Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction
Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction
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DOI：
10.1103/physreva.86.012103
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发表时间：
2012-07-10
影响因子：
2.9
通讯作者：
Spekkens, Robert W.
中科院分区：
文献类型：
--
作者：
Bartlett, Stephen D.;Rudolph, Terry;Spekkens, Robert W.
如果世界的本体论是经典力学的本体论，但每个主体都面临着对经典状态的了解程度的限制，那么世界在我们看来会是什么样子？我们表明，在大多数情况下，它似乎是量子的。经典力学的统计理论，它规定了相空间上的概率分布如何在哈密顿演化和测量下演化，通常被称为刘维尔力学，所以我们在这里探索的理论是具有认识限制的刘维尔力学。我们把特定的认识限制作为我们的基本假设，它规定了两个限制。第一个约束是海森堡测不准原理的经典模拟;由表征代理人知识的相空间分布定义的位置和动量的二阶矩需要满足与量子态的位置和动量观测量的矩所满足的约束相同的约束。第二个约束是，对于给定的时刻，分布应该具有最大熵。从这个假设开始，我们推导出允许的准备，测量和变换，并证明它们与高斯量子力学中允许的那些同构，并产生相同的实验统计。我们认为，高斯量子力学的这种重建构成了支持一个研究计划的额外证据，其中量子态被解释为不完整知识的状态，而高斯量子力学中没有出现的现象为如何重建完整的量子理论提供了最好的线索。
How would the world appear to us if its ontology was that of classical mechanics but every agent faced a restriction on how much they could come to know about the classical state? We show that in most respects it would appear to us as quantum. The statistical theory of classical mechanics, which specifies how probability distributions over phase space evolve under Hamiltonian evolution and under measurements, is typically called Liouville mechanics, so the theory we explore here is Liouville mechanics with an epistemic restriction. The particular epistemic restriction we posit as our foundational postulate specifies two constraints. The first constraint is a classical analog of Heisenberg's uncertainty principle; the second-order moments of position and momentum defined by the phase-space distribution that characterizes an agent's knowledge are required to satisfy the same constraints as are satisfied by the moments of position and momentum observables for a quantum state. The second constraint is that the distribution should have maximal entropy for the given moments. Starting from this postulate, we derive the allowed preparations, measurements, and transformations and demonstrate that they are isomorphic to those allowed in Gaussian quantum mechanics and generate the same experimental statistics. We argue that this reconstruction of Gaussian quantum mechanics constitutes additional evidence in favor of a research program wherein quantum states are interpreted as states of incomplete knowledge and that the phenomena that do not arise in Gaussian quantum mechanics provide the best clues for how one might reconstruct the full quantum theory.