Quantum Foundations and Quantum Information

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，这是物理学家关于自然界最基本的理论，如果这个理论从未被发明出来，这是不可能的。 鉴于这一成功，人们可能会认为量子力学现在应该和现代科学的其他基石，如热力学和相对论一样被理解。 相反，正如世纪伟大的物理学家之一理查德·费曼（Richard Feynman）所说：“没有人理解量子力学。“很明显，费曼所指的缺乏清晰的理解并没有阻止量子力学被应用于广泛的技术设备。但是，当学生们试图从教师和教科书中学习这门学科时，他们感到沮丧，因为教师和教科书的缺乏清晰度说明了费曼所说的真理。清理其基础中的概念混乱肯定不会减损，甚至可能有助于，量子力学的技术应用，并且很可能证明对量子计算和量子密码学等领域的未来发展很重要，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。 正如标题所示，这个研究项目有两个重点。一个是使用量子历史--一种由包括默里·盖尔曼（Murray Gell-Mann）在内的许多人开发的有前途的方法，盖尔曼曾是费曼在加州理工学院的同事--来解决和澄清量子理论基础中的概念困难。 几个主要的悖论，包括著名的双缝，已经解决了使用历史的方法，这种方法摆脱了神秘的长期影响，存在于一些旧的量子力学解释，这是很难调和的相对论。 然而，到目前为止，这些新的发展仅限于技术文献，如果他们想让下一代科学家更容易接触到这个主题，他们需要进入教室和教科书。 还有很多工作要做，既要通过简单的物理例子让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的（“哥本哈根”）方法更好的东西，费曼无法理解。 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。经典信息理论是由克劳德·香农在半个世纪前发展起来的，在现代通信理论中起着重要的作用，比如有效地利用微弱的无线电信号从遥远的太空探测器向地球传输信息。 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，虽然它取得了一些显著的成功，但也遇到了以下困难：香农的公式是基于概率的使用，但以一致的方式将概率引入量子力学是困扰费曼的许多概念困难的来源。 历史的方法解决了量子概率的问题，在一个一致的方式，允许立即扩展到量子领域的香农的许多想法。 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，以及从信息的产生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.