List of functions

This is a list of functions provided by QETLAB, arranged by category. If you would prefer an alphabetical list of all functions please see this page. Brief descriptions of these functions are provided here, as well as links to their documentation pages, where full details and numerous examples can be found.

Basic operations

IsPSD: Determines whether or not a matrix is positive semidefinite
Tensor: Kronecker tensor product of two or more matrices
TensorSum: Computes a vector or operator from its tensor decomposition

Distinguishing objects

ChannelDistinguishability: Computes the maximum probability of distinguishing two quantum channels
Distinguishability: Computes the maximum probability of distinguishing quantum states
UPBSepDistinguishable: Determines whether or not a UPB is distinguishable by separable measurements

Entanglement and separability

Pure states

IsProductVector: Determines if a pure state is a product vector
SchmidtDecomposition: Computes the Schmidt decomposition of a bipartite vector
SchmidtRank: Computes the Schmidt rank of a bipartite vector

Mixed states

FilterNormalForm: Computes the filter normal form of an operator
IsBlockPositive: Determines whether or not an operator is block positive
IsEntanglingGate: Determines if a unitary is an entangling gate
IsPPT: Determines whether or not a matrix has positive partial transpose
IsProductOperator: Determines if an operator is an elementary tensor
IsSeparable: Determines whether or not a bipartite operator is separable
OperatorSchmidtDecomposition: Computes the operator Schmidt decomposition of a bipartite operator
OperatorSchmidtRank: Computes the operator Schmidt rank of a bipartite operator
SymmetricExtension: Determines whether or not an operator has a symmetric extension
SymmetricInnerExtension: Determines whether or not an operator has a symmetric inner extension

Ball of separability

AbsPPTConstraints: Builds the eigenvalue matrices that determine whether or not a state is absolutely PPT
InSeparableBall: Checks whether or not an operator is in the ball of separability centered at the maximally-mixed state
IsAbsPPT: Determines whether or not a density matrix is absolutely PPT

Entanglement measures

Negativity: Computes the negativity of a bipartite density matrix

Information theory

Entropy: Computes the von Neumann entropy of a density matrix

Nonlocal games

XORClassicalValue: Computes the classical value of a nonlocal binary XOR game
XORQuantumValue: Computes the quantum value of a nonlocal binary XOR game

Norms and distance measures

Vectors and pure states

SkVectorNorm: Computes the s(k)-norm of a vector

Operators and mixed states

Fidelity: Computes the fidelity of two density matrices
kpNorm: Computes the (k,p)-norm of a vector or matrix
kpNormDual: Computes the dual of the (k,p)-norm of a vector or matrix
KyFanNorm: Computes the Ky Fan k-norm of an operator
SkOperatorNorm: Bounds the S(k)-norm of an operator
SchattenNorm: Computes the Schatten p-norm of an operator
TraceNorm: Computes the trace norm of an operator

Superoperators and channels

CBNorm: Computes the completely bounded norm of a superoperator
DiamondNorm: Computes the diamond norm of a superoperator
MaximumOutputFidelity: Computes the maximum output fidelity of two quantum channels

Permutations and symmetry of subsystems

AntisymmetricProjection: Produces the projection onto the antisymmetric subspace
PermutationOperator: Produces a unitary operator that permutes subsystems
PermuteSystems: Permutes subsystems within a state or operator
Swap: Swaps two subsystems within a state or operator
SwapOperator: Produces a unitary operator that swaps two subsystems
SymmetricProjection: Produces the projection onto the symmetric subspace

Random things

RandomDensityMatrix: Generates a random density matrix
RandomStateVector: Generates a random pure state vector
RandomSuperoperator: Generates a random superoperator (completely positive map)
RandomUnitary: Generates a random unitary or orthogonal matrix

Special states, vectors, and operators

Bell: Produces a Bell state
BrauerStates: Produces all Brauer states
ChessboardState: Produces a chessboard state
FourierMatrix: Generates the unitary matrix that implements the quantum Fourier transform
GellMann: Produces a Gell-Mann operator
GenGellMann: Produces a generalized Gell-Mann operator
GenPauli: Produces a generalized Pauli operator
IsotropicState: Produces an isotropic state
MaxEntangled: Produces a maximally entangled bipartite pure state
Pauli: Produces a Pauli operator
WernerState: Produces a Werner state

Superoperators

ApplyMap: Applies a superoperator to an operator
ChoiMatrix: Computes the Choi matrix of a superoperator
ChoiMap: Produces the Choi map or one of its generalizations
ComplementaryMap: Computes the complementary map of a superoperator
DepolarizingChannel: Produces a depolarizing channel
DualMap: Computes the dual of a superoperator in the Hilbert-Schmidt inner product
IsCP: Determines whether or not a superoperator is completely positive
IsHermPreserving: Determines whether or not a superoperator is Hermiticity preserving
KrausOperators: Computes a set of Kraus operators for a superoperator
PartialMap: Applies a superoperator to a subsystem of an operator
PartialTrace: Computes the partial trace of a matrix
PartialTranspose: Computes the partial transpose of a matrix
Realignment: Computes the realignment of a bipartite operator
ReductionMap: Produces the reduction map
Twirl: Twirls a bipartite or multipartite operator

Unextendible product bases

IsUPB: Determines whether or not a set of product vectors form a UPB
MinUPBSize: Gives the minimum cardinality of an unextendible product basis in given dimensions
UPB: Generates an unextendible product basis

Miscellaneous

Commutant: Computes the commutant of a set of matrices
IsTotallyNonsingular: Determines whether or not a matrix is totally nonsingular
IsTotallyPositive: Determines whether or not a matrix is totally positive
Majorizes: Determines whether or not a vector or matrix majorizes another
OperatorSinkhorn: Performs the operator Sinkhorn iteration, making all single-party reduced states proportional to the identity
Purity: Computes the purity of a quantum state

Helper functions

iden: Computes a sparse or full identity matrix
jacobi_poly: Computes the coefficients of Jacobi polynomials
normalize_cols: Scales the columns of a matrix to have norm 1
one_factorization: Computes a 1-factorization of a list of objects
opt_args: Handles optional input arguments for functions
opt_disp: Display a message to the user (sometimes)
perfect_matchings: Gives all perfect matchings of N objects
perm_inv: Computes the inverse of a permutation
perm_sign: Computes the sign of a permutation
sk_iterate: Computes a lower bound of the S(k)-norm of an operator
spnull: Returns a sparse orthonormal basis for the null space
sporth: Returns a sparse orthonormal basis for the range
superoperator_dims: Computes the input, output, and environment dimensions of a superoperator
vec_partitions: Produces all possible partitions of a vector