1. Intellectual merit Various issues in quantum information theory will be addressed using a consistent formulation of probabilities in the quantum domain, one not limited to macroscopic events or measurements. One class of problems involves various features of how information can be transferred between spatially separated quantum systems using the resources of entangled states, local quantum operations, and various types of communication channel. These include things like dense coding, unitary operations, and distinguishing different quantum states. A second class of problems involves the construction of quantum error correcting codes for the reliable transmission and storage of quantum information, and a better understanding of the fundamental principles underlying such codes. A third class, not unrelated to the preceding two, involves the fundamental nature of quantum information: in what respects it is different from and in what respects it uses the same principles as ordinary (Shannon)information theory, and whether such understanding can be useful for quantitative estimates of the location of quantum information. In addition to the standard methods of probability theory and quantum mechanics, computer simulations will be used to study model systems. 2. Broader impacts The research effort will contribute to the education program at Carnegie-Mellon University at both the undergraduate and graduate levels through providing research projects for students, including those working towards a PhD. Postdoctoral research associates will have an opportunity to sharpen their skills while participating in this research group, making them more valuable members of the scientific community. Students and postdocs will take part in an ongoing seminar series in quantum information, and occasional courses which address these subjects, both of which attract other scientists and science students living in Pittsburgh. Improvements in teaching quantum mechanics and quantum information will eventually prove beneficial to university students outside Pittsburgh as well as those in this city.
Physicists regard quantum mechanics as the fundamental theory of all processes in the physical world. For most situations encountered in everyday life classical mechanics, the laws of Newton, provides a very good approximation to the more fundamental (and much more complicated) quantum laws. In particular, classical mechanics works well when a quantum process known as DECOHERENCE is very rapid and effective. But in situations where decoherence is nearly absent a different set of specifically quantum effects can be observed. Quantum information studies how these effects, which often seem quite counterintuitive, can be used to transmit or to process information in new ways. Quantum computation is one application. Quantum computers using novel features of quantum information should be able to carry out certain computational problems, such as factoring very long integers, much more rapidly than conventional computers, whose capabilities are limited by the presence of decoherence. The quantum computers which are currently under development have to be carefully designed so as to suppress the effects of residual decoherence, and correct errors that arise from this or possibly some other source. This can be done using quantum codes that share information among several physical objects, so that if one of the objects decoheres the information can be recovered from the others. Our project involved studying such codes: understanding where the quantum information is located, how it is protected against decoherence, and how to make codes more efficient. As well as considering specific codes we studied what general quantum principles limit the capabilities of all codes. One of the ways quantum effects manifest themselves is in a special sort of quantum correlation between physical systems at different locations known as ENTANGLEMENT. Entanglement can be produced in the laboratory and then used to carry out certain information-processing tasks which cannot be accomplished using conventional computation or communication devices, which are always strongly influenced by decoherence. However, producing entanglement is not easy, and it tends to disappear rapidly if even a small amount of decoherence is present; in this sense it is an expensive resource. One of our projects was to find efficient ways to utilize entanglement, together with relatively cheap and robust classical devices, to carry out quantum information processing tasks simultaneously at two separate locations. We focused on a particular task, what specialists call a nonlocal unitary, but the algorithms we developed and the insights we gained can be extended to a larger set of problems. In some cases we showed that our methods are optimal: they use the minimum amount of entanglement needed to get the job done. In other cases we were able to put a lower bound on how much entanglement is required. There is a widespread, and we believe quite mistaken, belief that quantum entanglement can give rise to mysterious influences which, contrary to Einstein's theory of relativity, travel faster than the speed of light. Their existence would bring relativity theory and quantum mechanics, two of the best established parts of physics, into conflict. Those who believe in such influences acknowledge that they cannot be used to transmit (quantum or classical) information, and are therefore inaccessible to experimental test. Our research showed that the reason these influences cannot transmit information is that they do not exist. They result from an unsatisfactory understanding of quantum mechanics that arises from the inconsistent way in which introductory textbooks assign a special role to measurements. When the principles of quantum theory have been properly formulated in a consistent way, so that measurements can be seen to follow the same rules governing all other physical processes, the mysterious influences disappear, along with the supposed conflict between relativity and quantum mechanics.
