BRIEF DESCRIPTION OF RESEARCH
Carlton M. Caves
Updated 2005 December 10
My research career has proceeded through what appears to me---and perhaps to no one else---to be a natural progression of research topics. As a graduate student in the Caltech relativity group in the '70s, I got interested in the detection of gravitational waves. The two most promising techniques for detecting gravitational waves---Weber-bar detectors and laser interferometers---seemed to be confronted by sensitivity limits set by quantum mechanics. My interest in those limits and how to circumvent them introduced into my research several related themes: the theory of quantum measurements, the nature of quantum-mechanical noise, and the limits that quantum mechanics imposes on measurements. These themes characterized my research from about 1977 through 1992, as I worked on a variety of topics, including the theory of quantum nondemolition measurements, the use of squeezed light to reduce shot noise, the theory of quantum noise in linear amplifiers, the theory of nonclassical light, the quantum description of noninstantaneous measurements, and the quantum theory of phase measurements.
Beginning in late 1987, these themes were supplemented by and eventually merged with a new interest in the role of information in physics. The result is the present research of my group at the University of New Mexico on the physics of information. The thread running through this research is the dramatic discrepancy between the number of states available to a quantum system and the number of states available to its classical counterpart. Crudely speaking, the classical counterpart can occupy any one of a complete set of orthogonal quantum states, whereas the quantum system can occupy not only the orthogonal states, but also any linear superposition of the orthogonal states. Hilbert space is a big place!---this slogan underlies research on information and complexity in quantum systems. Even simple quantum systems, having only a few Hilbert-space dimensions, have the potential for considerable complexity because of quantum superposition.
My research group presently works in two areas of information physics. The first is quantum information theory. Classical information is information that is encoded in orthogonal quantum-mechanical alternatives which, being orthogonal, can be distinguished reliably. This distinguishability, which is equivalent to saying that classical information can be copied, is the hallmark of classical information. Quantum information is information that is encoded in nonorthogonal quantum states, which cannot be distinguished reliably and thus cannot be copied; the distinctive features of quantum information are a consequence of the quantum superposition that gives rise to nonorthogonal alternatives.
Quantum information theory is the study of how to manipulate and to use quantum information. The apparently crippling disadvantage that nonorthogonal alternatives cannot be distinguished reliably is exploited---perhaps surprisingly---to do information-processing jobs that are impossible with classical information. Quantum cryptography purchases security against eavesdropping---guaranteed by quantum mechanics---by using nonorthogonal alternatives. More dramatically, the superposition principle is exploited to make a quantum computer more powerful than any classical computer. Though the development of a useful quantum computer might well take decades, it will be one of the grand challenges of early 21st Century physics. Already the very notion of quantum computation has overturned the classical theory of computational complexity, by showing that the complexity of a computation depends on the laws of physics; computer scientists are being forced to reëxamine the very foundations of their discipline. Physicists, doing a little reëxamining themselves, are benefiting from a new question that turns on its head the usual attitude about quantum mechanics: how can the laws of quantum mechanics, instead of being a restriction, as in the uncertainty principle, be exploited to perform information-processing tasks that could not be performed in a world characterized by the local realism of classical physics?
When an overall quantum system is made of parts, the superposition principle leads inevitably to what are called entangled states, states in which one knows as much as possible about the whole system while not as much as possible---perhaps knowing nothing---about the parts. Almost all the states of a multipartite quantum system are entangled: the Hilbert space of a multipartite system is big place filled almost entirely with entangled states. A consequence of entanglement is that the results of measurements on the parts can be more tightly correlated than any classical correlations among objective properties of the parts. Because of this, one usually hears that entanglement is a manifestation of a nonlocality in quantum mechanics, but I think entanglement teaches a more radical lesson, that the properties we measure on a quantum system cannot be regarded as objective properties of the system. Entanglement is what allows quantum systems to access superposition states that have no realistic description without any of the parts having to grow in size or momentum or energy or any other physical resource. This easy access to states that have no efficient realistic description is what powers quantum information processing. Entanglement turns quantum mechanics from a nag into a liberator.
Work on quantum information in my research group focuses on fundamental consequences of quantum mechanics for information processing. It uses analytical techniques drawn from linear algebra, quantum measurement theory, information theory, and quantum optics. Topics under investigation include quantum statistical inference and high-precision measurements, quantum communication theory, quantum information processing, quantum entanglement, quantum cryptography, and quantum computation, and foundational questions in quantum mechanics.
My group's second area of research in information physics starts with the exorcism of Maxwell demons and proceeds to investigations of quantum chaotic dynamics. The key idea in exorcising Maxwell demons is that information has a thermodynamic cost, paid when the information is erased. The demon observes a physical system, thereby reducing the system's entropy and allowing the demon to extract useful work, but the thermodynamic cost of the acquired information exceeds the extracted work.
That information has a thermodynamic cost led me and former UNM postdoc Rüdiger Schack, now at the Royal Holloway campus of the University of London, to formulate the following question: when a system's dynamics is subjected to a small stochastic perturbation, perhaps by coupling to an external environment, how much information about the perturbation is required to reduce the system's entropy by a certain amount? When the information far exceeds the corresponding entropy reduction, we say that the system is hypersensitive to perturbation. Hypersensitivity to perturbation justifies, on the grounds of thermodynamic cost, the usual procedure of averaging over the perturbation and thus allowing the system entropy to increase.
Schack and I demonstrated that classical chaotic systems display an exponential hypersensitivity to perturbation, which is equivalent to the standard description of chaos in terms of exponential sensitivity to initial conditions. In contrast to sensitivity to initial conditions, however, hypersensitivity to perturbation can be applied to quantum systems, where it has been investigated numerically and seems to provide a characterization of quantum chaos. Exponential quantum hypersensitivity is apparently a consequence of the chaotic system dynamics and the perturbation acting in concert to drive the system into arbitrary superpositions in the system's Hilbert space. A slogan that captures these ideas and motivates our work is the following: "For classical chaotic system, a perturbation generates classical information, whereas for a quantum chaotic system, a perturbation generates quantum information." Work on quantum hypersensitivity continues, employing a combination of analytical and computational techniques.
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