At the thermal equilibrium, the density matrix of a 2 spin-half system is given by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\begin{displaymath}

\mathbf{\rho} =

\left(\begin{array}{cccc}

e^{-(1+c)/T} & 0 & 0 & 0\\

0 & cosh[(1-c)/T] & -sinh[(1-c)/T] & 0\\

0 & -sinh[(1-c)/T] & cosh[(1-c)/T] & 0\\

0 & 0 & 0 & e^{-(1+c)/T}

\end{array}\right)

\end{displaymath}

[/tex]

where c is a parameter.

How to find the reduced density matrix by tracing out the other spin?

i.e. [tex]\rho_{1} = tr_{2}\rho[/tex]

I only know how to find the reduced density matrix for a pure state, say like [tex]\frac{1}{\sqrt{2}}(\left|\downarrow\uparrow> - \left|\uparrow\downarrow> )[/tex]

But for this given density matrix, i have no idea. Are there any equations that i can use? What's the procedure?

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# Homework Help: Reduced density matrix

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