Fix tracedist (#495)

* fix tracedist 1/2 factor * add make file for testing and doc * rm makefile to avoid redun --------- Co-authored-by: Xiu-zhe (Roger) Luo <rogerluo.rl18@gmail.com>
QuantumBFS · Mar 12, 2024 · f44487b · f44487b
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diff --git a/lib/YaoAPI/src/registers.jl b/lib/YaoAPI/src/registers.jl
@@ -664,6 +664,8 @@ Trace distance is defined as following:
 \\frac{1}{2} || A - B ||_{\\rm tr}
 ```
 
+It takes values between 0 and 1.
+
 ### Examples
 
 ```jldoctest; setup=:(using Yao)
@@ -672,7 +674,7 @@ julia> reg1 = uniform_state(3);
 julia> reg2 = zero_state(3);
 
 julia> tracedist(reg1, reg2)
-1.8708286933869704
+0.9354143466934852
 ```
 
 ### References

diff --git a/lib/YaoArrayRegister/src/density_matrix.jl b/lib/YaoArrayRegister/src/density_matrix.jl
@@ -77,7 +77,7 @@ end
 YaoAPI.density_matrix(reg::ArrayReg{D}) where D = DensityMatrix{D}(reg.state * reg.state')
 YaoAPI.density_matrix(rho::DensityMatrix) = copy(rho)
 
-YaoAPI.tracedist(dm1::DensityMatrix{D}, dm2::DensityMatrix{D}) where {D} = trace_norm(dm1.state .- dm2.state)
+YaoAPI.tracedist(dm1::DensityMatrix{D}, dm2::DensityMatrix{D}) where {D} = trace_norm(dm1.state .- dm2.state) / 2.0
 
 """
     is_density_matrix(dm::AbstractMatrix; kw...)