27 #ifndef ENTANGLEMENT_H_
28 #define ENTANGLEMENT_H_
45 template<
typename Derived>
47 const std::vector<idx>& dims)
80 template<
typename Derived>
82 const std::vector<idx>& dims)
115 template<
typename Derived>
117 const std::vector<idx>& dims)
127 if (dims.size() != 2)
155 template<
typename Derived>
157 const std::vector<idx>& dims)
167 if (dims.size() != 2)
179 std::vector<double> result;
181 for (
idx i = 0; i < static_cast<idx>(scf.rows()); ++i)
182 result.push_back(std::pow(scf(i), 2));
198 template<
typename Derived>
200 const std::vector<idx>& dims)
210 if (dims.size() != 2)
237 template<
typename Derived>
255 if (d * d != static_cast<idx>(rA.rows()))
261 return d * std::abs(std::exp(2. / d *
logdet(
reshape(rA, d, d))));
271 template<
typename Derived>
273 const std::vector<idx>& dims)
283 if (dims.size() != 2)
305 template<
typename Derived>
307 const std::vector<idx>& dims)
317 if (dims.size() != 2)
330 return std::log2(2 *
negativity(rA, dims) + 1);
339 template<
typename Derived>
362 *
kron(sigmaY, sigmaY)).real();
364 std::vector<double> lambdas_sorted(lambdas.data(),
365 lambdas.data() + lambdas.size());
367 std::sort(std::begin(lambdas_sorted), std::end(lambdas_sorted),
368 std::greater<double>());
369 std::transform(std::begin(lambdas_sorted), std::end(lambdas_sorted),
370 std::begin(lambdas_sorted), [](
double elem)
372 return std::sqrt(std::abs(elem));
376 lambdas_sorted[0] - lambdas_sorted[1] - lambdas_sorted[2]
377 - lambdas_sorted[3]);
bool check_nonzero_size(const T &x) noexcept
Definition: util.h:112
Derived::Scalar logdet(const Eigen::MatrixBase< Derived > &A)
Logarithm of the determinant.
Definition: functions.h:173
std::vector< double > schmidtprobs(const Eigen::MatrixBase< Derived > &A, const std::vector< idx > &dims)
Schmidt probabilities of the bi-partite pure state A.
Definition: entanglement.h:156
bool check_cvector(const Eigen::MatrixBase< Derived > &A)
Definition: util.h:105
double gconcurrence(const Eigen::MatrixBase< Derived > &A)
G-concurrence of the bi-partite pure state A.
Definition: entanglement.h:238
double lognegativity(const Eigen::MatrixBase< Derived > &A, const std::vector< idx > &dims)
Logarithmic negativity of the bi-partite mixed state A.
Definition: entanglement.h:306
Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > dyn_mat
Dynamic Eigen matrix over the field specified by Scalar.
Definition: types.h:78
bool check_dims_match_mat(const std::vector< idx > &dims, const Eigen::MatrixBase< Derived > &A)
Definition: util.h:141
Quantum++ main namespace.
Definition: codes.h:30
double schatten(const Eigen::MatrixBase< Derived > &A, double p)
Schatten matrix norm.
Definition: functions.h:826
cmat svdU(const Eigen::MatrixBase< Derived > &A)
Left singular vectors.
Definition: functions.h:494
cmat schmidtA(const Eigen::MatrixBase< Derived > &A, const std::vector< idx > &dims)
Schmidt basis on Alice side.
Definition: entanglement.h:81
dyn_col_vect< double > svals(const Eigen::MatrixBase< Derived > &A)
Singular values.
Definition: functions.h:470
dyn_mat< typename T::Scalar > kron(const T &head)
Kronecker product.
Definition: functions.h:895
double entropy(const Eigen::MatrixBase< Derived > &A)
von-Neumann entropy of the density matrix A
Definition: entropies.h:43
Generates custom exceptions, used when validating function parameters.
Definition: exception.h:39
dyn_mat< typename Derived::Scalar > transpose(const Eigen::MatrixBase< Derived > &A)
Transpose.
Definition: functions.h:44
dyn_col_vect< cplx > evals(const Eigen::MatrixBase< Derived > &A)
Eigenvalues.
Definition: functions.h:304
idx get_dim_subsys(idx sz, idx N)
Definition: util.h:363
dyn_mat< typename Derived::Scalar > conjugate(const Eigen::MatrixBase< Derived > &A)
Complex conjugate.
Definition: functions.h:64
bool check_square_mat(const Eigen::MatrixBase< Derived > &A)
Definition: util.h:84
cmat schmidtB(const Eigen::MatrixBase< Derived > &A, const std::vector< idx > &dims)
Schmidt basis on Bob side.
Definition: entanglement.h:116
cmat svdV(const Eigen::MatrixBase< Derived > &A)
Right singular vectors.
Definition: functions.h:519
double entanglement(const Eigen::MatrixBase< Derived > &A, const std::vector< idx > &dims)
Entanglement of the bi-partite pure state A.
Definition: entanglement.h:199
Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > dyn_col_vect
Dynamic Eigen column vector over the field specified by Scalar.
Definition: types.h:90
static const Gates & get_instance() noexcept(std::is_nothrow_constructible< const Gates >::value)
Definition: singleton.h:90
dyn_mat< typename Derived::Scalar > ptranspose(const Eigen::MatrixBase< Derived > &A, const std::vector< idx > &subsys, const std::vector< idx > &dims)
Partial transpose.
Definition: operations.h:1469
Eigen::MatrixXcd cmat
Complex (double precision) dynamic Eigen matrix.
Definition: types.h:61
std::size_t idx
Non-negative integer index.
Definition: types.h:36
double concurrence(const Eigen::MatrixBase< Derived > &A)
Wootters concurrence of the bi-partite qubit mixed state A.
Definition: entanglement.h:340
cmat Y
Pauli Sigma-Y gate.
Definition: gates.h:46
dyn_col_vect< double > schmidtcoeffs(const Eigen::MatrixBase< Derived > &A, const std::vector< idx > &dims)
Schmidt coefficients of the bi-partite pure state A.
Definition: entanglement.h:46
dyn_mat< typename Derived::Scalar > reshape(const Eigen::MatrixBase< Derived > &A, idx rows, idx cols)
Reshape.
Definition: functions.h:1135
double negativity(const Eigen::MatrixBase< Derived > &A, const std::vector< idx > &dims)
Negativity of the bi-partite mixed state A.
Definition: entanglement.h:272