Symmetry is among the most fundamental and powerful concepts in nature, whose existence is usually taken as given, without explanation. We explore whether symmetry can be derived from more fundamental principles from the perspective of quantum information. Starting with a two-qubit system, we show there are only two minimally entangling logic gates: the identity and the $\mathrm{SWAP}$, which interchanges the two states of the qubits. We further demonstrate that, when viewed as an entanglement operator in the spin-space, the $S$-matrix in the two-body scattering of fermions in the $s$-wave channel is uniquely determined by unitarity and rotational invariance to be a linear combination of the identity and the $\mathrm{SWAP}$. Realizing a minimally entangling $S$-matrix would give rise to global symmetries, as exemplified in Wigner’s spin-flavor symmetry and Schrödinger’s conformal invariance in low energy quantum chromodynamics. For $N_q$ species of qubit, the identity gate is associated with an $[SU(2){]}^{N_q}$ symmetry, which is enlarged to $SU(2N_q)$ when there is a species-universal coupling constant.

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纠缠抑制的对称性

对称性是自然界中最基本和最强大的概念之一，它的存在通常被认为是既定的，没有解释。我们从量子信息的角度探索对称性是否可以从更基本的原理推导出来。从一个双量子位系统开始，我们证明只有两个最小纠缠逻辑门：身份和$\mathrm{交换}$，它交换了量子位的两种状态。我们进一步证明，当被视为自旋空间中的纠缠算子时，$秒$- 费米子二体散射中的矩阵 $秒$- 波通道由单一性和旋转不变性唯一确定为身份和 $\mathrm{交换}$. 实现最小纠缠$秒$-matrix 将产生全局对称性，如 Wigner 的自旋风味对称性和 Schrödinger 的低能量子色动力学中的共形不变性中的例证。为了$N_q$ 量子比特的种类，身份门与 $[秒你(2){]}^{N_q}$ 对称性，放大为 $秒你(2N_q)$ 当存在物种通用耦合常数时。