Loading picos/constraints/con_renyientr.py +2 −2 Original line number Diff line number Diff line Loading @@ -186,7 +186,7 @@ class BaseTrRenyiEntrEpiConstraint(Constraint): assert isinstance(divergence.X, required_type) assert isinstance(divergence.Y, required_type) super(BaseRenyiEntrConstraint, self).__init__(divergence._typeStr) super(BaseTrRenyiEntrEpiConstraint, self).__init__(divergence._typeStr) def _required_type(self): from ..expressions import AffineExpression Loading Loading @@ -277,7 +277,7 @@ class TrSandRenyiEntrEpiConstraint(BaseTrRenyiEntrEpiConstraint): return 1 <= alpha and alpha <= 2 class ComplexTrSandRenyiEntrEpiConstraint(TrRenyiEntrEpiConstraint): class ComplexTrSandRenyiEntrEpiConstraint(TrSandRenyiEntrEpiConstraint): """Upper bound of complex convex trace function used to define sandwiched Renyi entropies. """ Loading tests/ptest_renyi.py 0 → 100644 +138 −0 Original line number Diff line number Diff line # ------------------------------------------------------------------------------ # Copyright (C) 2024 Kerry He # # This file is part of PICOS Testbench. # # PICOS Testbench is free software: you can redistribute it and/or modify it # under the terms of the GNU General Public License as published by the Free # Software Foundation, either version 3 of the License, or (at your option) any # later version. # # PICOS Testbench is distributed in the hope that it will be useful, but WITHOUT # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS # FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. # # You should have received a copy of the GNU General Public License along with # this program. If not, see <http://www.gnu.org/licenses/>. # ------------------------------------------------------------------------------ """Test quantum relative entropy programs.""" import cvxopt import math import numpy as np import picos from .ptest import ProductionTestCase def mpower(A, p): D, U = np.linalg.eigh(A) return U @ np.diag(np.power(D, p)) @ U.conj().T class RMI_REAL(ProductionTestCase): """Renyi mutual information.""" def setUp(self): # noqa np.random.seed(42) # Primal problem. self.P = picos.Problem() self.X = picos.SymmetricVariable("X", 4) A = np.random.randn(16, 16) A = A @ A.T self.A = A / np.trace(A) self.tr2_A = picos.partial_trace(A, 1, (4, 4)) def _opt_renyi_mutual_information(self, alpha): A, tr2_A = self.A, self.tr2_A temp = mpower(tr2_A @ picos.I(4), 1 - alpha) @ mpower(A, alpha) temp = mpower(picos.partial_trace(temp, 0, (4, 4)), 1 / alpha) return temp / np.trace(temp) def _opt_sand_renyi_mutual_information(self, Xstar, alpha): A, tr2_A = self.A, self.tr2_A temp = mpower(tr2_A @ Xstar, (1 - alpha) / (2 * alpha)) temp = mpower(temp @ A @ temp, alpha) temp = picos.partial_trace(temp, 0, (4, 4)) return temp / np.trace(temp) def testRenyi(self): P, X, A, tr2_A = self.P, self.X, self.A, self.tr2_A alpha = 0.5 P.set_objective("min", picos.renyientr(A, tr2_A @ X, alpha)) P.add_constraint(picos.trace(X) == 1) Xstar = self._opt_renyi_mutual_information(alpha) self.primalSolve(self.P) self.expectVariable(self.X, cvxopt.matrix(Xstar)) def _test_trrenyi(self, alpha, direction): P, X, A, tr2_A = self.P, self.X, self.A, self.tr2_A P.set_objective(direction, picos.trrenyientr(A, tr2_A @ X, alpha)) P.add_constraint(picos.trace(X) == 1) Xstar = self._opt_renyi_mutual_information(alpha) self.primalSolve(self.P) self.expectVariable(self.X, cvxopt.matrix(Xstar)) def testTraceRenyi1(self): self._test_trrenyi(-0.5, "min") def testTraceRenyi2(self): self._test_trrenyi(0.5, "max") def testTraceRenyi3(self): self._test_trrenyi(1.5, "min") def testSandwichedRenyi(self): P, X, A, tr2_A = self.P, self.X, self.A, self.tr2_A alpha = 0.5 P.set_objective("min", picos.sandrenyientr(A, tr2_A @ X, alpha)) P.add_constraint(picos.trace(X) == 1) self.primalSolve(self.P) RHS = self._opt_sand_renyi_mutual_information(self.X, alpha) self.expectVariable(self.X, RHS.value) def _test_trsandrenyi(self, alpha, direction): P, X, A, tr2_A = self.P, self.X, self.A, self.tr2_A P.set_objective(direction, picos.trsandrenyientr(A, tr2_A @ X, alpha)) P.add_constraint(picos.trace(X) == 1) self.primalSolve(self.P) RHS = self._opt_sand_renyi_mutual_information(self.X, alpha) self.expectVariable(self.X, RHS.value) def testTraceSandwichedRenyi1(self): self._test_trsandrenyi(0.75, "max") def testTraceSandwichedRenyi2(self): self._test_trsandrenyi(1.5, "min") class RMI_COMPLEX(RMI_REAL): """Renyi mutual information.""" def setUp(self): # noqa np.random.seed(42) # Primal problem. self.P = picos.Problem() self.X = picos.HermitianVariable("X", 4) A = np.random.randn(16, 16) + np.random.randn(16, 16) * 1j A = A @ A.conj().T self.A = A / np.trace(A) self.tr2_A = picos.partial_trace(A, 1, (4, 4)) Loading
picos/constraints/con_renyientr.py +2 −2 Original line number Diff line number Diff line Loading @@ -186,7 +186,7 @@ class BaseTrRenyiEntrEpiConstraint(Constraint): assert isinstance(divergence.X, required_type) assert isinstance(divergence.Y, required_type) super(BaseRenyiEntrConstraint, self).__init__(divergence._typeStr) super(BaseTrRenyiEntrEpiConstraint, self).__init__(divergence._typeStr) def _required_type(self): from ..expressions import AffineExpression Loading Loading @@ -277,7 +277,7 @@ class TrSandRenyiEntrEpiConstraint(BaseTrRenyiEntrEpiConstraint): return 1 <= alpha and alpha <= 2 class ComplexTrSandRenyiEntrEpiConstraint(TrRenyiEntrEpiConstraint): class ComplexTrSandRenyiEntrEpiConstraint(TrSandRenyiEntrEpiConstraint): """Upper bound of complex convex trace function used to define sandwiched Renyi entropies. """ Loading
tests/ptest_renyi.py 0 → 100644 +138 −0 Original line number Diff line number Diff line # ------------------------------------------------------------------------------ # Copyright (C) 2024 Kerry He # # This file is part of PICOS Testbench. # # PICOS Testbench is free software: you can redistribute it and/or modify it # under the terms of the GNU General Public License as published by the Free # Software Foundation, either version 3 of the License, or (at your option) any # later version. # # PICOS Testbench is distributed in the hope that it will be useful, but WITHOUT # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS # FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. # # You should have received a copy of the GNU General Public License along with # this program. If not, see <http://www.gnu.org/licenses/>. # ------------------------------------------------------------------------------ """Test quantum relative entropy programs.""" import cvxopt import math import numpy as np import picos from .ptest import ProductionTestCase def mpower(A, p): D, U = np.linalg.eigh(A) return U @ np.diag(np.power(D, p)) @ U.conj().T class RMI_REAL(ProductionTestCase): """Renyi mutual information.""" def setUp(self): # noqa np.random.seed(42) # Primal problem. self.P = picos.Problem() self.X = picos.SymmetricVariable("X", 4) A = np.random.randn(16, 16) A = A @ A.T self.A = A / np.trace(A) self.tr2_A = picos.partial_trace(A, 1, (4, 4)) def _opt_renyi_mutual_information(self, alpha): A, tr2_A = self.A, self.tr2_A temp = mpower(tr2_A @ picos.I(4), 1 - alpha) @ mpower(A, alpha) temp = mpower(picos.partial_trace(temp, 0, (4, 4)), 1 / alpha) return temp / np.trace(temp) def _opt_sand_renyi_mutual_information(self, Xstar, alpha): A, tr2_A = self.A, self.tr2_A temp = mpower(tr2_A @ Xstar, (1 - alpha) / (2 * alpha)) temp = mpower(temp @ A @ temp, alpha) temp = picos.partial_trace(temp, 0, (4, 4)) return temp / np.trace(temp) def testRenyi(self): P, X, A, tr2_A = self.P, self.X, self.A, self.tr2_A alpha = 0.5 P.set_objective("min", picos.renyientr(A, tr2_A @ X, alpha)) P.add_constraint(picos.trace(X) == 1) Xstar = self._opt_renyi_mutual_information(alpha) self.primalSolve(self.P) self.expectVariable(self.X, cvxopt.matrix(Xstar)) def _test_trrenyi(self, alpha, direction): P, X, A, tr2_A = self.P, self.X, self.A, self.tr2_A P.set_objective(direction, picos.trrenyientr(A, tr2_A @ X, alpha)) P.add_constraint(picos.trace(X) == 1) Xstar = self._opt_renyi_mutual_information(alpha) self.primalSolve(self.P) self.expectVariable(self.X, cvxopt.matrix(Xstar)) def testTraceRenyi1(self): self._test_trrenyi(-0.5, "min") def testTraceRenyi2(self): self._test_trrenyi(0.5, "max") def testTraceRenyi3(self): self._test_trrenyi(1.5, "min") def testSandwichedRenyi(self): P, X, A, tr2_A = self.P, self.X, self.A, self.tr2_A alpha = 0.5 P.set_objective("min", picos.sandrenyientr(A, tr2_A @ X, alpha)) P.add_constraint(picos.trace(X) == 1) self.primalSolve(self.P) RHS = self._opt_sand_renyi_mutual_information(self.X, alpha) self.expectVariable(self.X, RHS.value) def _test_trsandrenyi(self, alpha, direction): P, X, A, tr2_A = self.P, self.X, self.A, self.tr2_A P.set_objective(direction, picos.trsandrenyientr(A, tr2_A @ X, alpha)) P.add_constraint(picos.trace(X) == 1) self.primalSolve(self.P) RHS = self._opt_sand_renyi_mutual_information(self.X, alpha) self.expectVariable(self.X, RHS.value) def testTraceSandwichedRenyi1(self): self._test_trsandrenyi(0.75, "max") def testTraceSandwichedRenyi2(self): self._test_trsandrenyi(1.5, "min") class RMI_COMPLEX(RMI_REAL): """Renyi mutual information.""" def setUp(self): # noqa np.random.seed(42) # Primal problem. self.P = picos.Problem() self.X = picos.HermitianVariable("X", 4) A = np.random.randn(16, 16) + np.random.randn(16, 16) * 1j A = A @ A.conj().T self.A = A / np.trace(A) self.tr2_A = picos.partial_trace(A, 1, (4, 4))
