In[Phys.Rev.A 107012427(2023)],Baldwin and Jones prove that Uhlmann–Jozsa’s fidelity between two quantum statesρandσ,i.e.,F(ρ,σ)=(Tr√√ρσ√ρ)^(2),can be written in a simplified form as F(ρ,σ)=(Tr√ρσ)^(2...In[Phys.Rev.A 107012427(2023)],Baldwin and Jones prove that Uhlmann–Jozsa’s fidelity between two quantum statesρandσ,i.e.,F(ρ,σ)=(Tr√√ρσ√ρ)^(2),can be written in a simplified form as F(ρ,σ)=(Tr√ρσ)^(2).In this article,we give an alternative proof of this result,using a function power series expansion and the properties of the trace function.Our approach not only reinforces the validity of the simplified expression but also facilitates the exploration of novel dissimilarity functions for quantum states and more complex trace functions of density operators.展开更多
文摘In[Phys.Rev.A 107012427(2023)],Baldwin and Jones prove that Uhlmann–Jozsa’s fidelity between two quantum statesρandσ,i.e.,F(ρ,σ)=(Tr√√ρσ√ρ)^(2),can be written in a simplified form as F(ρ,σ)=(Tr√ρσ)^(2).In this article,we give an alternative proof of this result,using a function power series expansion and the properties of the trace function.Our approach not only reinforces the validity of the simplified expression but also facilitates the exploration of novel dissimilarity functions for quantum states and more complex trace functions of density operators.
