I am not very good at this, but I really want to understand it.(adsbygoogle = window.adsbygoogle || []).push({});

Definition:

We say lψ>_{AB}is a purification of ρ_{A}if Tr_{B}[lψ><ψl_{AB}] = ρ_{A}.

Note that ρ_{A}is a density matrix.

My book proceeds to give an example of a purifying system as:

√ρ_{A}⊗ 1*lΦ>, where 1 is identity and lΦ> = ∑_{i}lii> = ∑_{i}li>⊗li>

How can I see that this is true? I am not sure I even know how to perform the tensor product on the LHS. Is this correct?

√ρ_{A}⊗ 1*lΦ> = √ρ_{A}⊗ (∑_{i}li>⊗li>) = (∑_{i}√ρ_{A}li>⊗√ρ_{A}li>)

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quantum purification

**Physics Forums | Science Articles, Homework Help, Discussion**