diff --git a/docs/src/api.md b/docs/src/api.md
index 5faf51d5..858e7590 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -10,6 +10,8 @@ CurrentModule = QuantumToolbox
 BraQuantumObject
 KetQuantumObject
 OperatorQuantumObject
+OperatorBraQuantumObject
+OperatorKetQuantumObject
 SuperOperatorQuantumObject
 QuantumObject
 Qobj
@@ -17,6 +19,8 @@ ket2dm
 isbra
 isket
 isoper
+isoperbra
+isoperket
 issuper
 size
 eltype
diff --git a/src/QuantumToolbox.jl b/src/QuantumToolbox.jl
index 7cfcf295..65ab6aff 100644
--- a/src/QuantumToolbox.jl
+++ b/src/QuantumToolbox.jl
@@ -37,8 +37,8 @@ include("arnoldi.jl")
 include("eigsolve.jl")
 include("negativity.jl")
 
-export QuantumObject, Qobj, BraQuantumObject, KetQuantumObject, OperatorQuantumObject, SuperOperatorQuantumObject, TimeEvolutionSol
-export isket, isbra, isoper, issuper, ket2dm
+export QuantumObject, Qobj, BraQuantumObject, KetQuantumObject, OperatorQuantumObject, OperatorBraQuantumObject, OperatorKetQuantumObject, SuperOperatorQuantumObject, TimeEvolutionSol
+export isket, isbra, isoper, isoperbra, isoperket, issuper, ket2dm
 export spre, spost, sprepost, lindblad_dissipator
 export fock, basis, coherent
 export sigmam, sigmap, sigmax, sigmay, sigmaz
diff --git a/src/quantum_object.jl b/src/quantum_object.jl
index fba34a53..00bdf836 100644
--- a/src/quantum_object.jl
+++ b/src/quantum_object.jl
@@ -33,6 +33,20 @@ Abstract type representing a super-operator ``\hat{\mathcal{O}}``.
 """
 abstract type SuperOperatorQuantumObject <: QuantumObjectType end
 
+@doc raw"""
+    OperatorBraQuantumObject <: QuantumObjectType
+
+Abstract type representing a bra state in the super-operator formalism ``\langle\langle\rho|``.
+"""
+abstract type OperatorBraQuantumObject <: QuantumObjectType end
+
+@doc raw"""
+    OperatorKetQuantumObject <: QuantumObjectType
+
+Abstract type representing a ket state in the super-operator formalism ``|\rho\rangle\rangle``.
+"""
+abstract type OperatorKetQuantumObject <: QuantumObjectType end
+
 @doc raw"""
     mutable struct QuantumObject{MT<:AbstractArray,ObjType<:QuantumObjectType}
         data::MT
@@ -134,6 +148,20 @@ Checks if the [`QuantumObject`](@ref) `A` is a [`OperatorQuantumObject`](@ref) s
 """
 isoper(A::QuantumObject{<:AbstractArray{T},OpType}) where {T,OpType<:QuantumObjectType} = A.type <: OperatorQuantumObject
 
+"""
+    isoperbra(A::QuantumObject)
+
+Checks if the [`QuantumObject`](@ref) `A` is a [`OperatorBraQuantumObject`](@ref) state.
+"""
+isoperbra(A::QuantumObject{<:AbstractArray{T},OpType}) where {T,OpType<:QuantumObjectType} = A.type <: OperatorBraQuantumObject
+
+"""
+    isoperket(A::QuantumObject)
+
+Checks if the [`QuantumObject`](@ref) `A` is a [`OperatorKetQuantumObject`](@ref) state.
+"""
+isoperket(A::QuantumObject{<:AbstractArray{T},OpType}) where {T,OpType<:QuantumObjectType} = A.type <: OperatorKetQuantumObject
+
 """
     issuper(A::QuantumObject)
 
@@ -213,7 +241,7 @@ LinearAlgebra.Hermitian(A::QuantumObject{<:AbstractArray{T},OpType}, uplo::Symbo
     QuantumObject(Hermitian(A.data, uplo), A.type, A.dims)
 
 function Base.show(io::IO, ::MIME"text/plain", QO::QuantumObject{<:AbstractArray{T},OpType}) where
-{T,OpType<:Union{BraQuantumObject,KetQuantumObject,SuperOperatorQuantumObject}}
+{T,OpType<:Union{BraQuantumObject,KetQuantumObject,OperatorBraQuantumObject,OperatorKetQuantumObject,SuperOperatorQuantumObject}}
 
     op_data = QO.data
     op_dims = QO.dims
@@ -222,6 +250,10 @@ function Base.show(io::IO, ::MIME"text/plain", QO::QuantumObject{<:AbstractArray
         op_type = "Ket"
     elseif op_type <: BraQuantumObject
         op_type = "Bra"
+    elseif op_type <: OperatorKetQuantumObject
+        op_type = "Operator-Ket"
+    elseif op_type <: OperatorBraQuantumObject
+        op_type = "Operator-Bra"
     else
         op_type = "SuperOperator"
     end