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Dynamic Quantum Tomography Model for Phase-Damping Channels

机译：相位阻尼通道的动态量子层析成像模型

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摘要

In this paper we propose a dynamic quantum tomography model for open quantum systems with evolution given by phase-damping channels. Mathematically, these channels correspond to completely positive trace-preserving maps defined by the Hadamard product of the initial density matrix with a time-dependent matrix which carries the knowledge about the evolution. Physically, there is a strong motivation for considering this kind of evolution because such channels appear naturally in the theory of open quantum systems. The main idea behind a dynamic approach to quantum tomography claims that by performing the same kind of measurement at some time instants one can obtain new data for state reconstruction. Thus, this approach leads to a decrease in the number of distinct observables which are required for quantum tomography; however, the exact benefit for employing the dynamic approach depends strictly on how the quantum system evolves in time. Algebraic analysis of phase-damping channels allows one to determine criteria for quantum tomography of systems in question. General theorems and observations presented in the paper are accompanied by a specific example, which shows step by step how the theory works. The results introduced in this paper can potentially be applied in experiments where there is a tendency to look at quantum tomography from the point of view of economy of measurements, because each distinct kind of measurement requires, in general, preparing a separate setup.
机译：在本文中，我们提出了一种开放量子系统的动态量子层析成像模型，该模型具有由相阻尼通道提供的演化。从数学上讲，这些通道对应于由初始密度矩阵的Hadamard乘积与时间相关的矩阵定义的完全正的迹线保留图，该矩阵携带有关演化的知识。从物理上讲，考虑这种演化的动机很强，因为这样的通道在开放量子系统的理论中自然而然地出现了。量子层析成像动态方法背后的主要思想主张，通过在某些时刻执行相同类型的测量，人们可以获取用于状态重建的新数据。因此，这种方法导致了量子层析成像所需的独特可观察物数量的减少。但是，采用动态方法的确切好处严格取决于量子系统如何随时间演化。相位衰减通道的代数分析可以确定有关系统的量子层析成像标准。本文介绍的一般定理和观察结果都带有一个特定的例子，它逐步显示了该理论的工作原理。本文介绍的结果可潜在地用于从测量经济性的角度看待量子层析成像的实验中，因为每种不同类型的测量通常都需要准备单独的装置。

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