Entanglement Measure
Geometric Measure of Entanglement (GME)
Accessible in both numqi.entangle (recommended) and numqi.entangle.measure
numqi.entangle.DensityMatrixGMEModel
Bases: Module
Solve geometric measure of entanglement (GME) for density matrix using gradient descent.
__init__(dim_list, num_ensemble, rank=None, CPrank=1, dtype='float64')
Initialize the model.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dim_list
|
tuple[int]
|
dimension of the density matrix. |
required |
num_ensemble
|
int
|
number of ensemble to sample. |
required |
rank
|
int
|
rank of the density matrix, if None, then rank is set to the maximum. |
None
|
CPrank
|
int
|
Canonical Polyadic rank rank of the state. |
1
|
dtype
|
str
|
data type of the state. |
'float64'
|
set_density_matrix(rho)
Set the density matrix.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
rho
|
ndarray
|
density matrix. |
required |
numqi.entangle.get_gme_2qubit(rho)
Calculate the geometric measure of entanglement (GME) for 2-qubit density matrix.
Geometric measure of entanglement and applications to bipartite and multipartite quantum states doi-link (eq-10)
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
rho
|
ndarray
|
2-qubit density matrix. |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ret |
float
|
GME. |
numqi.entangle.get_relative_entropy_of_entanglement_pure(psi, dimA, dimB, return_SEP=False, zero_eps=1e-10)
get the relative entropy of entanglement of pure state
reference: Closest separable state when measured by a quasi-relative entropy arxiv-link
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
psi
|
ndarray
|
the pure state of shape (dimA*dimB,) |
required |
dimA
|
int
|
the dimension of subsystem A |
required |
dimB
|
int
|
the dimension of subsystem B |
required |
return_SEP
|
bool
|
return the separable state or not |
False
|
zero_eps
|
float
|
the zero threshold |
1e-10
|
Returns:
| Name | Type | Description |
|---|---|---|
ret |
float
|
the relative entropy of entanglement |
sigma |
ndarray
|
the separable state, if |
numqi.entangle.get_linear_entropy_entanglement_ppt(rho, dim, use_tqdm=False, return_info=False)
Calculate the linear entropy of entanglement for density matrix using PPT approximation.
Evaluating Convex Roof Entanglement Measures doi-link
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
rho
|
ndarray
|
density matrix. support batch |
required |
dim
|
tuple[int]
|
dimension of the density matrix. must be length 2. |
required |
use_tqdm
|
bool
|
use tqdm for progress bar. |
False
|
return_info
|
bool
|
return additional information. |
False
|
Returns:
| Name | Type | Description |
|---|---|---|
ret |
(float, ndarray, list)
|
linear entropy of entanglement. |
numqi.entangle.DensityMatrixLinearEntropyModel
Bases: Module
Solve linear entropy of entanglement for density matrix using gradient descent.
__init__(dim, num_ensemble, rank=None, kind='convex', method='polar')
Initialize the model.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dim
|
tuple[int]
|
dimension of the density matrix. must be length 2. |
required |
num_ensemble
|
int
|
number of ensemble to sample. |
required |
rank
|
int
|
rank of the density matrix, if None, then rank is set to the maximum. |
None
|
kind
|
str
|
convex or concave. |
'convex'
|
method
|
str
|
parameterization method for Stiefel manifold. |
'polar'
|
set_density_matrix(rho)
Set the density matrix.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
rho
|
ndarray
|
density matrix. |
required |