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MIT 6 453 - Study guide

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MIT OpenCourseWarehttp://ocw.mit.edu 6.453 Quantum Optical Communication Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.453 Quantum Optical Communication Term-Paper Rules and Potential Topics Fall 2008 Date: Thursday, October 16, 2008 General Remarks: As part of 6.453, each student must do a term paper consisting of: (1) outside reading on a topic relevant to quantum optical communication, and (2) preparation and submission of a written report based on this reading. It is not the intent of the term-paper requirement that original research be perΩformed. You may choose a topic related to your thesis work, but the term paper should not be a reproduction of work already done for that thesis. In what follows there is a list of potential topics, each with some brief remarks and one or more (very) preliminary references to get you started. You are encouraged to seek topics that are not on this list, if you so desire. Please feel free to consult with Prof. Shapiro regarding any term-paper topic, whether or not it is listed below. In order to help you plan your time outlay, the following schedule has been established: Thursday, 10/16/08: Term paper rules and suggested-topics list distributed, in class. 10/16/08–11/6/08: Preliminary reading in support of topic selection; consultation with Prof. Shapiro as necessary. Thursday, 11/6/08: One paragraph term-paper proposals due, in class. 11/6/08–12/9/08: Reading, and term-paper preparation. Tuesday, 12/9/08: Term papers due, in class. Before turning to the potential topics themselves, it is worth noting some useful general references. The reprint volume edited by Wheeler and Zurek1 includes many of the early, classic papers in quantum measurement theory, as well as works from the 1960’s and 1970’s on Bell’s inequalities, quantum non-demolition measurements, etc. Mandel and Wolf2 cover the fundamentals of quantum optics through work in the 1980’s and 1990’s on squeezing, and optical quantum non-demolition measureΩments. The book by Hermann Haus3 has a wealth of information on quantum noise, squeezing, and quantum non-demolition measurements. Bennett and Shor4 provide a review of quantum information theory, touching on many topics in quantum computaΩtion, quantum coding, etc. Bouwmeester, Ekert, and Zeilinger5 cover theoretical and experimental work in quantum cryptography, quantum teleportation, and quantum computation. Nielsen and Chuang6 is a comprehensive text on quantum computation and quantum information. The Web of Science7 makes it easy to search for recent 1relevant articles, many of which are available on-line in .pdf form through the MIT libraries’ VERA service8. If you want to see the very latest preprints, you can consult the quant-ph archive.9 1. J.A. Wheeler and W.H. Zurek, eds., Quantum Theory and Measurement, (PrinceΩton University Press, Princeton, 1983). 2. L. Mandel and E. Wolf Optical Coherence and Quantum Optics, (Cambridge University Press, Cambridge, 1995). 3. H.A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, Berlin, 2000). 4. C.H. Bennett and P.W. Shor, “Quantum Information Theory,” IEEE Trans. Inform. Theory 44, 2724–2742 (1998). 5. D. Bouwmeester, A. Ekert, and A. Zeilinger, eds. The Physics of Quantum Information (Springer, Berlin, 2000). 6. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Informa-tion (Cambridge University Press, Cambridge, 2000). 7. http://isiknowledge.com/wos 8. http://libraries.mit.edu 9. http://arXiv.org/archive/quant-ph Potential Topics: • Hidden Variables and Bell’s Inequalities: In the early days of quantum mechanics, the disturbing, fundamental presence of randomness in its theory of measurement led a number physicists to seek more complete, “hidden-variable” theories that would remove this unappealing feature of standard quantum mechanics. Bell’s inequalities afford experimental tests that can discriminate quantum theory (as it stands) from any such deΩterministic, hidden-variable theory. Moreover several optical experiments have been performed which confirm these inequalities, i.e., which confirm quantum mechanics and exclude hidden-variable theories. Bell’s original paper can be found in [1]. A readable short treatment is given in [2, Sect. 12.14], with referΩences to both theoretical and experimental work, see also [4, Sect. 2.6] • Quantum Non-Demolition Measurements: The photodetection measurements that we will discuss in class are annihilative, so the controversial projection postulate does not play a major role. Quantum non-demolition measurements do not destroy the optical field, and are of interest 2 1 The Web of Science® Citation Index requires a subscription.1in quantum mechanics more broadly. The early, fundamental work on this topic can be found in [3]. Additional theory appears in [5]. A readable short treatment in the quantum optics setting is given in [2, Sect. 22.6], with references to both theoretical and experimental work. • Quantum-State Tomography: A collection of optical homodyne measurements made at a variety of local-oscillator phase angles can be used measure the quantum state of a light beam via a tomographic reconstruction technique. For some theoretical work see [6]; for some experimental work see [7]. See [4, Sect. 8.4.2] for the related topic of quantum process tomography. • Quantum-State Source Coding: In classical communication theory, Shannon’s source-coding theorem sets a minΩimum value to the number of bits that must be used to represent the output of an information source. There is a corresponding theory of s ource coding for


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