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arXiv quant-ph/0412045quant-phcond-mat.stat-mech
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量子测量的动力学

Dynamics of a quantum measurement

Armen E. Allahverdyan, Roger Balian, Theo M. Nieuwenhuizen

摘要:

我们得到了一个精确可解的哈密顿模型,它保留了实际量子测量的所有特征。为了使用涉及系统和装置的交互过程作为测量,装置必须是宏观的。这意味着要用量子统计力学来处理它。展示了该过程的相关时间尺度。它开始于被测系统和设备的整个密度矩阵的非对角块的非常快速的消失。可能的复发是由后者的大尺寸阻碍。在更大的时间尺度上,设备记录结果:在指针的最终值和被测系统的密度矩阵的初始对角块之间建立相关性。因此,我们从动力学过程中推导出玻恩定则和冯·诺依曼的态约化。

英文摘要:

We work out an exactly solvable hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a measurement, it is necessary that the apparatus is macroscopic. This implies to treat it with quantum statistical mechanics. The relevant time scales of the process are exhibited. It begins with a very rapid disappearance of the off-diagonal blocks of the overall density matrix of the tested system and the apparatus. Possible recurrences are hindered by the large size of the latter. On a much larger time scale the apparatus registers the outcome: Correlations are established between the final values of the pointer and the initial diagonal blocks of the density matrix of the tested system. We thus derive Born's rule and von Neumann's reduction of the state from the dynamical process.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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