对称性与定域性对可实现幺正操作的限制
Restrictions on realizable unitary operations imposed by symmetry and locality
AI总结：
该研究指出全局连续对称性会打破定域幺正生成任意幺正变换的普适性，证明一般对称幺正无法用定域对称幺正近似实现，提出了探测相互作用定域性的实验方法，并给出量子热力学中该限制的催化规避方案。
摘要：
根据量子计算领域的一项基础结论，复合系统上的任意幺正变换都可以通过仅作用于两个子系统的所谓2-定域幺正（2-local unitaries）生成。除了在量子计算中的重要性外，这一结论也可被视为关于具有定域哈密顿量的系统动力学的陈述：尽管定域性对短期动力学施加了多种约束，但它并不会限制具有一般定域哈密顿量的复合系统在足够长时间后可能经历的幺正演化。本文表明，在守恒律和U(1)、SU(2)等全局连续对称性存在的情况下，这种普适性不再成立。具体而言，我们证明了一般的对称幺正即使是近似地也无法通过定域对称幺正实现。基于这一不可行定理（no-go theorem），我们提出了一种实验探测自然界中相互作用定域性的方法。在量子热力学的语境下，我们的结果意味着，复合系统上一般的能量守恒幺正变换无法仅通过组合各组分上的定域能量守恒幺正来实现。我们展示了如何通过催化（catalysis）来规避这一限制。
英文摘要：
According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this result can also be regarded as a statement about the dynamics of systems with local Hamiltonians: although locality puts various constraints on the short-term dynamics, it does not restrict the possible unitary evolutions that a composite system with a general local Hamiltonian can experience after a sufficiently long time. Here we show that this universality does not remain valid in the presence of conservation laws and global continuous symmetries such as U(1) and SU(2). In particular, we show that generic symmetric unitaries cannot be implemented, even approximately, using local symmetric unitaries. Based on this no-go theorem, we propose a method for experimentally probing the locality of interactions in nature. In the context of quantum thermodynamics, our results mean that generic energy-conserving unitary transformations on a composite system cannot be realized solely by combining local energy-conserving unitaries on the components. We show how this can be circumvented via catalysis.
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