# This file is part of QuTiP: Quantum Toolbox in Python.
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# Significant parts of this code was contributed by Jonas Neergaard-Nielsen
###############################################################################
__all__ = ['partial_transpose']
import numpy as np
import scipy.sparse as sp
from qutip.qobj import Qobj
from qutip.states import (state_index_number, state_number_index,
state_number_enumerate)
[docs]def partial_transpose(rho, mask, method='dense'):
"""
Return the partial transpose of a Qobj instance `rho`,
where `mask` is an array/list with length that equals
the number of components of `rho` (that is, the length of
`rho.dims[0]`), and the values in `mask` indicates whether
or not the corresponding subsystem is to be transposed.
The elements in `mask` can be boolean or integers `0` or `1`,
where `True`/`1` indicates that the corresponding subsystem
should be tranposed.
Parameters
----------
rho : :class:`qutip.qobj`
A density matrix.
mask : *list* / *array*
A mask that selects which subsystems should be transposed.
method : str
choice of method, `dense` or `sparse`. The default method
is `dense`. The `sparse` implementation can be faster for
large and sparse systems (hundreds of quantum states).
Returns
-------
rho_pr: :class:`qutip.qobj`
A density matrix with the selected subsystems transposed.
"""
if method == 'sparse':
return _partial_transpose_sparse(rho, mask)
else:
return _partial_transpose_dense(rho, mask)
def _partial_transpose_dense(rho, mask):
"""
Based on Jonas' implementation using numpy.
Very fast for dense problems.
"""
nsys = len(mask)
pt_dims = np.arange(2 * nsys).reshape(2, nsys).T
pt_idx = np.concatenate([[pt_dims[n, mask[n]] for n in range(nsys)],
[pt_dims[n, 1 - mask[n]] for n in range(nsys)]])
data = rho.data.toarray().reshape(
np.array(rho.dims).flatten()).transpose(pt_idx).reshape(rho.shape)
return Qobj(data, dims=rho.dims)
def _partial_transpose_sparse(rho, mask):
"""
Implement the partial transpose using the CSR sparse matrix.
"""
data = sp.lil_matrix((rho.shape[0], rho.shape[1]), dtype=complex)
for m in range(len(rho.data.indptr) - 1):
n1 = rho.data.indptr[m]
n2 = rho.data.indptr[m + 1]
psi_A = state_index_number(rho.dims[0], m)
for idx, n in enumerate(rho.data.indices[n1:n2]):
psi_B = state_index_number(rho.dims[1], n)
m_pt = state_number_index(
rho.dims[1], np.choose(mask, [psi_A, psi_B]))
n_pt = state_number_index(
rho.dims[0], np.choose(mask, [psi_B, psi_A]))
data[m_pt, n_pt] = rho.data.data[n1 + idx]
return Qobj(data.tocsr(), dims=rho.dims)
def _partial_transpose_reference(rho, mask):
"""
This is a reference implementation that explicitly loops over
all states and performs the transpose. It's slow but easy to
understand and useful for testing.
"""
A_pt = np.zeros(rho.shape, dtype=complex)
for psi_A in state_number_enumerate(rho.dims[0]):
m = state_number_index(rho.dims[0], psi_A)
for psi_B in state_number_enumerate(rho.dims[1]):
n = state_number_index(rho.dims[1], psi_B)
m_pt = state_number_index(
rho.dims[1], np.choose(mask, [psi_A, psi_B]))
n_pt = state_number_index(
rho.dims[0], np.choose(mask, [psi_B, psi_A]))
A_pt[m_pt, n_pt] = rho.data[m, n]
return Qobj(A_pt, dims=rho.dims)