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理论物理通讯：英文版

Partial Trace Method for Deriving Density Operators of Light Field

范洪义, 唐绪兵, 胡利云

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

在在操作符的一个订的产品以内的集成的技术的帮助下，我们能充分显示部分踪迹方法推出轻地的一些新密度操作符。单个模式的密度操作员的一般表格这样被导出从一使二模式的概括挤压的纯状态正常化密度操作员。

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In nature, there exists superposition of Gaussian light and chaotic light, so we introduce the density operator for describing the Gaussian-enhanced chaotic light (GECL). By virtue of the method of integration within ordered product (IWOP) of operators, we derive its normalization constant. Then, by virtue of the partial trace method, we derive its thermo vacuum state and this may greatly simplify the calculation of photon number average and quantum fluctuation in GECL. It is demonstrated that the second-order degree of coherence of GECL is larger than 2.
The partial trace is commonly introduced in quantum mechanics as an algebraic operation used to define reduced states of composite systems. However, the probabilistic origin of this operation goes systematically unnoticed in the literature. Here, we show that the partial trace emerges naturally from the requirement of consistency between the Born rule for measurement probabilities and the classical marginalization of probability mass functions. Starting from the classical marginalization rule relating joint and marginal probability distributions, we impose that the reduced density operator of a subsystem must reproduce the local measurement statistics derived from the global state. We show that this requirement directly leads to the standard expression of the partial trace. From this perspective, the reduced density operator appears not as an ad hoc algebraic construction, but as a natural consequence of the probabilistic structure of quantum mechanics.