diff --git a/Project.toml b/Project.toml
index 365054b..4e96312 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "KroneckerArrays"
 uuid = "05d0b138-81bc-4ff7-84be-08becefb1ccc"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
-version = "0.1.16"
+version = "0.1.17"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
diff --git a/src/fillarrays/kroneckerarray.jl b/src/fillarrays/kroneckerarray.jl
index 0a39106..f8d17b1 100644
--- a/src/fillarrays/kroneckerarray.jl
+++ b/src/fillarrays/kroneckerarray.jl
@@ -228,6 +228,7 @@ function _BroadcastStyle(::Type{<:Eye})
   return EyeStyle()
 end
 Base.BroadcastStyle(style1::EyeStyle, style2::EyeStyle) = EyeStyle()
+Base.BroadcastStyle(style1::EyeStyle, style2::DefaultArrayStyle) = style2
 
 function Base.similar(bc::Broadcasted{EyeStyle}, elt::Type)
   return Eye{elt}(axes(bc))
diff --git a/src/kroneckerarray.jl b/src/kroneckerarray.jl
index 05f9b26..b20f9b3 100644
--- a/src/kroneckerarray.jl
+++ b/src/kroneckerarray.jl
@@ -323,6 +323,65 @@ function Base.broadcasted(
   return broadcasted(style, Base.Fix2(/, f.args[2]), a)
 end
 
+# Simplification rules similar to those for FillArrays.jl:
+# https://github.com/JuliaArrays/FillArrays.jl/blob/v1.13.0/src/fillbroadcast.jl
+using FillArrays: Zeros
+function Base.broadcasted(
+  style::KroneckerStyle,
+  ::typeof(+),
+  a::KroneckerArray,
+  b::KroneckerArray{<:Any,<:Any,<:Zeros,<:Zeros},
+)
+  # TODO: Promote the element types.
+  return a
+end
+function Base.broadcasted(
+  style::KroneckerStyle,
+  ::typeof(+),
+  a::KroneckerArray{<:Any,<:Any,<:Zeros,<:Zeros},
+  b::KroneckerArray,
+)
+  # TODO: Promote the element types.
+  return b
+end
+function Base.broadcasted(
+  style::KroneckerStyle,
+  ::typeof(+),
+  a::KroneckerArray{<:Any,<:Any,<:Zeros,<:Zeros},
+  b::KroneckerArray{<:Any,<:Any,<:Zeros,<:Zeros},
+)
+  # TODO: Promote the element types and axes.
+  return b
+end
+function Base.broadcasted(
+  style::KroneckerStyle,
+  ::typeof(-),
+  a::KroneckerArray,
+  b::KroneckerArray{<:Any,<:Any,<:Zeros,<:Zeros},
+)
+  # TODO: Promote the element types.
+  return a
+end
+function Base.broadcasted(
+  style::KroneckerStyle,
+  ::typeof(-),
+  a::KroneckerArray{<:Any,<:Any,<:Zeros,<:Zeros},
+  b::KroneckerArray,
+)
+  # TODO: Promote the element types.
+  # TODO: Return `broadcasted(-, b)`.
+  return -b
+end
+function Base.broadcasted(
+  style::KroneckerStyle,
+  ::typeof(-),
+  a::KroneckerArray{<:Any,<:Any,<:Zeros,<:Zeros},
+  b::KroneckerArray{<:Any,<:Any,<:Zeros,<:Zeros},
+)
+  # TODO: Promote the element types and axes.
+  return b
+end
+
 # TODO: Define by converting to a broadcast expession (with MapBroadcast.jl)
 # and then constructing the output with `similar`.
 function Base.map(f, a1::KroneckerArray, a_rest::KroneckerArray...)
diff --git a/test/test_blocksparsearrays.jl b/test/test_blocksparsearrays.jl
index d5d0e56..1d37e15 100644
--- a/test/test_blocksparsearrays.jl
+++ b/test/test_blocksparsearrays.jl
@@ -159,14 +159,13 @@ end
   @test_broken a[Block.(1:2), Block(2)]
 
   @testset "Block deficient" begin
-    d = Dict(Block(1, 1) => Eye{elt}(2, 2) ⊗ dev(randn(elt, 2, 2)))
-    a = @constinferred dev(blocksparse(d, r, r))
+    da = Dict(Block(1, 1) => Eye{elt}(2, 2) ⊗ dev(randn(elt, 2, 2)))
+    a = @constinferred dev(blocksparse(da, r, r))
 
-    d = Dict(Block(2, 2) => Eye{elt}(3, 3) ⊗ dev(randn(elt, 3, 3)))
-    b = @constinferred dev(blocksparse(d, r, r))
+    db = Dict(Block(2, 2) => Eye{elt}(3, 3) ⊗ dev(randn(elt, 3, 3)))
+    b = @constinferred dev(blocksparse(db, r, r))
 
-    @test_broken a + b
-    # @test Array(a + b) ≈ Array(a) + Array(b)
-    # @test Array(2a) ≈ 2Array(a)
+    @test Array(a + b) ≈ Array(a) + Array(b)
+    @test Array(2a) ≈ 2Array(a)
   end
 end
diff --git a/test/test_fillarrays.jl b/test/test_fillarrays.jl
index 001cda9..f852ef9 100644
--- a/test/test_fillarrays.jl
+++ b/test/test_fillarrays.jl
@@ -1,9 +1,9 @@
 using DerivableInterfaces: zero!
-using FillArrays: Eye
+using FillArrays: Eye, Zeros
 using KroneckerArrays: KroneckerArrays, KroneckerArray, ⊗
 using LinearAlgebra: det, norm, pinv
 using StableRNGs: StableRNG
-using Test: @test, @testset
+using Test: @test, @test_throws, @testset
 
 @testset "FillArrays.Eye" begin
   MATRIX_FUNCTIONS = KroneckerArrays.MATRIX_FUNCTIONS
@@ -190,3 +190,29 @@ using Test: @test, @testset
 
   @test det(a) ≈ det(collect(a)) ≈ 1
 end
+
+@testset "FillArrays.Zeros" begin
+  a = randn(2, 2) ⊗ randn(2, 2)
+  b = Zeros(2, 2) ⊗ Zeros(2, 2)
+  for (x, y) in ((a, b), (b, a))
+    @test x + y == a
+    @test x .+ y == a
+    @test map!(+, similar(a), x, y) == a
+    @test (similar(a) .= x .+ y) == a
+  end
+
+  @test a - b == a
+  @test a .- b == a
+  @test map!(-, similar(a), a, b) == a
+  @test (similar(a) .= a .- b) == a
+
+  @test b - a == -a
+  @test b .- a == -a
+  @test map!(-, similar(a), b, a) == -a
+  @test (similar(a) .= b .- a) == -a
+
+  @test b + b == b
+  @test b .+ b == b
+  @test b - b == b
+  @test b .- b == b
+end