dicke

`numqi.dicke.Dicke(*klist)`

return Dicke state for n qudits

see arxiv-link for more information

Parameters:

Name	Type	Description	Default
`klist`	`tuple[int]`	list of int, each int is the number of qudit in each level, `dim=len(klist)`, `num_qudit=sum(klist)`	`()`

Returns:

Name	Type	Description
`ret`	`ndarray`	shape (dim**num_qudit)

return Dicke basis for n qudits

see arxiv-link for more information

Parameters:

Name	Type	Description	Default
`num_qudit`	`int`	number of qudits	required
`dim`	`int`	dimension of each qudit	required

Returns:

Name	Type	Description
`ret`	`ndarray`	shape (binom{num_qudit+dim-1}{num_qudit}, dim**num_qudit) float64

return klist for n qudit Dicke state

Parameters:

Name	Type	Description	Default
`num_qudit`	`int`	number of qudit	required
`dim`	`int`	dimension of qudit	required

Returns:

Name	Type	Description
`ret`	`list`	list of klist, each element is a tuple of int. the list is of length `scipy.special.binom(n+d-1, d-1)`. the tuple is of length `dim` and the sum of each tuple is `num_qudit`

return partial trace of qubit Dicke state

Parameters:

Name	Type	Description	Default
`num_qubit`	`int`	number of qubit	required

Returns:

return index for partial trace of qudit Dicke state numqi.dicke.partial_trace_ABk_to_AB

\[ B_{rsab} = \mathrm{Tr}_{A^{n-1}} \left[ \langle r|D_{na}\rangle\langle D_{nb}| s\rangle \right] \]

Parameters:

Name	Type	Description	Default
`num_qudit`	`int`	number of qudit	required
`dim`	`int`	dimension of qudit	required
`return_tensor`	`bool`	if True, return \(B_{rsab}\), otherwise return indexing used for \(B_{rsab}\). `return_tensor=True` is useful for unittest. `return_tensor=False` use less memory	`False`

Returns:

Name	Type	Description
`ret`	`(list, ndarray)`	if `return_tensor=False`, list of tuple, each tuple is of length 3, and the first two elements are list of int, the third element is np.ndarray of `float64`. if `return_tensor=True`, return \(B_{rsab}\), shape (dim, dim, #klist, #klist)