4861454641

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github

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Commit Message

Merge 817c8b246 into 7644f36f9

Pull Request Pull Request #103: Bloch vector

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50.0

/src/ptranspose.jl

export ptranspose
"""
$(SIGNATURES)
- `ρ`: quantum state.
- `idims`: dimensins of subsystems.
- `isystems`: transposed subsystems.

Return [partial transposition](http://en.wikipedia.org/wiki/Peres-Horodecki_criterion) of matrix `ρ` over the subsystems determined by `isystems`.
"""
function ptranspose(ρ::AbstractMatrix, idims::Vector{Int}, isystems::Vector{Int})
    dims = reverse(idims)
    systems = length(idims) .- isystems .+ 1

    if size(ρ,1)!=size(ρ,2)
        throw(ArgumentError("Non square matrix passed to ptrace"))
    end
    if prod(dims)!=size(ρ,1)
        throw(ArgumentError("Product of dimensions do not match shape of matrix."))
    end
    if maximum(systems) > length(dims) ||  minimum(systems) < 1
        throw(ArgumentError("System index out of range"))
    end

    offset = length(dims)
    tensor = reshape(ρ, [dims; dims]...)
    perm = collect(1:(2offset))
    for s in systems
        idx1 = findfirst(x->x==s, perm)
        idx2 = findfirst(x->x==(s + offset), perm)
        perm[idx1], perm[idx2] = perm[idx2], perm[idx1]
    end
    tensor = permutedims(tensor, invperm(perm))
    reshape(tensor, size(ρ))
end

"""
$(SIGNATURES)
- `ρ`: quantum state.
- `idims`: dimensins of subsystems.
- `sys`: transposed subsystem.
"""
ptranspose(ρ::AbstractMatrix, idims::Vector{Int}, sys::Int) = ptranspose(ρ, idims, [sys])

function _ptranspose(ρ::AbstractMatrix{<:Number}, idims::Vector{Int}, isystems::Vector{Int})
    ns = length(idims)

    ex1 = Expr(:ref, :x)
    ex2 = Expr(:ref, ρ)

    I = Expr(:tuple, [gensym() for _=1:ns]...)
    J = Expr(:tuple, [gensym() for _=1:ns]...)

    K = copy(I)
    L = copy(J)

    r = Expr(:tuple)
    for (k, (i, j)) in enumerate(zip(K.args, L.args))
        push!(r.args, :($i:$(idims[k])), :($j:$(idims[k])))
    end
    for s in isystems
        K.args[s], L.args[s] = L.args[s], K.args[s]
    end
    push!(ex1.args, I, J)
    push!(ex2.args, L, K)

    ex = Expr(:(:=), ex1, ex2)
    ex, r
    @eval @cast $ex $r
end

1	export ptranspose
2	"""
3	$(SIGNATURES)
4	- `ρ`: quantum state.
5	- `idims`: dimensins of subsystems.
6	- `isystems`: transposed subsystems.
7
8	Return [partial transposition](http://en.wikipedia.org/wiki/Peres-Horodecki_criterion) of matrix `ρ` over the subsystems determined by `isystems`.
9	"""
10	function ptranspose(ρ::AbstractMatrix, idims::Vector{Int}, isystems::Vector{Int})	14✔
11	dims = reverse(idims)	14✔
12	systems = length(idims) .- isystems .+ 1	28✔
13
14	if size(ρ,1)!=size(ρ,2)	14✔
15	throw(ArgumentError("Non square matrix passed to ptrace"))	1✔
16	end
17	if prod(dims)!=size(ρ,1)	26✔
18	throw(ArgumentError("Product of dimensions do not match shape of matrix."))	1✔
19	end
20	if maximum(systems) > length(dims) \|\| minimum(systems) < 1	24✔
21	throw(ArgumentError("System index out of range"))	1✔
22	end
23
24	offset = length(dims)	11✔
25	tensor = reshape(ρ, [dims; dims]...)	11✔
26	perm = collect(1:(2offset))	44✔
27	for s in systems	11✔
28	idx1 = findfirst(x->x==s, perm)	35✔
29	idx2 = findfirst(x->x==(s + offset), perm)	79✔
30	perm[idx1], perm[idx2] = perm[idx2], perm[idx1]	11✔
31	end	22✔
32	tensor = permutedims(tensor, invperm(perm))	11✔
33	reshape(tensor, size(ρ))	11✔
34	end
35
36	"""
37	$(SIGNATURES)
38	- `ρ`: quantum state.
39	- `idims`: dimensins of subsystems.
40	- `sys`: transposed subsystem.
41	"""
42	ptranspose(ρ::AbstractMatrix, idims::Vector{Int}, sys::Int) = ptranspose(ρ, idims, [sys])	12✔
43
44	function _ptranspose(ρ::AbstractMatrix{<:Number}, idims::Vector{Int}, isystems::Vector{Int})	×
45	ns = length(idims)	×
46
47	ex1 = Expr(:ref, :x)	×
48	ex2 = Expr(:ref, ρ)	×
49
50	I = Expr(:tuple, [gensym() for _=1:ns]...)	×
51	J = Expr(:tuple, [gensym() for _=1:ns]...)	×
52
53	K = copy(I)	×
54	L = copy(J)	×
55
56	r = Expr(:tuple)	×
57	for (k, (i, j)) in enumerate(zip(K.args, L.args))	×
58	push!(r.args, :($i:$(idims[k])), :($j:$(idims[k])))	×
59	end	×
60	for s in isystems	×
61	K.args[s], L.args[s] = L.args[s], K.args[s]	×
62	end	×
63	push!(ex1.args, I, J)	×
64	push!(ex2.args, L, K)	×
65
66	ex = Expr(:(:=), ex1, ex2)	×
67	ex, r	×
68	@eval @cast $ex $r	×
69	end

iitis / QuantumInformation.jl / 4861454641

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