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

[munirah]

Good day,

Homework Statement

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

Homework Equations

(ρ)=−Tr(ρlog2ρ)

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.

 

[mfb]

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

 

[BvU]

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

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

 

[munirah]

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

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

 

[munirah]

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

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

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

 

[BvU]

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

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

 

[munirah]

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

it means only for diagonal matrices?

 

[BvU]

Just a guess.

 

[munirah]

Just a guess.

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

 

[mfb]

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

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