We prove that, replacing the left Jordan–Wigner [Formula: see text]-embedding by the symmetric [Formula: see text]-embedding described in Sec. 2, the result of the corresponding central limit theorem changes drastically with respect to those obtained in Ref. 5. In fact, in the former case, for any [Formula: see text], the limit space is precisely the [Formula: see text]-mode Interacting Fock Space (IFS) that realizes the canonical quantum decomposition of the limit classical random variable. In the latter case, this happens if and only if [Formula: see text]. Furthermore, as shown in Sec. 4, the limit classical random variable turns out to coincide with the [Formula: see text]-mode version of the [Formula: see text]-deformed quantum Brownian introduced by Parthasarathy[Formula: see text], and extended to the general context of bi-algebras by Schürman[Formula: see text]. The last section of the paper (Appendix) describes this continuous version in white noise language, leading to a simplification of the original proofs, based on quantum stochastic calculus.

中文翻译：

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qq-bit (III)：对称 q-Jordan–Wigner 嵌入

我们证明，将左 Jordan–Wigner [公式：见文本]-嵌入替换为第 2 节中描述的对称 [公式：见文本]-嵌入。2，相应的中心极限定理的结果相对于参考文献中获得的结果发生了巨大变化。5.其实前一种情况，对于任何[公式：见文]，极限空间正是[公式：见文]-模交互福克空间(IFS)，它实现了极限经典随机数的规范量子分解多变的。在后一种情况下，当且仅当 [公式：参见文本] 时才会发生这种情况。此外，如第二节所示。4，极限经典随机变量结果与 Parthasarathy 引入的 [公式：见文本]-变形量子布朗量的 [公式：见文本]-模式版本一致 [公式：见文本]，并由 Schürman 扩展到双代数的一般背景[公式：见正文]。论文的最后一部分（附录）用白噪声语言描述了这个连续版本，从而简化了基于量子随机演算的原始证明。