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test_partial_transpose.py
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test_partial_transpose.py
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# This file is part of QuTiP: Quantum Toolbox in Python.
#
# Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
# of its contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
# PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
# HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################
"""
Unit tests for QuTiP partial transpose functions.
"""
import numpy
from numpy.testing import assert_, assert_equal, run_module_suite
from qutip import *
from qutip.partial_transpose import _partial_transpose_reference
def test_partial_transpose_bipartite():
"""partial transpose of bipartite systems"""
rho = Qobj(arange(16).reshape(4, 4), dims=[[2, 2], [2, 2]])
# no transpose
rho_pt = partial_transpose(rho, [0, 0])
assert_(numpy.abs(numpy.max(rho_pt.full() - rho.full())) < 1e-12)
# partial transpose subsystem 1
rho_pt = partial_transpose(rho, [1, 0])
rho_pt_expected = array([[0, 1, 8, 9],
[4, 5, 12, 13],
[2, 3, 10, 11],
[6, 7, 14, 15]])
assert_(numpy.abs(numpy.max(rho_pt.full() - rho_pt_expected)) < 1e-12)
# partial transpose subsystem 2
rho_pt = partial_transpose(rho, [0, 1])
rho_pt_expected = array([[0, 4, 2, 6],
[1, 5, 3, 7],
[8, 12, 10, 14],
[9, 13, 11, 15]])
assert_(numpy.abs(numpy.max(rho_pt.full() - rho_pt_expected)) < 1e-12)
# full transpose
rho_pt = partial_transpose(rho, [1, 1])
assert_(numpy.abs(numpy.max(rho_pt.full() - rho.trans().full())) < 1e-12)
def test_partial_transpose_comparison():
"""partial transpose: comparing sparse and dense implementations"""
N = 10
rho = tensor(rand_dm(N, density=0.5), rand_dm(N, density=0.5))
# partial transpose of system 1
rho_pt1 = partial_transpose(rho, [1, 0], method="dense")
rho_pt2 = partial_transpose(rho, [1, 0], method="sparse")
numpy.abs(numpy.max(rho_pt1.full() - rho_pt1.full())) < 1e-12
# partial transpose of system 2
rho_pt1 = partial_transpose(rho, [0, 1], method="dense")
rho_pt2 = partial_transpose(rho, [0, 1], method="sparse")
numpy.abs(numpy.max(rho_pt1.full() - rho_pt1.full())) < 1e-12
def test_partial_transpose_randomized():
"""partial transpose: randomized tests on tripartite system"""
rho = tensor(rand_dm(2, density=1),
rand_dm(2, density=1),
rand_dm(2, density=1))
mask = numpy.random.randint(2, size=3)
rho_pt_ref = _partial_transpose_reference(rho, mask)
rho_pt1 = partial_transpose(rho, mask, method="dense")
numpy.abs(numpy.max(rho_pt1.full() - rho_pt_ref.full())) < 1e-12
rho_pt2 = partial_transpose(rho, mask, method="sparse")
numpy.abs(numpy.max(rho_pt2.full() - rho_pt_ref.full())) < 1e-12
if __name__ == "__main__":
run_module_suite()