如何最小化由黑洞引起的退相干
How to Minimize the Decoherence Caused by Black Holes
AI总结：
本文研究了黑洞视界软辐射导致的量子叠加态退相干问题，通过求解最优实验协议与辐射“最优纯化”，发现重新打开已关闭的叠加态可进一步减少净退相干。
摘要：
我们考虑一位实验主义者Alice，她在黑洞外部（或更一般地，在存在Killing视界的情况下）创造了一个带电或大质量物体的量子叠加态。先前的研究表明，如果该叠加态保持开放足够长的时间，向黑洞发射软光子/引力子将导致叠加态各分量发生退相干。然而，在过程中的任意有限时刻$t_c$，已经不可逆地发生了多少退相干并不明显。等价地，黑洞内的观察者在$t_c$之前能从Alice的叠加态中提取多少信息也不明显。在本文中，我们求解了Alice在$t > t_c$时应遵循的最优实验协议，以最小化其叠加态各分量的退相干。更精确地说，给定在Alice的实验室中对应于时间$t = t_c$的截面$\mathcal C$之前穿过视界的纠缠辐射，我们确定了该辐射在$\mathcal C$之外的“最优纯化”，使得穿过视界的辐射的全局量子态与Hartle-Hawking或Unruh真空具有最大重叠（量子保真度）。由于量子场论真空态复杂的低频纠缠结构，我们发现这种最优纯化是非平凡的。特别是，即使Alice已经通过将各分量重新聚拢而“关闭”了她的叠加态，我们发现她仍然可以通过重新打开它并执行进一步操作，在一定程度上减少其叠加态各分量的净退相干。
英文摘要：
We consider an experimentalist, Alice, who creates a quantum superposition of a charged or massive body outside of a black hole (or, more generally, in the presence of a Killing horizon). It was previously shown that emission of soft photons/gravitons into the black hole will result in the decoherence of the components of the superposition if it is held open for a sufficiently long span of time. However, at any finite time, $t_c$, during the process, it is not obvious how much decoherence has irrevocably occurred. Equivalently, it is not obvious how much information an observer inside the black hole can extract about Alice's superposition prior to time $t_c$. In this paper, we solve for the optimal experimental protocol to be followed by Alice for $t > t_c$ so as to minimize the decoherence of the components of her superposition. More precisely, given the entangling radiation that has passed through the horizon prior to the cross-section $\mathcal C$ corresponding to the time $t = t_c$ in Alice's lab, we determine the "optimal purification" of this radiation beyond $\mathcal C$ such that the global quantum state of the radiation through the horizon has maximal overlap (quantum fidelity) with the Hartle-Hawking or Unruh vacuum. Due to the intricate low frequency entanglement structure of the quantum field theory vacuum state, we find this optimal purification to be nontrivial. In particular, even if Alice has already "closed" her superposition by bringing the components back together, we find that she can decrease the net decoherence of the components of her superposition somewhat by re-opening it and performing further manipulations.
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