一句话:从范畴公理重构有限维量子理论,证明其等价于环 S 上的广义量子理论,且无需层析假设。
本文从范畴论原理重构有限维量子理论。作者考虑由 dagger compact category 描述且可“discard”对象的物理理论,给出若干性质,使该理论等价于在合适环 S 上的广义有限维量子理论。所用原理类似 Chiribella、D'Ariano 与 Perinotti 的重构原则,但公理和证明完全范畴化,特别是不需要 tomography 假设。将结果特化到概率理论时,得到要么是 S 为复数的传统量子理论,要么是 S 为实数、基于实 Hilbert 空间的量子理论。
We reconstruct finite-dimensional quantum theory from categorical principles. That is, we provide properties ensuring that a given physical theory described by a dagger compact category in which one may `discard' objects is equivalent to a generalised finite-dimensional quantum theory over a suitable ring $S$. The principles used resemble those due to Chiribella, D'Ariano and Perinotti. Unlike previous reconstructions, our axioms and proof are fully categorical in nature, in particular not requiring tomography assumptions. Specialising the result to probabilistic theories we obtain either traditional quantum theory with $S$ being the complex numbers, or that over real Hilbert spaces with $S$ being the reals.