论文标题
对对称和地方实施的可实现的统一操作的限制
Restrictions on realizable unitary operations imposed by symmetry and locality
论文作者
论文摘要
根据量子计算的基本结果，可以使用仅在两个子系统上起作用的所谓的2个局部单位来生成复合系统上的任何统一转换。除了其在量子计算中的重要性之外，该结果还可以被视为关于与本地汉密尔顿人的系统动态的陈述：尽管当地性在短期动态上构成了各种限制，但它不限制与当地一般汉密尔顿的复合系统可以经历足够长的时间后能够体验到的统一发展。在这里，我们表明，这种普遍性在存在保护法和全球连续对称性（例如U（1）和SU（2）等全球连续对称性的情况下，这种普遍性无效。特别是，我们表明，即使是使用局部对称的单位，也无法实现通用的对称单位。基于这个无关定理，我们提出了一种实验探测自然界相互作用的位置的方法。在量子热力学的背景下，我们的结果意味着，复合系统上的通用能量持续的统一转换不能仅通过在组件上的局部能量持有能量的单位组合来实现。我们展示了如何通过催化来规避这一点。
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.
