and added with the factor (i); otherwise the vector is real. The sampled vector is normalized to have unit Euclidean norm. When k_param is strictly positive, the returned state describes a bipartite system of dimensions dim (or [dim, dim] if dim is an integer) with Schmidt rank at most k_param. This is achieved by drawing local factors and combining them with a maximally entangled resource state.

Examples

We may generate a random state vector. For instance, here is an example where we can generate a (2)-dimensional random state vector.

```python exec=”1” source=”above” session=”vec_example” from toqito.rand import random_state_vector

vec = random_state_vector(2)

print(vec) ```

We can verify that this is in fact a valid state vector by computing the corresponding density matrix of the vector and checking if the density matrix is pure.

```python exec=”1” source=”above” session=”vec_example” from toqito.state_props import is_pure

dm = vec @ vec.conj().T

print(is_pure(dm)) ```

It is also possible to pass a seed for reproducibility.

```python exec=”1” source=”above” session=”vec_example” from toqito.rand import random_state_vector

vec = random_state_vector(2, seed=42)

print(vec) ```

We can once again verify that this is in fact a valid state vector by computing the corresponding density matrix of the vector and checking if the density matrix is pure.

```python exec=”1” source=”above” session=”vec_example” from toqito.state_props import is_pure

dm = vec @ vec.conj().T

print(is_pure(dm)) ```

Parameters:

  • dim (list[int] | tuple[int, Ellipsis] | int) – Either a positive integer giving the total Hilbert-space dimension, or a length-2 sequence specifying the

  • sampling. (individual subsystem dimensions for bipartite)

  • is_real (bool) – Boolean denoting whether the returned vector has real entries. Default is False, which produces

  • amplitudes. (complex)

  • k_param (int) – Optional upper bound on the Schmidt rank when dim describes a bipartite system. Set to 0

  • smaller ((default) to ignore the Schmidt rank constraint. Must be non-negative and strictly less than the)

  • used. (subsystem dimension when)

  • seed (int | None) – A seed used to instantiate numpy’s random number generator.

Returns:

A normalized column vector of shape (total_dim, 1) where total_dim equals dim if dim is an integer and equals the product of entries in dim otherwise.

Return type:

numpy.ndarray