Entanglement Measure via Seesaw Optimization

Accessible in both numqi.entangle (recommended) and numqi.entangle.measure_seesaw

numqi.entangle.get_GME_pure_seesaw(np0, converge_eps=1e-07, num_repeat=1, maxiter=1000, psi_list=None, seed=None)

Get the Geometric Measure of Entanglement (GME) of a pure state using the seesaw algorithm.

reference: Simple algorithm for computing the geometric measure of entanglement doi-link

Parameters:

Name	Type	Description	Default
np0	ndarray	pure state, shape=(d1,d2,...,dN)	required
converge_eps	float	convergence threshold	1e-07
num_repeat	int	number of repeat to get the best result	1
maxiter	int	maximum number of iterations	1000
psi_list	list	initial states, len(psi_list)==N, psi_list[ind0].shape==(dim_list[ind0],). If None, random initial states will be used. When num_repeat>1, psi_list must be None.	None
seed	(int, None)	random seed	None

Returns:

Name	Type	Description
GME	float	non-negative number, the Geometric Measure of Entanglement
psi_list	list	final states, len(psi_list)==N, psi_list[ind0].shape==(dim_list[ind0],)

numqi.entangle.get_GME_subspace_seesaw(np0, converge_eps=1e-07, num_repeat=1, maxiter=1000, psi_list=None, seed=None)

Get the Geometric Measure of Entanglement (GME) of a subspace using the seesaw algorithm.

reference: Simple algorithm for computing the geometric measure of entanglement doi-link

Parameters:

Name	Type	Description	Default
np0	ndarray	pure state, shape=(N,d1,d2,...,dN)	required
converge_eps	float	convergence threshold	1e-07
num_repeat	int	number of repeat to get the best result	1
maxiter	int	maximum number of iterations	1000
psi_list	list	initial states, len(psi_list)==N, psi_list[ind0].shape==(dim_list[ind0],). If None, random initial states will be used. When num_repeat>1, psi_list must be None.	None
seed	(int, None)	random seed	None

Returns:

Name	Type	Description
GME	float	non-negative number, the Geometric Measure of Entanglement
psi_list	list	final states, len(psi_list)==N, psi_list[ind0].shape==(dim_list[ind0],)

numqi.entangle.get_GME_seesaw(rho, dim_list, maxiter=1000, init_coeffq=None, init_phi_list=None, num_state=None, converge_eps=1e-10, num_repeat=1, maxiter_inner=100, converge_eps_inner=1e-07, zero_eps=1e-10, return_info=False, seed=None)

Get the Geometric Measure of Entanglement (GME) of a density matrix using the seesaw algorithm.

reference: Simple algorithm for computing the geometric measure of entanglement doi-link

Parameters:

Name	Type	Description	Default
rho	ndarray	density matrix, shape=(d1*d2*...*dN,d1*d2*...*dN)	required
dim_list	tuple[int]	dimension list, len(dim_list)==N, dim_list[ind0] is the dimension of the ind0-th party	required
maxiter	int	maximum number of iterations	1000
init_coeffq	(ndarray, None)	initial probability distribution, shape=(num_state,)	None
init_phi_list	(list, None)	initial states, len(init_phi_list)==N, init_phi_list[ind0].shape==(num_state,dim_list[ind0])	None
num_state	(int, None)	number of states, default is 2*dim_total	None
converge_eps	float	convergence threshold	1e-10
num_repeat	int	number of repeat to get the best result	1
maxiter_inner	int	maximum number of iterations for inner loop	100
converge_eps_inner	float	convergence threshold for inner loop	1e-07
zero_eps	float	zero threshold	1e-10
return_info	bool	return additional information	False
seed	(int, None)	random seed	None

Returns:

Name	Type	Description
GME	float	non-negative number, the Geometric Measure of Entanglement
info	dict	additional information, if return_info==True