diff --git a/CHANGELOG.md b/CHANGELOG.md
index 2fbea819e..84bc5139e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,7 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
 ## [Unreleased](https://github.com/qutip/QuantumToolbox.jl/tree/main)
+- Add error message for bad input in state/operator generating functions ([#603])
 
 ## [v0.39.1]
 Release date: 2025-11-19
@@ -381,3 +382,4 @@ Release date: 2024-11-13
 [#589]: https://github.com/qutip/QuantumToolbox.jl/issues/589
 [#591]: https://github.com/qutip/QuantumToolbox.jl/issues/591
 [#596]: https://github.com/qutip/QuantumToolbox.jl/issues/596
+[#603]: https://github.com/qutip/QuantumToolbox.jl/issues/603
diff --git a/src/qobj/operators.jl b/src/qobj/operators.jl
index fb0c2041f..b921e349a 100644
--- a/src/qobj/operators.jl
+++ b/src/qobj/operators.jl
@@ -477,7 +477,7 @@ _Jordan_Wigner(N::Int, j::Int, op::QuantumObject{Operator}) = _Jordan_Wigner(Val
 
 function _Jordan_Wigner(::Val{N}, j::Int, op::QuantumObject{Operator}) where {N}
     (N < 1) && throw(ArgumentError("The total number of sites (N) cannot be less than 1"))
-    ((j > N) || (j < 1)) && throw(ArgumentError("The site index (j) should satisfy: 1 ≤ j ≤ N"))
+    (1 <= j <= N) || throw(ArgumentError("The site index (j) should satisfy: 1 ≤ j ≤ N"))
 
     σz = sigmaz().data
     Z_tensor = kron(1, 1, fill(σz, j - 1)...)
@@ -493,8 +493,12 @@ end
 
 Generates the projection operator ``\hat{O} = |i \rangle\langle j|`` with Hilbert space dimension `N`.
 """
-projection(N::Int, i::Int, j::Int) =
-    QuantumObject(sparse([i + 1], [j + 1], [1.0 + 0.0im], N, N), type = Operator(), dims = N)
+function projection(N::Int, i::Int, j::Int)
+    (0 <= i < N) || throw(ArgumentError("Invalid argument i, must satisfy: 0 ≤ i ≤ N-1"))
+    (0 <= j < N) || throw(ArgumentError("Invalid argument j, must satisfy: 0 ≤ j ≤ N-1"))
+
+    return QuantumObject(sparse([i + 1], [j + 1], [1.0 + 0.0im], N, N), type = Operator(), dims = N)
+end
 
 @doc raw"""
     tunneling(N::Int, m::Int=1; sparse::Union{Bool,Val{<:Bool}}=Val(false))
diff --git a/src/qobj/states.jl b/src/qobj/states.jl
index dd79bee8d..38cddd6c9 100644
--- a/src/qobj/states.jl
+++ b/src/qobj/states.jl
@@ -2,7 +2,7 @@
 Functions for generating (common) quantum states.
 =#
 
-export zero_ket, fock, basis, coherent, rand_ket
+export zero_ket, fock, coherent, rand_ket
 export fock_dm, coherent_dm, thermal_dm, maximally_mixed_dm, rand_dm
 export spin_state, spin_coherent
 export bell_state, singlet_state, triplet_states, w_state, ghz_state
@@ -25,6 +25,7 @@ zero_ket(dimensions::Union{Dimensions,AbstractVector{Int},Tuple}) =
 
 @doc raw"""
     fock(N::Int, j::Int=0; dims::Union{Int,AbstractVector{Int},Tuple}=N, sparse::Union{Bool,Val}=Val(false))
+    basis(N::Int, j::Int=0; dims::Union{Int,AbstractVector{Int},Tuple}=N, sparse::Union{Bool,Val}=Val(false))
 
 Generates a fock state ``\ket{\psi}`` of dimension `N`. 
 
@@ -32,8 +33,12 @@ It is also possible to specify the list of dimensions `dims` if different subsys
 
 !!! warning "Beware of type-stability!"
     If you want to keep type stability, it is recommended to use `fock(N, j, dims=dims, sparse=Val(sparse))` instead of `fock(N, j, dims=dims, sparse=sparse)`. Consider also to use `dims` as a `Tuple` or `SVector` from [StaticArrays.jl](https://github.com/JuliaArrays/StaticArrays.jl) instead of `Vector`. See [this link](https://docs.julialang.org/en/v1/manual/performance-tips/#man-performance-value-type) and the [related Section](@ref doc:Type-Stability) about type stability for more details.
+
+!!! note
+    `basis(N, j; dims = dims, sparse = sparse)` is a synonym of `fock(N, j; dims = dims, sparse = sparse)`.
 """
 function fock(N::Int, j::Int = 0; dims::Union{Int,AbstractVector{Int},Tuple} = N, sparse::Union{Bool,Val} = Val(false))
+    (0 <= j < N) || throw(ArgumentError("Invalid argument j, must satisfy: 0 ≤ j ≤ N-1"))
     if getVal(sparse)
         array = sparsevec([j + 1], [1.0 + 0im], N)
     else
@@ -42,18 +47,6 @@ function fock(N::Int, j::Int = 0; dims::Union{Int,AbstractVector{Int},Tuple} = N
     return QuantumObject(array; type = Ket(), dims = dims)
 end
 
-@doc raw"""
-    basis(N::Int, j::Int = 0; dims::Union{Int,AbstractVector{Int},Tuple}=N)
-
-Generates a fock state like [`fock`](@ref).
-
-It is also possible to specify the list of dimensions `dims` if different subsystems are present.
-
-!!! warning "Beware of type-stability!"
-    If you want to keep type stability, it is recommended to use `basis(N, j, dims=dims)` with `dims` as a `Tuple` or `SVector` from [StaticArrays.jl](https://github.com/JuliaArrays/StaticArrays.jl) instead of `Vector`. See [this link](https://docs.julialang.org/en/v1/manual/performance-tips/#man-performance-value-type) and the [related Section](@ref doc:Type-Stability) about type stability for more details.
-"""
-basis(N::Int, j::Int = 0; dims::Union{Int,AbstractVector{Int},Tuple} = N) = fock(N, j, dims = dims)
-
 @doc raw"""
     coherent(N::Int, α::Number)
 
@@ -203,7 +196,7 @@ function spin_state(j::Real, m::Real)
         throw(ArgumentError("Invalid eigenvalue m: (j - m) must be a non-negative integer."))
     (m < (-j)) && throw(ArgumentError("Invalid eigenvalue m, must satisfy: -j ≤ m ≤ j"))
 
-    return basis(Int(J), Int(Δ))
+    return fock(Int(J), Int(Δ))
 end
 
 @doc raw"""
@@ -318,6 +311,8 @@ Returns the `n`-qubit [W-state](https://en.wikipedia.org/wiki/W_state):
     If you want to keep type stability, it is recommended to use `w_state(Val(n))` instead of `w_state(n)`. See [this link](https://docs.julialang.org/en/v1/manual/performance-tips/#man-performance-value-type) and the [related Section](@ref doc:Type-Stability) for more details.
 """
 function w_state(::Val{n}) where {n}
+    (n >= 2) || throw(ArgumentError("Invalid argument n, must satisfy: n ≥ 2"))
+
     nzind = 2 .^ (0:(n-1)) .+ 1
     nzval = fill(ComplexF64(1 / sqrt(n)), n)
     data = zeros(ComplexF64, 2^n)
@@ -341,6 +336,9 @@ Here, `d` specifies the dimension of each qudit. Default to `d=2` (qubit).
     If you want to keep type stability, it is recommended to use `ghz_state(Val(n))` instead of `ghz_state(n)`. See [this link](https://docs.julialang.org/en/v1/manual/performance-tips/#man-performance-value-type) and the [related Section](@ref doc:Type-Stability) for more details.
 """
 function ghz_state(::Val{n}; d::Int = 2) where {n}
+    (n >= 2) || throw(ArgumentError("Invalid argument n, must satisfy: n ≥ 2"))
+    (d >= 2) || throw(ArgumentError("Invalid argument d, must satisfy: d ≥ 2"))
+
     nzind = collect((0:(d-1)) .* Int((d^n - 1) / (d - 1)) .+ 1)
     nzval = fill(ComplexF64(1 / sqrt(d)), d)
     data = zeros(ComplexF64, d^n)
diff --git a/src/qobj/synonyms.jl b/src/qobj/synonyms.jl
index 224c73b59..fa73ad396 100644
--- a/src/qobj/synonyms.jl
+++ b/src/qobj/synonyms.jl
@@ -4,6 +4,7 @@ Synonyms of the functions for QuantumObject
 
 export Qobj, QobjEvo, shape, isherm
 export trans, dag, matrix_element, unit
+export basis
 export tensor, ⊗
 export qeye, qeye_like, qzero_like
 export vector_to_operator, operator_to_vector
@@ -33,6 +34,8 @@ const trans = transpose
 
 const dag = adjoint
 
+const basis = fock
+
 @doc raw"""
     matrix_element(i::QuantumObject, A::QuantumObject, j::QuantumObject)
 
diff --git a/test/core-test/states_and_operators.jl b/test/core-test/states_and_operators.jl
index 6d0aef108..ad2814233 100644
--- a/test/core-test/states_and_operators.jl
+++ b/test/core-test/states_and_operators.jl
@@ -20,6 +20,7 @@
         # fock, basis, and fock_dm
         @test fock_dm(4; dims = (2, 2), sparse = true) ≈ ket2dm(basis(4; dims = (2, 2)))
         @test_throws DimensionMismatch fock(4; dims = 2)
+        @test_throws ArgumentError fock(4, 4)
     end
 
     @testset "coherent state" begin
@@ -121,16 +122,21 @@
         @test_throws ArgumentError bell_state(0, 2)
         @test_throws ArgumentError bell_state(3, 1)
         @test_throws ArgumentError bell_state(2, 3)
+        @test_throws ArgumentError w_state(1)
+        @test_throws ArgumentError ghz_state(1)
+        @test_throws ArgumentError ghz_state(2; d = 1)
     end
 
     @testset "bosonic operators" begin
         # destroy, create, num, position, momentum
         n = 10
+        i, j = rand(0:(n-1), 2)
         a = destroy(n)
         ad = create(n)
         N = num(n)
         x = position(n)
         p = momentum(n)
+        Pij = projection(n, i, j)
         @test isoper(x)
         @test isoper(p)
         @test a.dims == ad.dims == N.dims == x.dims == p.dims == [n]
@@ -138,6 +144,9 @@
         @test commutator(N, a) ≈ -a
         @test commutator(N, ad) ≈ ad
         @test all(diag(commutator(x, p))[1:(n-1)] .≈ 1.0im)
+        @test fock(n, i) == Pij * fock(n, j)
+        @test_throws ArgumentError projection(n, n, 0)
+        @test_throws ArgumentError projection(n, 0, n)
     end
 
     @testset "displacement and squeezing operators" begin