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arXiv 1306.2570quant-ph
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具有六个单粒子态的三费米子纯态的正则形式

Canonical form of three-fermion pure-states with six single particle states

Lin Chen, Dragomir Z Djokovic, Markus Grassl, Bei Zeng

备注：
42 pages
发表信息：
J. Math. Phys. 55, 082203 (2014)
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摘要：

在局域么正（LU）变换下，我们构造了$\bwe^3(\bC^6)$（具有六个单粒子态的三费米子系统）中纯态的一个标准形，即，酉群$\Un(6)$。我们还构造了$\bwe^3(\bC^6)$上多项式$\Un(6)$ -不变量代数的生成元的极小集.事实证明，这个代数同构于三个量子比特的多项式LU-不变量的代数，这些不变量在量子比特置换下也是不变的。作为这个令人惊讶的事实的结果，我们推断，在$\bwe^3(\bC^6)$中的纯三费米子态的$\Un(6)$ -轨道和纯三量子比特态的LU轨道之间存在一一对应，当允许量子比特排列时。作为一个重要的副产品，我们得到了一个新的标准形式下的LU变换$\Un(2)\times\Un(2)\times\Un(2)$（不允许量子位排列）的纯三量子位态。

英文摘要：

We construct a canonical form for pure states in $\bwe^3(\bC^6)$, the three-fermion system with six single particle states, under local unitary (LU) transformations, i.e., the unitary group $\Un(6)$. We also construct a minimal set of generators of the algebra of polynomial $\Un(6)$-invariants on $\bwe^3(\bC^6)$. It turns out that this algebra is isomorphic to the algebra of polynomial LU-invariants of three-qubits which are additionally invariant under qubit permutations. As a consequence of this surprising fact, we deduce that there is a one-to-one correspondence between the $\Un(6)$-orbits of pure three-fermion states in $\bwe^3(\bC^6)$ and the LU orbits of pure three-qubit states when qubit permutations are allowed. As an important byproduct, we obtain a new canonical form for pure three-qubit states under LU transformations $\Un(2)\times\Un(2)\times\Un(2)$ (no qubit permutations allowed).

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