Ranyiliu Chen<br />陈然一鎏

Ranyiliu Chen
陈然一鎏

PhD sutdent in quantum info

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A parity-dependent lowerbound

1 minute read

Published:

We show that for flip operator $F$, and the family of maximally entangled states \(\operatorname{MAXE}=\{|{\Phi}\rangle||{\Phi}\rangle=\sum|{j_Aj_B}\rangle/\sqrt{d},\{|j\rangle\}\text{ is ONB}\},\) the range of the overlap between $F$ and $|{\Phi}\rangle$ depends on the parity of the dimension. Specifically, \(\{\langle{\Phi|F|\Phi}\rangle||{\Phi}\rangle\in\operatorname{MAXE}\}=\begin{cases}[-1,1]&d=2k\\ [-\frac{d-2}{d},1]&d=2k+1\end{cases}\)

Far from any separable and maximally entangled states

1 minute read

Published:

We show that there is some entangled states that are far from any separable and maximally entangled states. As a consequence, there exists entanglement witness that cannot witness any maximally entangled states. At the first sight it seems to be the opposite: the maximally entangled states contains the ‘most’ entanglement in some sense, so at least one of them should be detected by a fixed entanglement witness. Unfortunately it does not hold.

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