Decoding a black hole: quantum information theory meets quantum gravity

被扔进黑洞的信息会被摧毁吗？还是会从黑洞蒸发时发出的霍金辐射中恢复？黑洞信息之谜最初由霍金在20世纪70年代提出，一直是理论物理学中最迷人但最具挑战性的开放问题之一，突出了调和广义相对论与量子力学的挑战。来自弦理论的证据，即AdS/CFT对应，表明信息，而不是被破坏，可以编码在黑洞的内部自由度，并最终转移到向外辐射。然而，这个问题仍然存在争议，信息从黑洞逃逸的机制仍然难以捉摸。 量子信息理论解决了量子系统中信息获取、传输和处理的定量问题。虽然量子信息理论本身无法解决黑洞信息之谜，但它可以提供直觉和分析/数值工具，帮助我们加深对这个问题的理解。过去五年见证了从量子信息科学到量子引力问题的理论思想的应用如何导致突破性的想法。最近卓有成效的协同作用的一个标志是我自己的工作的玩具模型的AdS/CFT对应的基础上一个新的结构的量子纠错码。该模型通过量子编码理论的透镜，为引力和量子纠缠之间令人惊讶的关系提供了清晰的见解。 在这个研究项目中，我将利用现代量子信息理论的技术来解决包括上述信息问题在内的有关黑洞和量子引力的各种难题。这个研究方向，解决量子引力和弦理论前沿的基本问题，提供了一个链接到量子信息理论的活跃领域，如量子信道/通信，量子纠错码，张量网络技术和量子算法。此外，它在量子引力、量子信息理论和凝聚态理论之间的界面上开辟了新的研究途径。通过量子信息理论的透镜研究黑洞的奇异性质也将为量子信息理论本身提供有用的新工具/概念。对黑洞混沌行为的实验模拟可以为证明量子系统优于经典系统提供一个理想的平台。这些问题也将带来理论物理学的见解，以进一步推进我们对量子信息理论本身的理解。

Will the information thrown into a black hole be destroyed, or might it be recovered from the Hawking radiation that is emitted as the black hole evaporates? The black hole information puzzle, originally posed by Hawking in 1970s, has remained as one of the most fascinating yet challenging open questions in theoretical physics, highlighting the challenge in reconciling general relativity with quantum mechanics. Evidence from string theory, namely the AdS/CFT correspondence, suggests that the information, rather than being destroyed, can be encoded in the black hole's internal degrees of freedom and eventually transferred to the outgoing radiation. However, the issue remains controversial, and the mechanism by which the information escapes from a black hole remains elusive. Quantum information theory addresses quantitative questions about the acquisition, transmission, and processing of information in quantum systems. Though quantum information theory by itself cannot resolve the black hole information puzzle, it can provide intuition and analytical/numerical tools that help to sharpen our understanding of the question. The last five years witnessed how applications of theoretical ideas from quantum information science to quantum gravity questions lead to breakthrough ideas. A hallmark of recent fruitful synergy is my own work on a toy model of the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes. The model provided sharp insights on a rather surprising relation between gravity and quantum entanglement through the lens of quantum coding theory. In this research program, I will address various puzzles concerning black holes and quantum gravity, including the aforementioned information problem, by utilizing techniques from modern quantum information theory. This direction of research, addressing fundamental questions at the forefront of quantum gravity and string theory, provides a link to active areas in quantum information theory, such as quantum channels/communication, quantum error-correcting codes, tensor network techniques and quantum algorithms. Furthermore, it opens new research avenues at the interface between quantum gravity, quantum information theory and condensed matter theory. Studies of exotic properties of black holes through the lens of quantum information theory will also provide useful new tools/concepts for quantum information theory itself. Experimental simulations of the chaotic behaviour of black holes may provide an ideal platform for demonstrating the advantage of quantum systems over classical systems. These questions will also bring insights from theoretical physics to further advance our understanding of quantum information theory itself.