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Welcome to the toqito wiki!

Mission: Enable scientists to discover new results in quantum information theory via sophisticated software.

Objective: To act as the primary software arsenal for tackling numerical problems pertaining to quantum states, channels, and measurements in quantum information theory.

Contributing: Consult the contribution guide for instructions on how to help improve the toqito project and accelerate our numerical tools for this field.

2024 - 2025 Roadmap

Goals

• Port cvxquad from MATLAB to functions within channels/*.

  • lieb_ando.m
  • matrix_geo_mean_epi_cone.m
  • matrix_geo_mean_hypo_cone.m
  • op_rel_entr_epi_cone.m
  • quantum_cond_entr.m
  • quantum_entr.m
  • quantum_rel_entr.m
  • rel_entr_quad.m
  • trace_logm.m
  • trace_mpower.m
  • cq_channel_capacity.m
  • degradable_channels_capacity.m
  • entanglement_assisted_capacity.m
  • nearest_correlation_matrix.m
  • rel_entr_entanglement.m
  • rel_entr_recovery.m

• Port QETLAB functions from MATLAB to functions within toqito:

  • AbsPPTConstraints.m
  • AntisymmetricProjection.m (perms/antisymmetric_projection.py)
  • ApplyMap.m (channel_ops/apply_channel.py)
  • BCSGameLB.m (nonlocal_games/nonlocal_game.py)
  • BCSGameValue.m (nonlocal_games/nonloca_game.py)
  • Bell.m (states/bell.py)
  • BellInequalityMax.m
  • BellInequalityMaxQubits.m
  • BrauerStates.m (states/brauer.py)
  • BreuerStates.m (states/breuer.py)
  • CBNorm.m (channel_metrics/completely_bounded_trace_norm.py)
  • ChannelDistinguishability.m
  • ChessboardState.m (states/chessboard.py)
  • ChoiMap.m (channels/choi.py)
  • ChoiMatrix.m
  • CliqueNumber.m
  • Commutant.m
  • ComplementaryMap.m
  • Concurrence.m (state_props/concurrence.py)
  • CopositivePolynomial.m
  • DephasingChannel.m (channels/dephasing_channel.py)
  • DepolarizingChannel.m (channels/depolarizing_channel.py)
  • DiamondNorm.m (channel_props/diamond_norm.py)
  • DickeState.m
  • Distinguishability.m
  • DualMap.m (channel_ops/dual_channel.py)
  • EntFormation.m (state_props/entanglement_of_formation.py)
  • EntangledSubspace.m
  • Entropy.m (state_props/von_neumann_entropy.py)
  • Fidelity.m (state_metrics/fidelity.py)
  • FilterNormalForm.m
  • FourierMatrix.m (matrices/fourier_matrix.py)
  • GHZState.m (states/ghz_state.py)
  • GellMann.m (matrices/gell_mann.py)
  • GenGellMann.m (matrices/gen_gell_mann.py)
  • GenPauli.m (matrices/gen_pauli.py)
  • GisinState.m (states/gisin_state.py)
  • HorodeckiState.m (states/horodecki_state.py)
  • InSeparableBall.m (state_props/in_separable_ball.py)
  • InducedMatrixNorm.m
  • InducedSchattenNorm.m
  • IsAbsPPT.m
  • IsBlockPositive.m (matrix_props/is_block_positive.py)
  • IsCP.m (channel_props/is_completely_positive.py)
  • IsCopositive.m
  • IsEntanglingGate.m
  • IsHermPreserving.m (channel_props/is_herm_preserving.py)
  • IsPPT.m (state_props/is_ppt.py)
  • IsPSD.m (matrix_props/is_positive_semidefinite.py)
  • IsProductOperator.m (state_props/is_product.py)
  • IsProductVector.m (state_props/is_product.py)
  • IsSeparable.m (state_props/is_separable.py)
  • IsTotallyNonsingular.m
  • IsTotallyPositive.m (matrix_props/is_totally_positive.py)
  • IsUPB.m (state_props/is_unextendible_product_basis.py)
  • IsotropicState.m (states/isotropic_state.py)
  • KrausOperators.m (channel_ops/kraus_to_choi.py) and (channel_ops/choi_to_kraus.py)
  • KyFanNorm.m
  • L1NormCoherence.m (matrix_props/l1_norm_coherence.py)
  • LocalDistinguishability.m
  • Majorizes.m (state_props/majorizes.py)
  • MatsumotoFidelity.m (state_metrics/matsumoto_fidelity.py)
  • MaxEntangled.m (states/max_entangled.py)
  • MaximumOutputFidelity.m
  • MinUPBSize.m
  • NPAHierarchy.m (helper/npa_hierarchy.py)
  • Negativity.m (state_props/negativity.py)
  • NonlocalGameLB.m (nonlocal_games/nonlocal_game.py)
  • OperatorSchmidtDecomposition.m (state_ops/schmidt_decomposition.py)
  • OperatorSchmidtRank.m (state_props/schmidt_rank.py)
  • OperatorSinkhorn.m
  • ParallelRepetition.m (nonlocal_games/nonlocal_game.py)
  • PartialMap.m (channels/partial_channel.py)
  • PartialTrace.m (channels/partial_trace.py)
  • PartialTranspose.m (channels/partial_transpose.py)
  • Pauli.m (matrices/pauli.py)
  • PauliChannel.m
  • PermutationOperator.m (perms/permutation_operator.py)
  • PermuteSystems.m (perms/permutate_systems.py)
  • PolynomialAsMatrix.m
  • PolnyomialOptimize.m
  • PolynomialSOS.m
  • Purity.m (state_props/purity.py)
  • RandomDensityMatrix.m (rand/random_density_matrix.py)
  • RandomGraph.m
  • RandomPOVM.m (rand/random_povm.py)
  • RandomPPTState.m
  • RandomProbabilities.m
  • RandomStateVector.m (rand/random_state_vector.py)
  • RandomSuperoperator.m
  • RandomUnitary.m (rand/random_unitary.py)
  • Realignment.m (channels/realignment.py)
  • ReductionMap.m (channels/reduction.py)
  • RelEntCoherence.m
  • RobustnessCoherence.m
  • SchattenNorm.m
  • SchmidtDecomposition.m (state_ops/schmidt_decomposition.py)
  • SchmidtRank.m (state_props/schmidt_rank.py)
  • SkOperatorNorm.m (matrix_props/sk_norm.py)
  • SkVectorNorm.m (state_props/sk_vec_norm.py)
  • Swap.m (perms/swap.py)
  • SwapOperator.m (perms/swap_operator.py)
  • SymmetricExtension.m (state_opt/symmetric_extension_hierarchy.py)
  • SymmetricInnerExtension.m
  • SymmetricProjection.m (perms/symmetric_projection.py)
  • Tensor.m (matrix_ops/tensor.py)
  • TensorSum.m
  • TraceDistanceCoherence.m
  • TraceNorm.m (state_props/trace_norm.py)
  • Twirl.m
  • UPB.m
  • UPBSepDistinguishable.m
  • WState.m (states/w_state.py)
  • WernerState.m (states/werner.py)
  • XORGameValue.m (nonlocal_games/xor_game.py)
  • kpNorm.m (matrix_props/kp_norm.py)
  • kpNormDual.m