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arXiv quant-ph/0612126quant-ph
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量子参考系的动力学

Dynamics of a Quantum Reference Frame

David Poulin, Jon Yard

摘要:

我们分析了一个量子力学陀螺仪,它被建模为一个大的自旋,并作为一个参考,以测量自旋1/2粒子的角动量。这些测量引起的反作用的参考,这是我们的研究的中心焦点。我们首先推导出明确的表达式的量子信道表示的反作用。然后,我们分析了动力学所引起的参考时,它是用来顺序测量粒子从一个固定的合奏。我们证明了参考热化与测量的粒子,并发现,一般来说,热状态达到的时间尺度与参考的大小呈线性关系。这与Bartlett等人最近的结论形成对比,Bartlett等人认为,当粒子完全非极化时,这需要二次量的时间。现在我们用一个基于对称性和守恒定律的简单物理原理来理解他们的结果。最后,我们开始研究的非平衡动力学的参考。在这里,我们发现,当测量偏振粒子时,相干态中的参考基本上保持在一个状态,同时旋转自身以最终与粒子的偏振对齐。

英文摘要:

We analyze a quantum mechanical gyroscope which is modeled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the central focus of our study. We begin by deriving explicit expressions for the quantum channel representing the back-action. Then, we analyze the dynamics incurred by the reference when it is used to sequentially measure particles drawn from a fixed ensemble. We prove that the reference thermalizes with the measured particles and find that generically, the thermal state is reached in time which scales linearly with the size of the reference. This contrasts a recent conclusion of Bartlett et al. that this takes a quadratic amount of time when the particles are completely unpolarized. We now understand their result in terms of a simple physical principle based on symmetries and conservation laws. Finally, we initiate the study of the non-equilibrium dynamics of the reference. Here we find that a reference in a coherent state will essentially remain in one when measuring polarized particles, while rotating itself to ultimately align with the polarization of the particles.

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