[论文解读] Equivalence between classical epidemic model and non-dissipative and dissipative quantum tight-binding model

Krzysztof Pomorski|arXiv (Cornell University)|Dec 17, 2020

Quantum Information and Cryptography参考文献 12被引用 5

一句话总结

本文建立了经典流行病模型与非耗散及耗散量子紧束缚模型之间的数学等价性，表明诸如量子纠缠、叠加态、拉比振荡以及阿哈诺夫-玻姆效应等量子现象可完全通过经典统计系统再现。关键结果是，量子力学行为——尤其是基于位置的量子比特系统——可由具有加倍状态空间的经典随机有限状态机有效模拟。

ABSTRACT

The equivalence between classical epidemic model and nondissipative and dissipative quantum tight-binding model is derived. Classical epidemic model can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results shows that quantum mechanical phenomena might be almost entirely simulated by classical statistical model. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of classical physics can be the base for possible incorporation of quantum technologies and in particular for quantum like computation and quantum like communication. The classical density matrix is derived and described by the equation of motion in terms of anticommutator. Existence of Rabi like oscillations is pointed in classical epidemic model. Furthermore the existence of Aharonov-Bohm effect in quantum systems can also be reproduced by the classical epidemic model. Every quantum system made from quantum dots and described by simplistic tight-binding model by use of position-based qubits can be effectively described by classical model with very specific structure of S matrix that has twice bigger size as it is the case of quantum matrix Hamiltonian. Obtained results partly question fundamental and unique character of quantum mechanics and are placing ontology of quantum mechanics much in the framework of classical statistical physics what can bring motivation for emergence of other fundamental theories bringing suggestion that quantum mechanical is only effective and phenomenological but not fundamental picture of reality.

研究动机与目标

• 在非耗散和耗散两种情形下，建立经典流行病模型与量子紧束缚模型之间的正式等价性。
• 研究诸如纠缠和叠加等类量子现象是否可从经典统计系统中涌现。
• 探讨量子力学可能并非基本理论，而是源于经典统计动力学的有效描述。
• 将基于位置的量子点系统映射为具有 2N×2N 转移矩阵 S 的经典流行病模型。
• 证明关键量子效应——拉比振荡与类阿哈诺夫-玻姆行为——可在经典框架中重现。

提出的方法

• 通过时间依赖的随机转移矩阵 S(t) 推导经典流行病模型，表示健康状态与患病状态之间的状态转移。
• 通过运动方程的反对易关系定义经典密度矩阵，将经典概率与类量子形式体系联系起来。
• 解析求解 S 矩阵的本征值与本征向量，以识别经典系统中类量子能级与态的对应关系。
• 将量子紧束缚哈密顿量映射为维度加倍（2N×2N）的经典 S 矩阵，以编码叠加与纠缠。
• 通过 S 矩阵中本征值的虚部（复数部分）引入耗散效应，以模拟电子隧穿与注入。
• 利用正切平方关系（如 tan²(Θ) = p₂/p₁）编码相位动力学，以模拟量子相位演化及类似阿哈诺夫-玻姆的拓扑效应。

实验结果

研究问题

• RQ1 经典流行病模型是否能在非耗散与耗散系统中，通过冯诺依曼熵测量重现量子纠缠？
• RQ2 经典随机状态转移在多大程度上可模拟量子系统中的类拉比振荡？
• RQ3 通过在转移矩阵中引入相位调制，能否在经典流行病模型中复现量子系统中的阿哈诺夫-玻姆效应？
• RQ4 量子紧束缚模型与经典随机有限状态机之间是否存在结构等价性，特别是在基于位置的量子比特系统中？
• RQ5 经典模型中类量子行为的涌现是否挑战了量子力学在基础理论上的独特性？

主要发现

• 经典流行病模型在非耗散与耗散情形下均通过冯诺依曼熵再现了量子纠缠，表明纠缠并非本质上的量子现象。
• 通过时变概率振幅，经典模型自然涌现出类拉比振荡，模拟了量子拉比动力学。
• 通过在转移矩阵中引入矢势项调制相位差，经典框架成功再现了阿哈诺夫-玻姆效应。
• 经典模型的 S 矩阵维度为 2N×2N，有效将状态空间加倍，从而在经典概率中编码叠加与纠缠。
• S 矩阵本征值中的虚部成分可建模耗散与隧穿，使开放量子系统的模拟成为可能。
• 经典系统可模拟时间晶体及其他凝聚态物理现象，表明流行病模型作为量子系统有效经典类比具有更广泛的应用潜力。