I am currently learning about quantum channels and am sadly stuck at a rudimentary problem, where I don’t understand, how to find the Kraus Matrices of a quantum channel:

The amplitude damping channel is described by the following action on the computational basis states:

 \begin{aligned} \mathcal E: |0\rangle \otimes |0\rangle &\mapsto |0\rangle \otimes |0\rangle, \\ \mathcal E: |1\rangle \otimes |0\rangle &\mapsto \sqrt{1-p} |1\rangle \otimes |0\rangle + \ \sqrt{p} |0\rangle \otimes |1\rangle. \end{aligned}

Now unfortunately I don’t know where to start to find the Kraus operators. Also, I was wondering how I could check if this evolution takes place unitarely?

Thanks a lot for all hints in advance!

I am currently learning about quantum channels and am sadly stuck at a rudimentary problem, where I don't understand how to find the Kraus matrices of a quantum channel.

The amplitude damping channel is described by the following action on the computational basis states:  \begin{aligned} \mathcal E: |0\rangle \otimes |0\rangle &\mapsto |0\rangle \otimes |0\rangle, \\ \mathcal E: |1\rangle \otimes |0\rangle &\mapsto \sqrt{1-p} |1\rangle \otimes |0\rangle + \ \sqrt{p} |0\rangle \otimes |1\rangle. \end{aligned}

Now unfortunately I don’t know where to start to find the Kraus operators. Also, I was wondering how I could check if this evolution takes place unitarily?

I am currently learning about quantum channels and am sadly stuck at a rudimentary problem, where I don’t understand, how to find the Kraus Matrices of a quantum channel:

The amplitude damping channel is described by the following action on the computational basis states:

[ \begin{aligned} \varepsilon: |0\rangle \otimes |0\rangle &\mapsto |0\rangle \otimes |0\rangle, \\ \varepsilon: |1\rangle \otimes |0\rangle &\mapsto \sqrt{1-p} |1\rangle \otimes |0\rangle + \ \sqrt{p} |0\rangle \otimes |1\rangle. \end{aligned} ]

Now unfortunately I don’t know where to start to find the Kraus operators. Also, I was wondering how I could check if this evolution takes place unitarely?

Thanks a lot for all hints in advance!

I am currently learning about quantum channels and am sadly stuck at a rudimentary problem, where I don’t understand, how to find the Kraus Matrices of a quantum channel:

The amplitude damping channel is described by the following action on the computational basis states:

\begin{aligned} \mathcal E: |0\rangle \otimes |0\rangle &\mapsto |0\rangle \otimes |0\rangle, \\ \mathcal E: |1\rangle \otimes |0\rangle &\mapsto \sqrt{1-p} |1\rangle \otimes |0\rangle + \ \sqrt{p} |0\rangle \otimes |1\rangle. \end{aligned}

Now unfortunately I don’t know where to start to find the Kraus operators. Also, I was wondering how I could check if this evolution takes place unitarely?

Thanks a lot for all hints in advance!