量子测量问题与物理实在：计算理论的观点
The quantum measurement problem and physical reality: a computation theoretic perspective
摘要：
宇宙是可计算的吗？如果是，它在计算上是一个多项式位置吗？在标准的量子力学中，允许无限的平行性和状态的无限精确说明，不排除对这两个问题的否定回答。另一方面，经验证据表明，NP完全问题在物理世界中是难以解决的。同样，已知在算法上不可计算的计算问题似乎也不能通过任何物理手段计算。我们认为，如果假设宇宙是算法的，那么抽象算法的效率和能力与物理计算机的效率和能力之间的这种密切对应就可以找到一种自然的解释;也就是说，物理现实是离散子物理信息处理的产物，相当于概率图灵机的动作。这个假设可以与微观尺度下量子系统的指数性相协调，以及在该尺度下实现肖尔量子多项式时间算法的可能性，前提是叠加的程度本质上是有上限的。如果这个界限与量子-经典分界（海森堡分割）相联系，那么量子测量问题就自然得到解决。从这个观点来看，宏观经典性是宇宙处于BPP中的证据，上面提出的两个问题都得到了肯定的回答。本文简要讨论了最近提出的一个量子测量计算模型，它把海森堡截和希尔伯特空间的离散性联系起来。注意到了与量子引力的联系。我们的结果是兼容的哲学，数学真理是独立的物理定律。
英文摘要：
Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not ruled out. On the other hand, empirical evidence suggests that NP-complete problems are intractable in the physical world. Likewise, computational problems known to be algorithmically uncomputable do not seem to be computable by any physical means. We suggest that this close correspondence between the efficiency and power of abstract algorithms on the one hand, and physical computers on the other, finds a natural explanation if the universe is assumed to be algorithmic; that is, that physical reality is the product of discrete sub-physical information processing equivalent to the actions of a probabilistic Turing machine. This assumption can be reconciled with the observed exponentiality of quantum systems at microscopic scales, and the consequent possibility of implementing Shor's quantum polynomial time algorithm at that scale, provided the degree of superposition is intrinsically, finitely upper-bounded. If this bound is associated with the quantum-classical divide (the Heisenberg cut), a natural resolution to the quantum measurement problem arises. From this viewpoint, macroscopic classicality is an evidence that the universe is in BPP, and both questions raised above receive affirmative answers. A recently proposed computational model of quantum measurement, which relates the Heisenberg cut to the discreteness of Hilbert space, is briefly discussed. A connection to quantum gravity is noted. Our results are compatible with the philosophy that mathematical truths are independent of the laws of physics.
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