How can I do when I make a Log2 towards zero?

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1. Aug 1, 2016

munirah

Good day,

1. The problem statement, all variables and given/known data

I want to make a measurement on qubit by using formula von Neumann entropy using Mathematica given as below;

2. Relevant equations

(ρ)=−Tr(ρlog2ρ)

3. The attempt at a solution

The
ρ={{0.5,0},{0,0.5}}

My problem is, when I make the

log2{{0.5,0},{0,0.5}}
I get the output

{{−1,∞},{∞,−1}}

How can I deal with this value in my measurement since it cannot be calculated?

Thank you.

2. Aug 1, 2016

Staff: Mentor

Looks like you take the logarithm of each entry in the matrix. I don't think that is what you want.
Matrix log?

3. Aug 1, 2016

BvU

Can you put in some lower limit, like $2^{-20}$ ?
 Ha !

[edit2] Isn't it so that you have already diagonalized $\rho$ so you can use the $S = - \sum \eta\ln\eta$ here ?

Last edited: Aug 1, 2016
4. Aug 1, 2016

munirah

I'm not sure about the matrix log.I think it different

5. Aug 1, 2016

munirah

thank you for the input. I will search it and learn

6. Aug 1, 2016

BvU

My guess is the matrix log coincides with taking log of the diagonal elements once the matrix is diagonalized ...

7. Aug 1, 2016

munirah

it means only for diagonal matrices?

8. Aug 1, 2016

BvU

Just a guess.

9. Aug 1, 2016

munirah

ok. thank you very much. i will look about it.

10. Aug 1, 2016

Staff: Mentor

Sure. This should be easy to see if you take the matrix exponential again.