Quantum Foundations and Quantum Information

[00:99 . 74]格里菲思许多现代技术，包括计算机、激光和磁共振成像，都利用了量子力学的原理。量子力学是物理学家关于自然的最基本理论，如果量子力学没有被发明出来，这些技术就不可能实现。鉴于这一成功，人们可能会认为，到目前为止，量子力学应该像热力学和相对论等现代科学的其他基础一样被人们所理解。相反，正如20世纪最伟大的物理学家之一理查德·费曼（Richard Feynman）曾经说过的那样，“没有人理解量子力学。”费曼所指的对量子力学缺乏清晰的认识，显然并没有妨碍量子力学在广泛的技术设备上的应用。但是，当学生们试图从教师和教科书中学习这门学科时，他们会感到沮丧，因为这些教师和教科书缺乏清晰度，说明了费曼的话的真实性。在量子力学的基础上清理概念上的混乱当然不会减损，甚至可能有助于量子力学的技术应用，而且对量子计算和量子密码学等领域的未来发展很重要，在这些领域，令人印象深刻的进步伴随着我们目前理解中同样惊人的差距。这个研究项目，如题目所示，有双重重点。一种是利用量子历史——这是一种很有前途的方法，由包括诺贝尔奖获得者默里·盖尔曼（Murray Gell-Mann）在内的许多人开发，他曾是费曼在加州理工学院的同事——用于解决和澄清量子理论基础中的概念性困难。几个主要的悖论，包括著名的双缝，已经用历史的方法解决了，这种方法摆脱了一些古老的量子力学解释中存在的神秘的远程影响，这些影响很难与相对论相调和。然而，到目前为止，这些新的发展还局限于技术文献，如果要让下一代科学家更容易接触到这门学科，就需要把它们搬到教室和教科书中。还有很多工作要做，既要通过简单的物理例子使抽象的数学公式更容易理解，又要说服教师和教科书作者，让他们相信学生应该得到比传统（“哥本哈根”）方法更好的东西，而传统方法是费曼无法理解的。这项研究的第二个重点是量子信息理论，这是量子计算和量子密码学背后的基础科学。经典信息理论是半个世纪前由克劳德·德·夏农提出的，它在现代通信理论中发挥着重要作用，因为它有效地利用微弱的无线电信号将信息从遥远的太空探测器传输到地球。量子信息理论将香农的观点推广到量子效应很重要的情况下，虽然它取得了一些显著的成功，但它也遇到了以下困难：香农的公式是基于概率的使用，但是以一致的方式将概率纳入量子力学是困扰费曼的许多概念困难的来源。历史方法以一种一致的方式解决了量子概率的问题，这使得香农的许多思想可以立即扩展到量子领域。这是否为量子信息理论提供了一个令人满意的基础还有待观察，但它看起来很有希望。如果它成功了，将会有双重好处：更清楚地了解量子计算和密码学能做什么和不能做什么，以及从信息生成和传输的角度思考量子力学过程的新方法。

0139974Griffiths Much of modern technology, including computers, lasers, and magneticresonance imaging, utilizes the principles of quantum mechanics, thephysicist's most fundamental theory of nature, and would not be possible ifthis theory had never been invented. Given this success, one might supposethat quantum mechanics would by now be as well understood as other foundationstones of modern science, such as thermodynamics and relativity theory. On thecontrary, as Richard Feynman, one of the great physicists of the 20th century,once put it, "Nobody understands quantum mechanics." The lack of a clearunderstanding, to which Feynman was referring, has not, obviously, preventedquantum mechanics from being applied to a vast range of technological devices.But students are frustrated when they try and learn the subject from teachersand textbooks whose lack of clarity illustrates the truth of Feynman's remark.Clearing up the conceptual mess in its foundations would certainly not detractfrom, and might even assist in, the technological applications of quantummechanics, and could well prove important for future developments in areas suchas quantum computation and quantum cryptography, where impressive advances areaccompanied by equally spectacular gaps in our current understanding. This research project, as indicated in the title, has a double focus.One is the use of quantum histories - a promising approach developed by variouspeople including Murray Gell-Mann, a Nobel laureate who at one time wasFeynman's colleague at Cal Tech - for addressing and clearing up the conceptualdifficulties in the foundations of quantum theory. Several major paradoxes,including the famous double slit, have been resolved using the historiesapproach, and this method gets rid of mysterious long-range influences that arepresent in some older interpretations of quantum mechanics, and which are hardto reconcile with relativity theory. However, up till now these newdevelopments have been confined to the technical literature, and they need tobe moved into classrooms and textbooks if they are to make the subject moreaccessible to the next generation of scientists. There is plenty of work to bedone, both in making abstract mathematical formulations more understandablethrough simple physical examples, and in convincing teachers and textbookwriters that students deserve something better than the traditional("Copenhagen") approach, the one Feynman could not understand. The second focus of this research is quantum information theory, thefundamental science behind both quantum computing and quantum cryptography.Classical information theory was developed half a century ago by ClaudeShannon, and plays an important role in the modern theory of communication, asin the efficient use of weak radio signals to transmit information from distantspace probes to the earth. Quantum information theory generalizes Shannon'sideas to situations where quantum effects are important, and while it has hadsome notable successes, it has also run into the following difficulty:Shannon's formulation is based on the use of probabilities, but incorporatingprobabilities into quantum mechanics in a consistent way is the source of manyof the conceptual difficulties that troubled Feynman. The histories approachresolves the problem of quantum probabilities in a consistent manner thatallows an immediate extension of many of Shannon's ideas into the quantumdomain. Whether this provides a satisfactory foundation for quantuminformation theory remains to be seen, but it looks promising. If it succeeds,there will be a double benefit: a clearer understanding of what quantumcomputing and cryptography can and cannot do, and a new way to think aboutquantum mechanical processes in terms of the generation and transmission ofinformation.