guo-jyun

The pdf link is disabled. Therefore, I upload the pdf file. question.pdf

This question is not a homework, but it has been bothering me for a long time. If you know the algorithm, please let me know. The detail of the question is https://www.papeeria.com/d/file/15def8a2-7af6-4670-a776-7c9455d90206/15def8a2-7af6-4670-a776-7c9455d90206.pdf/Demo - main.pdf I am a beginner. If the concept is wrong, please correct me.

No, that's what's bothering me right now. I can't use my existing literature knowledge to calculate him. If you know the answer, please tell me. I know, but I choose the latex type.... Please try this pdf https://www.papeeria.com/d/file/15def8a2-7af6-4670-a776-7c9455d90206/15def8a2-7af6-4670-a776-7c9455d90206.pdf/Demo - main.pdf

If I have four states in \ket{S_1}=\frac{1}{\sqrt{2}}(\ket{00}+\ket{+1})_{AB} \ket{S_2}=\frac{1}{\sqrt{2}}(\ket{-1}-\ket{10})_{AB} \ket{S_3}=\frac{1}{\sqrt{2}}(\ket{00}+\ket{+1})_{AB} \ket{S_4}=\frac{1}{\sqrt{2}}(\ket{00}+\ket{-1})_{AB}, and its density matrix is \rho=frac{1}{2}(\ket{S_1}\bra{S_1}+\ket{S_2}\bra{S_2}+\ket{S_3}\bra{S_3}+\ket{S_4}\bra{S_4}). Using the Holevo's theorem the bound of mutual information can be calculated as I(X;Y)\leqslant S(\rho)-\frac{1}{4}(S(\ket{S_1}\bra{S_1})+S(\ket{S_2}\bra{S_2})+S(\ket{S_3}\bra{S_3})+S(\ket{S_4}\bra{S_4}))=1.60087603669285. How to calculate the best measurement probability p from the accessible information? For example to simple explain my question, a density matrix in mixed state \rho=\frac{1}{2}(\ket{0}\bra{0}+\ket{+}\ket{+}), where \ket{0}=\begin{pmatrix}1 \\ 0\end{pmatrix} and \ket{+}=\frac{1}{\sqrt{2}}\begin{pmatrix}1 \\ 1\end{pmatrix}. We can then calculate the mutual information and its accessible information. After that, we can estimate the best p from Shannon entropy as -p\log_2(p)-(1-p)\log_2(1-p)=S(\rho)-\frac{1}{2}(S(\ket{0}\bra{0})+S(\ket{+}\bra{+}))=0.600876036692856, and thus p=0.85355. I am a beginner. If the concept is wrong, please correct me.