Cosmetics

src/basic.jl

@@ -198,7 +198,7 @@ export pauli
     gellmann([T=ComplexF64,], d::Integer = 3)
 
 Constructs the set `G` of generalized Gell-Mann matrices in dimension `d` such that
-`G[1] = I` and `Tr(G[i]*G[j]) = 2 δ_ij`.
+`G₁ = I` and `Tr(GᵢGⱼ) = 2 δᵢⱼ`.
 
 Reference: [Generalizations of Pauli matrices](https://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices)
 """

src/entanglement.jl

@@ -139,14 +139,14 @@ end
 Upper bound on the random robustness of `ρ` such that it has a Schmidt number `s`.
 
 If a state ``ρ`` with local dimensions ``d_A`` and ``d_B`` has Schmidt number ``s``, then there is
-a PSD matrix ``ω`` in the extended space ``AA′B′B``, where ``A′`` and ``B^′`` have dimension ``s``,
-such that ``ω / s`` is separable  against ``AA′|B′B`` and ``Π† ω Π = ρ``, where ``Π = 1_A ⊗ s ψ^+ ⊗ 1_B``,
+a PSD matrix ``ω`` in the extended space ``AA'B'B``, where ``A'`` and ``B'`` have dimension ``s``,
+such that ``ω / s`` is separable  against ``AA'|B'B`` and ``Π^† ω Π = ρ``, where ``Π = 1_A ⊗ s ψ^+ ⊗ 1_B``,
 and ``ψ^+`` is a non-normalized maximally entangled state. Separabiity is tested with the DPS hierarchy,
-with `n` controlling the how many copies of the ``B′B`` subsystem are used.
+with `n` controlling the how many copies of the ``B'B`` subsystem are used.
 
 References:
-    Hulpke, Bruss, Lewenstein, Sanpera [arXiv:quant-ph/0401118](https://arxiv.org/abs/quant-ph/0401118)\
-Weilenmann, Dive, Trillo, Aguilar, Navascués [arXiv:1912.10056](https://arxiv.org/abs/1912.10056)
+- Hulpke, Bruss, Lewenstein, Sanpera [arXiv:quant-ph/0401118](https://arxiv.org/abs/quant-ph/0401118)
+- Weilenmann, Dive, Trillo, Aguilar, Navascués [arXiv:1912.10056](https://arxiv.org/abs/1912.10056)
 """
 function schmidt_number(
     ρ::AbstractMatrix{T},
@@ -240,8 +240,7 @@ export random_robustness
 
 Constrains state `ρ` of dimensions `dims` in JuMP model `model` to respect the DPS constraints of level `n`.
 
-References:
-    Doherty, Parrilo, Spedalieri [arXiv:quant-ph/0308032](https://arxiv.org/abs/quant-ph/0308032)
+Reference: Doherty, Parrilo, Spedalieri, [arXiv:quant-ph/0308032](https://arxiv.org/abs/quant-ph/0308032)
 """
 function _dps_constraints!(
     model::JuMP.GenericModel{T},

src/multilinear.jl

@@ -276,7 +276,7 @@ end
     permute_systems(X::AbstractMatrix, perm::Vector, dims::Matrix)
 
 Permutes the order of the subsystems of the matrix `X`, which is composed by subsystems of dimensions `dims`, according to the permutation `perm`.
-`dims` should be a n x 2 matrix where `dims[i, 1]` is the number of rows of subsystem i, and `dims[i,2]` is its number of columns.
+`dims` should be a n x 2 matrix where `dims[i, 1]` is the number of rows of subsystem i, and `dims[i, 2]` is its number of columns.
 """
 function permute_systems(X::AbstractMatrix, perm::AbstractVector{<:Integer}, dims::Matrix{<:Integer})
     perm == 1:length(perm) && return X

src/nonlocal.jl

@@ -407,9 +407,9 @@ export tensor_probability
 """
     tensor_correlation(p::AbstractArray{T, N2}, behaviour::Bool = false; marg::Bool = true)
 
-Converts a 2x...x2xmx...xm probability array into
-- a mx...xm correlation array (no marginals)
-- a (m+1)x...x(m+1) correlation array (marginals).
+Converts a 2 x ... x 2 x m x ... x m probability array into
+- an m x ... x m correlation array (no marginals)
+- an (m+1) x ... x (m+1) correlation array (marginals).
 If `behaviour` is `true` do the transformation for behaviours. Doesn't assume normalization.
 
 Also accepts the arguments of `tensor_probability` (state and measurements) for convenience.

src/states.jl

@@ -71,7 +71,7 @@ export state_bell
 """
     state_phiplus_ket([T=ComplexF64,] d::Integer = 2)
 
-Produces the ket of the maximally entangled state Φ⁺ of local dimension `d`.
+Produces the ket of the maximally entangled state ϕ⁺ of local dimension `d`.
 """
 function state_phiplus_ket(::Type{T}, d::Integer = 2; kwargs...) where {T<:Number}
     return state_ghz_ket(T, d, 2; kwargs...)
@@ -82,7 +82,7 @@ export state_phiplus_ket
 """
     state_phiplus([T=ComplexF64,] d::Integer = 2; v::Real = 1)
 
-Produces the maximally entangled state Φ⁺ of local dimension `d` with visibility `v`.
+Produces the maximally entangled state ϕ⁺ of local dimension `d` with visibility `v`.
 """
 function state_phiplus(::Type{T}, d::Integer = 2; v::Real = 1) where {T<:Number}
     rho = ketbra(state_phiplus_ket(T, d; coeff = one(T)))