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dq.random.dm 

dm(
    key: PRNGKeyArray, dims: int | tuple[int, ...], *, batch: int | tuple[int, ...] = ()
) -> QArray

Returns a random density matrix (hermitian, positive semi-definite, and unit trace).

Parameters:

  • key –

    A PRNG key used as the random key.

  • dims –

    Hilbert space dimension of each subsystem.

  • batch –

    Batch shape of the returned qarray.

Returns:

  • (qarray of shape (*batch, prod(dims), prod(dims))) –

    Random density matrix.

Examples:

>>> key = jax.random.PRNGKey(42)

Random density matrix for an individual system:

>>> dq.random.dm(key, 2)
QArray: shape=(2, 2), dims=(2,), dtype=complex64, layout=dense
[[ 0.198+0.j    -0.044-0.392j]
 [-0.044+0.392j  0.802+0.j   ]]

Batched random density matrices for an individual system:

>>> dq.random.dm(key, 2, batch=3)
QArray: shape=(3, 2, 2), dims=(2,), dtype=complex64, layout=dense
[[[ 0.198+0.j    -0.044-0.392j]
  [-0.044+0.392j  0.802+0.j   ]]

 [[ 0.476+0.j     0.021+0.06j ]
  [ 0.021-0.06j   0.524+0.j   ]]

 [[ 0.473+0.j    -0.286-0.173j]
  [-0.286+0.173j  0.527+0.j   ]]]

Random density matrix for a composite system:

>>> dq.random.dm(key, (2, 3))
QArray: shape=(6, 6), dims=(6,), dtype=complex64, layout=dense
[[ 0.178+0.j     0.012+0.021j -0.047+0.057j -0.007+0.072j -0.092-0.033j
   0.033+0.002j]
 [ 0.012-0.021j  0.16 +0.j    -0.019-0.036j  0.013-0.089j -0.003+0.031j
  -0.118-0.052j]
 [-0.047-0.057j -0.019+0.036j  0.137+0.j     0.024+0.012j  0.015+0.03j
   0.041-0.007j]
 [-0.007-0.072j  0.013+0.089j  0.024-0.012j  0.176+0.j     0.007+0.056j
  -0.026-0.087j]
 [-0.092+0.033j -0.003-0.031j  0.015-0.03j   0.007-0.056j  0.133+0.j
  -0.05 -0.002j]
 [ 0.033-0.002j -0.118+0.052j  0.041+0.007j -0.026+0.087j -0.05 +0.002j
   0.216+0.j   ]]

Batched random density matrices for a composite system:

>>> dq.random.dm(key, (2, 3), batch=(4, 5, 6, 7)).shape
(4, 5, 6, 7, 6, 6)