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arXiv 1408.4491quant-phgr-qchep-th
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量子黑洞经典信息传输能力的参数下转换

Parametric down conversion with a depleted pump as a model for classical information transmission capacity of quantum black holes

Paul M. Alsing

备注：
53 pages, 24 figures; accepted Class. and Quant. Grav (2Feb2015)
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摘要：

在本文中，我们扩展了Adami和Ver Steeg [Class.量子重力\textbf{31}，075015（2014）]，以将黑洞粒子发射的过程有效地处理为具有动态（耗尽对非耗尽）“泵浦”源模式的参数下转换（PDC）的类似量子光学过程，该模式对蒸发的黑洞（BH）能量自由度进行建模。我们研究了量子态的短时间（非耗尽泵）和长时间（耗尽泵）机制，以及在存在霍金辐射的情况下，它对Holevo通道从遥远的过去到遥远的未来传递信息的容量的影响。在这项工作中引入的新功能是通过共同的黑洞“源泵”模式的耦合发射的霍金辐射模式，这在唯象上代表了一个量子化的能量自由度的引力场。这个（零维）模型作为一个简化的舞台，探索BH粒子的生产/蒸发和反作用的影响下，一个明确的单一的演变，强制执行量子化的能量/粒子守恒。在我们类似的量子光学模型中，我们研究了通过黑洞（BH）蒸发“泵浦”源耦合的两个发射粒子/反粒子和反粒子/粒子对之间的纠缠。我们还分析和动态验证的“页面信息时间”为我们的模型，这是指传统的信念，在BH辐射的信息变得显着后，黑洞已蒸发一半的初始能量到传出的辐射。最后，我们研究了BH粒子的产生/蒸发对BH事件视界外部区域中最初最大纠缠的两个模式的影响，其中一个模式向内下降并与黑洞相互作用，另一个模式永远保持在外部并且不相互作用。

英文摘要：

In this paper we extend the investigation of Adami and Ver Steeg [Class. Quantum Grav. \textbf{31}, 075015 (2014)] to treat the process of black hole particle emission effectively as the analogous quantum optical process of parametric down conversion (PDC) with a dynamical (depleted vs. non-depleted) `pump' source mode which models the evaporating black hole (BH) energy degree of freedom. We investigate both the short time (non-depleted pump) and long time (depleted pump) regimes of the quantum state and its impact on the Holevo channel capacity for communicating information from the far past to the far future in the presence of Hawking radiation. The new feature introduced in this work is the coupling of the emitted Hawking radiation modes through the common black hole `source pump' mode which phenomenologically represents a quantized energy degree of freedom of the gravitational field. This (zero-dimensional) model serves as a simplified arena to explore BH particle production/evaporation and back-action effects under an explicitly unitary evolution which enforces quantized energy/particle conservation. Within our analogous quantum optical model we examine the entanglement between two emitted particle/anti-particle and anti-particle/particle pairs coupled via the black hole (BH) evaporating `pump' source. We also analytically and dynamically verify the `Page information time' for our model which refers to the conventionally held belief that the information in the BH radiation becomes significant after the black hole has evaporated half its initial energy into the outgoing radiation. Lastly, we investigate the effect of BH particle production/evaporation on two modes in the exterior region of the BH event horizon that are initially maximally entangled, when one mode falls inward and interacts with the black hole, and the other remains forever outside and non-interacting.

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