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Documentation

Index

A list of all documentation sorted by module.

Base.convert — Method
convert(_, Φ)
  • ?: type.
  • Φ: list of Kraus operators.

Transforms list of Kraus operators into dynamical matrix.

Base.convert — Method
convert(_, Φ)
  • ?: type.
  • Φ: super-operator matrix.

Transforms super-operator matrix into dynamical matrix.

Base.convert — Method
convert(_, Φ)
  • ?: type.
  • Φ: dynamical matrix.

Transforms dynamical matrix into list of Kraus operators.

Base.convert — Method
convert(_, Φ)
  • ?: type.
  • Φ: super-operator matrix.

Transforms super-operator matrix into list of Kraus operators.

Base.convert — Method
convert(_, Φ)
  • ?: type.
  • Φ: dynamical matrix.

Transforms dynamical matrix into Stinespring representation of quantum channel.

Base.convert — Method
convert(_, Φ)
  • ?: type.
  • Φ: list of Kraus operators.

Transforms list of Kraus operators into Stinespring representation of quantum channel.

Base.convert — Method
convert(_, Φ)
  • ?: type.
  • Φ: super-operator matrix.

Transforms super-operator matrix into Stinespring representation of quantum channel.

Base.convert — Method
convert(_, Φ)
  • ?: type.
  • Φ: dynamical matrix.

Transforms dynamical matrix into super-operator matrix.

Base.convert — Method
convert(_, Φ)
  • ?: type.
  • Φ: list of Kraus operators.

Transforms list of Kraus operators into super-operator matrix.

QuantumInformation.applychannel — Method
applychannel(Φ, ρ)
  • 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
applychannel(Φ, ρ)
  • Φ: Stinespring representation of quantum channel.
  • ρ: quantum state.
  • dims: dimensions of registers of ρ.

Application of Stinespring representation of quantum channel into state ρ.

QuantumInformation.applychannel — Method
applychannel(Φ, ρ)
  • Φ: super-operator matrix.
  • ρ: quantum state.

Application of super-operator matrix into state ρ.

QuantumInformation.bra — Method
bra(val, dim)
  • 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.iscp — Function
  • Φ: A subtype of AbstractQuantumOperation.
  • atol: tolerance of approximation.

Checks if an object is completely positive.

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.ket — Method
ket(val, dim)
  • 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 vector
  • odim: length of the bra vector

Return outer product $|valk\rangle\langle vakb|$ of states $|valk\rangle$ and $|valb\rangle$.

QuantumInformation.ketbra — Method
ketbra(valk, valb, dim)
  • 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.max_entangled — Method
max_entangled(d)
  • 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
max_mixed(d)
  • 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.permutesystems — Method
permutesystems(ρ, dims, systems)
  • ρ: input state.
  • dims: dimensions of registers of ρ.
  • systems: permuted registers.

Returns state ρ with permuted registers denoted by systems.

QuantumInformation.proj — Method
proj(ψ)
  • ket: input column vector.

Return outer product $|ket\rangle\langle ket|$ of ket.

QuantumInformation.ptrace — Method
ptrace(ρ, idims, sys)
  • ρ: quantum state.
  • idims: dimensins of subsystems.
  • sys: traced subsystem.
QuantumInformation.ptrace — Method
ptrace(ρ, idims, isystems)
  • 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
ptrace(ψ, idims, sys)
  • ψ: quantum state pure state (ket).
  • idims: dimensins of subsystems - only bipartite states accepted.
  • sys: traced subsystem.
QuantumInformation.res — Method
res(ρ)
  • ρ: input matrix.

Returns vec(ρ.T). Reshaping maps matrix ρ into a vector row by row.

QuantumInformation.reshuffle — Method
reshuffle(ρ)
  • 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.werner_state — Method
werner_state(d, α)
  • d: length of the vector.
  • α: real number from [0, 1].

Returns Werner state given by $\frac{\alpha}{d}\left(\sum_{i=0}^{\sqrt{d}-1}|ii\rangle\right) \left(\sum_{i=0}^{\sqrt{d}-1}\langle ii|\right)+ \frac{1-\alpha}{d}\sum_{i=0}^{d-1}|i\rangle\langle i|$.