iitis / QuantumInformation.jl / 402

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Build # 402

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travis-ci

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pgawron

Commit Message

Merge branch 'master' into pg/channels

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/src/channels/applications.jl

export applychannel

################################################################################
# Application of channels
################################################################################
"""
$(SIGNATURES)
- `Φ`: dynamical matrix.
- `ρ`: quantum state.

Application of dynamical matrix into state `ρ`.
"""
function applychannel(Φ::DynamicalMatrix{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{T}) where T<:Number
    ptrace(Φ.matrix * (Diagonal{T}(I, Φ.odim)⊗transpose(ρ)), [Φ.odim, Φ.idim], [2])
end

"""
$(SIGNATURES)
- `Φ`: list of vectors.
- `ρ`: input matrix.

Return application of channel `Φ`` on `ρ`. 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\$.
"""
function applychannel(Φ::KrausOperators{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
    sum(k * ρ * k' for k in Φ.matrices)
end

"""
$(SIGNATURES)
- `Φ`: super-operator matrix.
- `ρ`: quantum state.

Application of super-operator matrix into state `ρ`.
"""
function applychannel(Φ::SuperOperator{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
    unres(Φ.matrix * res(ρ))
end

"""
$(SIGNATURES)
- `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`.
"""
function applychannel(Φ::Stinespring{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
    s = Φ.matrix * ρ * Φ.matrix'
    ptrace(s, [Φ.odim, Φ.odim*Φ.idim], [2])
end

function applychannel(Φ::IdentityChannel{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
    # TODO: promote type
    ρ
end

function applychannel(Φ::UnitaryChannel{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
    # TODO: promote type
    Φ.matrix*ρ*Φ.matrix'
end

function applychannel(Φ::AbstractQuantumOperation, ψ::AbstractVector{<:Number})
    # TODO: promote type
    applychannel(Φ, proj(ψ))
end

function applychannel(Φ::UnitaryChannel{<:AbstractMatrix{<:Number}}, ψ::AbstractVector{<:Number})
    # TODO: promote type
    Φ.matrix*ψ
end

function applychannel(Φ::IdentityChannel{<:AbstractMatrix{<:Number}}, ψ::AbstractVector{<:Number})
    # TODO: promote type
    ψ
end

function applychannel(Φ::POVMMeasurement{T}, ρ::AbstractMatrix{<:Number}) where T<:AbstractMatrix{<:Number}
    # TODO: Check if idim and odim are compatible with matrix and length
    probs = [real(tr(p'*ρ)) for p in Φ.matrices]
    Diagonal(probs)
end

function applychannel(Φ::PostSelectionMeasurement{T}, ρ::AbstractMatrix{<:Number}) where T<:AbstractMatrix{<:Number}
    # TODO: Check if idim and odim are compatible with matrix and length
    e = Φ.matrix
    e * ρ * e'
end

################################################################################
# making channels callable
################################################################################
for qop in (:KrausOperators, :SuperOperator, :DynamicalMatrix, :Stinespring,
    :UnitaryChannel, :POVMMeasurement, :PostSelectionMeasurement)
    @eval begin
        function (Φ::$qop)(ρ)
            applychannel(Φ, ρ)
        end
    end
end

1	export applychannel
2
3	################################################################################
4	# Application of channels
5	################################################################################
6	"""
7	$(SIGNATURES)
8	- `Φ`: dynamical matrix.
9	- `ρ`: quantum state.
10
11	Application of dynamical matrix into state `ρ`.
12	"""
13	function applychannel(Φ::DynamicalMatrix{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{T}) where T<:Number
14	ptrace(Φ.matrix * (Diagonal{T}(I, Φ.odim)⊗transpose(ρ)), [Φ.odim, Φ.idim], [2])	6✔
15	end
16
17	"""
18	$(SIGNATURES)
19	- `Φ`: list of vectors.
20	- `ρ`: input matrix.
21
22	Return application of channel `Φ`` on `ρ`. Kraus representation of quantum channel
23	\$\\Phi\$ is a set \$\\{K_i\\}_{i\\in I}\$ of bounded operators on \$\\mathcal{H}\$
24	such that \$\\sum_{i\\in I} K_i^\\dagger K_i = \\mathcal{1}\$.
25	Then \$\\Phi(\\rho)=\\sum_{i\\in I} K_i \\rho K_i^\\dagger\$.
26	"""
27	function applychannel(Φ::KrausOperators{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
28	sum(k * ρ * k' for k in Φ.matrices)	4✔
29	end
30
31	"""
32	$(SIGNATURES)
33	- `Φ`: super-operator matrix.
34	- `ρ`: quantum state.
35
36	Application of super-operator matrix into state `ρ`.
37	"""
38	function applychannel(Φ::SuperOperator{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
39	unres(Φ.matrix * res(ρ))	12✔
40	end
41
42	"""
43	$(SIGNATURES)
44	- `Φ`: Stinespring representation of quantum channel.
45	- `ρ`: quantum state.
46	- `dims`: dimensions of registers of `ρ`.
47
48	Application of Stinespring representation of quantum channel into state `ρ`.
49	"""
50	function applychannel(Φ::Stinespring{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
51	s = Φ.matrix * ρ * Φ.matrix'	10✔
52	ptrace(s, [Φ.odim, Φ.odim*Φ.idim], [2])	4✔
53	end
54
55	function applychannel(Φ::IdentityChannel{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
56	# TODO: promote type
57	ρ	×
58	end
59
60	function applychannel(Φ::UnitaryChannel{<:AbstractMatrix{<:Number}}, ρ::AbstractMatrix{<:Number})
61	# TODO: promote type
62	Φ.matrixρΦ.matrix'	×
63	end
64
65	function applychannel(Φ::AbstractQuantumOperation, ψ::AbstractVector{<:Number})
66	# TODO: promote type
67	applychannel(Φ, proj(ψ))	×
68	end
69
70	function applychannel(Φ::UnitaryChannel{<:AbstractMatrix{<:Number}}, ψ::AbstractVector{<:Number})
71	# TODO: promote type
72	Φ.matrix*ψ	×
73	end
74
75	function applychannel(Φ::IdentityChannel{<:AbstractMatrix{<:Number}}, ψ::AbstractVector{<:Number})
76	# TODO: promote type
77	ψ	×
78	end
79
80	function applychannel(Φ::POVMMeasurement{T}, ρ::AbstractMatrix{<:Number}) where T<:AbstractMatrix{<:Number}
81	# TODO: Check if idim and odim are compatible with matrix and length
82	probs = [real(tr(p'*ρ)) for p in Φ.matrices]	×
83	Diagonal(probs)	×
84	end
85
86	function applychannel(Φ::PostSelectionMeasurement{T}, ρ::AbstractMatrix{<:Number}) where T<:AbstractMatrix{<:Number}
87	# TODO: Check if idim and odim are compatible with matrix and length
88	e = Φ.matrix	×
89	e * ρ * e'	×
90	end
91
92	################################################################################
93	# making channels callable
94	################################################################################
95	for qop in (:KrausOperators, :SuperOperator, :DynamicalMatrix, :Stinespring,
96	:UnitaryChannel, :POVMMeasurement, :PostSelectionMeasurement)
97	@eval begin
98	function (Φ::$qop)(ρ)
99	applychannel(Φ, ρ)	30✔
100	end
101	end
102	end

iitis / QuantumInformation.jl / 402

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