论文标题
施密特的三分之一的代表
Schmidt representation of 3-qubits with real amplitudes
论文作者
论文摘要
从Schmidt表示，我们可以将每个2 Qubit的状态都写成$ [ϕ \ rangle =λ_1[00 \ rangle+λ_2[11 \ rangle $，带有$λ_1$ and $λ_1$和$λ_2$实数。对于3 Qubit的状态，众所周知，PRL 2000 85，可以将每个3量态的每3量状态延长为$ [ϕ \ rangle =λ_1[000 \ rangle+λ_2e^{iθ}} [iθ} [100 \ rangle+λ_3]使用$λ_i\ ge0 $和$ 0 \leθ\leπ$。在本文中，我们表明，没有一个具有真实振幅的每个3量状态可以以$ $ [ϕ \ rangle =λ_1[000 \ rangle+λ_2[100 \ rangle+λ_3[101 \ rangle+λ_4[110 \ rangle+λ_5[111+λ_5[111 \ range $ g range in of Fane in of Fane in fane grounge）由$ r_y（θ）$和$ x $门生成。我们还表明，在正交组的本地大门中，每3量幅度都可以写入$ [ϕ \ rangle =λ_1[000 \ rangle+λ_2[011 \ rangle+λ_3[101 \ rangle+vis+λ_4[110 $ unge+λ_$ langle+langle+langle+lang+λ实数。可以在YouTube视频\ url {https://youtu.be/gdn20qhzsoq}中找到此结果的解释。
From the Schmidt representation we have that, up to local gates, every 2-qubit state can be written as $[ϕ\rangle=λ_1 [00\rangle+λ_2 [11\rangle$ with $λ_1$ and $λ_2$ real numbers. For 3-qubits states, it is known, PRL 2000 85, that up to local gates every 3-qubit state can be written as $[ϕ\rangle=λ_1 [000\rangle+λ_2 e^{i θ}[100\rangle+λ_3[101\rangle+λ_4[110\rangle+λ_5[111\rangle$ with $λ_i\ge0$ and $0\le θ\le π$. In this paper, we show that no every 3-qubit state with real amplitudes can be transform in the form $[ϕ\rangle=λ_1 [000\rangle+λ_2 [100\rangle+λ_3[101\rangle+λ_4[110\rangle+λ_5[111\rangle$ by using local gates in the orthogonal group (the group generated by $R_y(θ)$ and $X$ gates). We also show that, up to local gates in the orthogonal group, every 3-qubit with real amplitudes can be written as $[ϕ\rangle=λ_1 [000\rangle+λ_2 [011\rangle+λ_3[101\rangle+λ_4[110\rangle+λ_5[111\rangle$ with the $λ_i$ real numbers. An explanation of this result can be found in the youtube video \url{https://youtu.be/gDN20QHzsoQ}
