Decoding a black hole: quantum information theory meets quantum gravity

扔进黑洞的信息会被摧毁吗，或者会从黑洞蒸发时发出的霍金辐射中恢复过来？黑洞信息之谜最初由霍金在20世纪70年代提出，至今仍是理论物理学中最迷人但最具挑战性的悬而未决的问题之一，突显了将广义相对论与量子力学相协调的挑战。来自弦理论的证据，即ADS/CFT对应，表明信息可以被编码到黑洞的内部自由度中，最终转移到发出的辐射中，而不是被摧毁。然而，这个问题仍然存在争议，信息逃离黑洞的机制仍然难以捉摸。量子信息论解决了关于量子系统中信息的获取、传输和处理的定量问题。虽然量子信息理论本身不能解决黑洞信息之谜，但它可以提供直观和分析/数值工具，帮助我们加深对这个问题的理解。在过去的五年里，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工作的一个标志是我自己基于一种新的量子纠错码构造的ADS/CFT通信的玩具模型。该模型通过量子编码理论的透镜，对引力和量子纠缠之间的一种相当令人惊讶的关系提供了敏锐的见解。在这个研究计划中，我将利用现代量子信息论的技术，解决关于黑洞和量子引力的各种谜题，包括前面提到的信息问题。这一研究方向解决了量子引力和弦理论前沿的基本问题，提供了与量子信息理论活跃领域的联系，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，它还在量子引力、量子信息理论和凝聚态理论之间开辟了新的研究途径。通过量子信息论的透镜研究黑洞的奇异性质也将为量子信息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能为证明量子系统相对于经典系统的优势提供了一个理想的平台。这些问题也将带来理论物理的见解，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.