Documentation
Index
A list of all documentation sorted by module.
QuantumInformation.QuantumInformationQuantumInformation.ChannelBasisIteratorQuantumInformation.DynamicalMatrixQuantumInformation.IdentityChannelQuantumInformation.KrausOperatorsQuantumInformation.StinespringQuantumInformation.SuperOperatorQuantumInformation.SuperOperatorQuantumInformation.UnitaryChannelBase.convertBase.convertBase.convertBase.convertBase.convertBase.convertBase.convertBase.convertBase.convertQuantumInformation.applychannelQuantumInformation.applychannelQuantumInformation.applychannelQuantumInformation.applychannelQuantumInformation.applychannelQuantumInformation.applychannelQuantumInformation.applychannelQuantumInformation.applychannelQuantumInformation.applychannelQuantumInformation.bloch_vectorQuantumInformation.braQuantumInformation.bures_angleQuantumInformation.bures_distanceQuantumInformation.channelbasisQuantumInformation.combineQuantumInformation.concurrenceQuantumInformation.diamond_distanceQuantumInformation.fidelityQuantumInformation.fidelity_sqrtQuantumInformation.gate_fidelityQuantumInformation.groverQuantumInformation.hadamardQuantumInformation.hermitianbasisQuantumInformation.hs_distanceQuantumInformation.iscpQuantumInformation.iscptniQuantumInformation.iscptpQuantumInformation.iseffectQuantumInformation.isidentityQuantumInformation.ispositiveQuantumInformation.ispovmQuantumInformation.istniQuantumInformation.istpQuantumInformation.js_divergenceQuantumInformation.ketQuantumInformation.ketbraQuantumInformation.ketbraQuantumInformation.kl_divergenceQuantumInformation.log_negativityQuantumInformation.max_entangledQuantumInformation.max_mixedQuantumInformation.mixedradix2numberQuantumInformation.negativityQuantumInformation.norm_diamondQuantumInformation.norm_hsQuantumInformation.norm_traceQuantumInformation.number2mixedradixQuantumInformation.permutesystemsQuantumInformation.pptQuantumInformation.projQuantumInformation.ptraceQuantumInformation.ptraceQuantumInformation.ptraceQuantumInformation.ptransposeQuantumInformation.ptransposeQuantumInformation.purityQuantumInformation.qftQuantumInformation.relative_entropyQuantumInformation.renormalize!QuantumInformation.renormalize!QuantumInformation.renyi_entropyQuantumInformation.representQuantumInformation.resQuantumInformation.reshuffleQuantumInformation.shannon_entropyQuantumInformation.shannon_entropyQuantumInformation.superfidelityQuantumInformation.trace_distanceQuantumInformation.unresQuantumInformation.vonneumann_entropyQuantumInformation.werner_state
QuantumInformation.QuantumInformation — Module
Main module for QuantumInformation.jl – a Julia package for numerical computation in quantum information theory.
QuantumInformation.DynamicalMatrix — Type
T: quantum channel map.
Representation of quantum channel by Dynamical matrix operators.
QuantumInformation.IdentityChannel — Type
T: quantum channel map.
Representation of identity channel.
QuantumInformation.KrausOperators — Type
T: quantum channel map.
Representation of quantum channel by Kraus operators.
QuantumInformation.Stinespring — Type
T: quantum channel map.
Stinespring representation of quantum channel.
QuantumInformation.SuperOperator — Type
T: quantum channel map.
Representation of quantum channel by super-operator.
QuantumInformation.SuperOperator — Method
channel: quantum channel map.idim: square root of the super-operator matrix input dimension.odim: square root of the super-operator matrix output dimension.
Transforms quntum channel into super-operator matrix.
QuantumInformation.UnitaryChannel — Type
T: quantum channel map.
Representation of unitary channel.
Base.convert — Method
- ?: type.
Φ: list of Kraus operators.
Transforms list of Kraus operators into dynamical matrix.
Base.convert — Method
- ?: type.
Φ: super-operator matrix.
Transforms super-operator matrix into dynamical matrix.
Base.convert — Method
- ?: type.
Φ: dynamical matrix.
Transforms dynamical matrix into list of Kraus operators.
Base.convert — Method
- ?: type.
Φ: super-operator matrix.
Transforms super-operator matrix into list of Kraus operators.
Base.convert — Method
- ?: type.
Φ: dynamical matrix.
Transforms dynamical matrix into Stinespring representation of quantum channel.
Base.convert — Method
- ?: type.
Φ: list of Kraus operators.
Transforms list of Kraus operators into Stinespring representation of quantum channel.
Base.convert — Method
- ?: type.
Φ: super-operator matrix.
Transforms super-operator matrix into Stinespring representation of quantum channel.
Base.convert — Method
- ?: type.
Φ: dynamical matrix.
Transforms dynamical matrix into super-operator matrix.
Base.convert — Method
- ?: type.
Φ: list of Kraus operators.
Transforms list of Kraus operators into super-operator matrix.
QuantumInformation.applychannel — Method
Φ: quantum channel.ψ: quantum state vector.
Return application of channel Φ on state vector ψ.
QuantumInformation.applychannel — Method
Φ: Identity channel.ρ: quantum state.
Return application of Identity channel Φ on ρ.
QuantumInformation.applychannel — Method
Φ: Identity channel.ψ: quantum state vector.
Return application of Identity channel Φ on state vector ψ.
QuantumInformation.applychannel — Method
Φ: list of vectors.ρ: input matrix.
Return application of channel Φonρ`. Kraus representation of quantum channel $\Phi$ is a set $\{K_i\}_{i\in I}$ of bounded operators on $\mathcal{H}$ such that $\sum_{i\in I} K_i^\dagger K_i = \mathcal{1}$. Then $\Phi(\rho)=\sum_{i\in I} K_i \rho K_i^\dagger$.
QuantumInformation.applychannel — Method
Φ: Stinespring representation of quantum channel.ρ: quantum state.dims: dimensions of registers ofρ.
Application of Stinespring representation of quantum channel into state ρ.
QuantumInformation.applychannel — Method
Φ: super-operator matrix.ρ: quantum state.
Application of super-operator matrix into state ρ.
QuantumInformation.applychannel — Method
Φ: Unitary channel.ρ: quantum state.
Return application of Unitary channel Φ on ρ.
QuantumInformation.applychannel — Method
Φ: Unitary channel.ψ: quantum state vector.
Return application of Unitary channel Φ on state vector ψ.
QuantumInformation.applychannel — Method
Φ: dynamical matrix.ρ: quantum state.
Application of dynamical matrix into state ρ.
QuantumInformation.bloch_vector — Method
ρ: input qubit density matrix.
Return the Bloch vector corresponding to the inpu quit state.
QuantumInformation.bra — Method
val: non-zero entry - label.dim: length of the vector
Return Hermitian conjugate $\langle val| = |val\rangle^\dagger$ of the ket with the same label.
QuantumInformation.bures_angle — Method
ρ: quantum state.σ: quantum state.
Return Bures angle between quantum states ρ and σ.
QuantumInformation.bures_distance — Method
ρ: quantum state.σ: quantum state.
Return Bures distance between quantum states ρ and σ.
QuantumInformation.channelbasis — Function
T: Type of the matrices in the basis.idim: Input dimension.odim: Output dimension.
Returns a basis for quantum channels.
QuantumInformation.combine — Method
basis: A basis represented by a sub-type ofAbstractMatrixBasis.v: Vector of coefficients.
Returns a matrix constructed from the basis elements weighted by the coefficients in v.
QuantumInformation.concurrence — Method
ρ: quantum state.
Calculates the concurrence of a two-qubit system ρ.
QuantumInformation.diamond_distance — Method
Φ1: DynamicalMatrixΦ2: DynamicalMatrix
Return diamond distance between dynamical matrices Φ1 and Φ2.
QuantumInformation.fidelity — Method
ρ: matrix.σ: matrix.
Return fidelity between matrices ρ and σ.
QuantumInformation.fidelity_sqrt — Method
ρ: matrix.σ: matrix.
Return square root of fidelity between matrices ρ and σ.
QuantumInformation.gate_fidelity — Method
U: quantum gate.V: quantum gate.
Return fidelity between gates U and V.
QuantumInformation.grover — Method
d: dimension of operator.
Prepares Grover operator of dimension d.
QuantumInformation.hadamard — Method
d: dimension of operator.
Prepares Hadamard operator of dimension d.
QuantumInformation.hermitianbasis — Method
dim: dimensions of the matrix.
Returns elementary hermitian matrices of dimension dim x dim.
QuantumInformation.hs_distance — Method
A: matrix.B: matrix.
Return Hilbert–Schmidt distance between matrices A and B.
QuantumInformation.iscp — Function
Φ: A subtype of AbstractQuantumOperation.atol: tolerance of approximation.
Checks if an object is completely positive.
QuantumInformation.iscptni — Function
Φ: A subtype of AbstractQuantumOperation.atol: tolerance of approximation.
Checks if an object is completely positive and trace non-increasing.
QuantumInformation.iscptp — Function
Φ: A subtype of AbstractQuantumOperation.atol: tolerance of approximation.
Checks if an object is completely positive and trace preserving.
QuantumInformation.iseffect — Method
Φ: Post-selection Measurement.
Checks if a matrix represents a valid quantum effect (0 <= E <= I).
QuantumInformation.isidentity — Function
ρ: Input matrix.atol: Absolute tolerance.
Checks if the matrix ρ is approximately the identity matrix.
QuantumInformation.ispositive — Function
ρ: Input matrix.atol: Absolute tolerance.
Checks if the matrix ρ is positive semi-definite.
QuantumInformation.ispovm — Method
Φ: POVM Measurement.
Checks if a set of matrices forms a valid POVM (Positive Operator-Valued Measure).
QuantumInformation.istni — Function
Φ: A subtype of AbstractQuantumOperation.atol: tolerance of approximation.
Checks if an object is trace non-increasing.
QuantumInformation.istp — Function
Φ: A subtype of AbstractQuantumOperation.atol: tolerance of approximation.
Checks if an object is trace preserving.
QuantumInformation.js_divergence — Method
ρ: quantum state.σ: quantum state.
Return Jensen–Shannon divergence of quantum state ρ with respect to σ.
QuantumInformation.ket — Method
val: non-zero entry - label.dim: length of the vector.
Return complex column vector $|val\rangle$ of unit norm describing quantum state.
QuantumInformation.ketbra — Method
valk: non-zero entry - label.valb: non-zero entry - label.idim: length of the ket vectorodim: length of the bra vector
Return outer product $|valk\rangle\langle vakb|$ of states $|valk\rangle$ and $|valb\rangle$.
QuantumInformation.ketbra — Method
valk: non-zero entry - label.valb: non-zero entry - label.dim: length of the ket and bra vectors
Return outer product $|valk\rangle\langle vakb|$ of states $|valk\rangle$ and $|valb\rangle$.
QuantumInformation.kl_divergence — Method
ρ: quantum state.σ: quantum state.
Return Kullback–Leibler divergence of quantum state ρ with respect to σ.
QuantumInformation.log_negativity — Method
ρ: quantum state.dims: dimensions of subsystems.sys: transposed subsystem.
Return log negativity of quantum state ρ.
QuantumInformation.max_entangled — Method
d: length of the vector.
Return maximally entangled state $\frac{1}{\sqrt{d}}\sum_{i=0}^{\sqrt{d}-1}|ii\rangle$ of length $\sqrt{d}$.
QuantumInformation.max_mixed — Method
d: length of the vector.
Return maximally mixed state $\frac{1}{d}\sum_{i=0}^{d-1}|i\rangle\langle i |$ of length $d$.
QuantumInformation.mixedradix2number — Method
digits: Vector of coefficients in mixed radix representation.radices: Vector of mixed radices.
Returns the integer number corresponding to the mixed radix representation.
QuantumInformation.negativity — Method
ρ: quantum state.dims: dimensions of subsystems.sys: transposed subsystem.
Return negativity of quantum state ρ.
QuantumInformation.norm_diamond — Function
Φ: DynamicalMatrix
Return diamond norm of dynamical matrix Φ.
QuantumInformation.norm_hs — Method
A: matrix.
Return Hilbert–Schmidt norm of matrix A.
QuantumInformation.norm_trace — Method
A: matrix.
Return trace norm of matrix A.
QuantumInformation.number2mixedradix — Method
n: Number to be converted (integer).radices: Vector of mixed radices.
Returns the representation of n in the mixed radix system defined by radices.
QuantumInformation.permutesystems — Method
ρ: input state.dims: dimensions of registers ofρ.systems: permuted registers.
Returns state ρ with permuted registers denoted by systems.
QuantumInformation.ppt — Method
ρ: quantum state.dims: dimensions of subsystems.sys: transposed subsystem.
Return minimum eigenvalue of positive partial transposition of quantum state ρ.
QuantumInformation.proj — Method
ket: input column vector.
Return outer product $|ket\rangle\langle ket|$ of ket.
QuantumInformation.ptrace — Method
ρ: quantum state.idims: dimensins of subsystems.sys: traced subsystem.
QuantumInformation.ptrace — Method
ρ: quantum state.idims: dimensins of subsystems.isystems: traced subsystems.
Return partial trace of matrix ρ over the subsystems determined by isystems.
QuantumInformation.ptrace — Method
ψ: quantum state pure state (ket).idims: dimensins of subsystems - only bipartite states accepted.sys: traced subsystem.
QuantumInformation.ptranspose — Method
ρ: quantum state.idims: dimensins of subsystems.sys: transposed subsystem.
QuantumInformation.ptranspose — Method
ρ: quantum state.idims: dimensins of subsystems.isystems: transposed subsystems.
Return partial transposition of matrix ρ over the subsystems determined by isystems.
QuantumInformation.purity — Method
ρ: matrix.
Return the purity of ρ ∈ [1/d, 1]
QuantumInformation.qft — Method
d: dimension of operator.
Prepares gate realized a quantum Fourier transform of dimension d.
QuantumInformation.relative_entropy — Method
ρ: quantum state.σ: quantum state.
Return quantum relative entropy of quantum state ρ with respect to σ.
QuantumInformation.renormalize! — Method
ρ: Input matrix.
Renormalizes the matrix ρ in-place so that its trace is 1.
QuantumInformation.renormalize! — Method
ψ: Input vector.
Renormalizes the vector ψ in-place so that its norm is 1.
QuantumInformation.renyi_entropy — Method
ρ: quantum state.α: order of Renyi entropy.
Return Renyi entropy of quantum state ρ.
QuantumInformation.represent — Method
basis: A basis represented by a sub-type ofAbstractMatrixBasis.m: Matrix to be represented in thebasis.
Returns a vector of coefficients of the matrix m in the basis basis.
QuantumInformation.res — Method
ρ: input matrix.
Returns vec(ρ.T). Reshaping maps matrix ρ into a vector row by row.
QuantumInformation.reshuffle — Method
ρ: reshuffled matrix.
Performs reshuffling of indices of a matrix. Given multiindexed matrix $M_{(m,μ),(n,ν)}$ it returns matrix $M_{(m,n),(μ,ν)}$.
QuantumInformation.shannon_entropy — Method
p: vector.
Return Shannon entorpy of vector p.
QuantumInformation.shannon_entropy — Method
x: real number.
Return binary Shannon entorpy given by $-x \log(x) - (1 - x) \log(1 - x)$.
QuantumInformation.superfidelity — Method
ρ: quantum state.σ: quantum state.
Return superfidelity between quantum states ρ and σ.
QuantumInformation.trace_distance — Method
A: matrix.B: matrix.
Return trace distance between matrices A and B.
QuantumInformation.unres — Method
ϕ: input matrix.
Return de-reshaping of the vector into a matrix.
QuantumInformation.vonneumann_entropy — Method
ρ: quantum state.
Return Von Neumann entropy of quantum state ρ.
QuantumInformation.werner_state — Method
d: length of the vector.α: real number from [0, 1].
Returns Werner state given by $\frac{\alpha}{d}\left(\sum_{i=0}^{\sqrt{d}-1}|ii\rangle\right) \left(\sum_{i=0}^{\sqrt{d}-1}\langle ii|\right)+ \frac{1-\alpha}{d}\sum_{i=0}^{d-1}|i\rangle\langle i|$.