Reconstruction theorems in quantum mechanics

Peter Mittelstaedt

Amit Hagar

Relying on the universality of quantum mechanics and on recent results known as the “threshold theorems,” quantum information scientists deem the question of the feasibility of large-scale, fault-tolerant, and computationally superior quantum computers as purely technological. Reconstructing this question in statistical mechanical terms, this article suggests otherwise by questioning the physical significance of the threshold theorems. The skepticism it advances is neither too strong (hence is consistent with the universality of quantum mechanics) nor too weak (hence is independent of technological contingencies).

Gianni Cassinelli, PEKKA J. LAHTI

We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

Peter Mittelstaedt

Jianbing Zhu

量子力学和广义相对论是现代物理的两大支柱,但它们在基础概念上存在深刻的张力:前者以概率振幅、测量和非定域性为中心,后者则基于时空几何、因果律和决定论。基于递归嵌套函数的朱亮定理,本文统一地将物理系统视为认知范畴 $\Cog$ 的对象,证明量子态对应递归元素的浅层投影,经典时空对应深递归元素的凝聚结构,测量过程是递归元素层之间的投影运算。广义相对论的场方程被重构为因果联系的自洽条件,而量子引力则对应于深递归元素的动力学。这一重构不仅统一了量子力学与广义相对论,还揭示了与“一花一世界”哲学智慧的深刻共鸣。

Simon Kochen