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(c) The quantum Hamiltonian H is essentially self-adjoint on the span of nitely many number eigenstates As a matter of fact, Hamiltonians that are semibounded, symmetric (Hermitian) polynomials of Q f and P f are admissible One can conclude that a continuous-time, Brownian motion regularization of the phase space path integral can be rigorously established It applies to a wide class of Hamiltonians It can also be proved that the formulation is fully covariant under general canonical coordinate transformations Recently, dos Santos and Aguiar [31] constructed a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator Their coherent state propagator provides an explicit connection between the Wigner and the Husimi representations of the evolution operator The dos Santos Aguiar representation is different from the usual path integral forms suggested by Klauder and Skagerstam presented in this section These different representations, although equivalent quantum mechanically, lead to different semiclassical limits



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Quantum information processing is about exploiting quantum mechanical features in all facets of information processing (data communication, computing) Excellent textbooks, monographs, and reviews exist which give all the material necessary to understand this fast-developping eld [32 34] The states act as information carriers, while the communication is processed through a sequence of quantum operations constituting the channel The sender encodes information by preparing the channel into a well-de ned quantum state belonging to an alphabet A = { 0 , 1 , , M } The receiver, following any relevant signal propagation, performs a measurement on the transmission channel to ascertain which state was transmitted by the sender Quantum information theory is mainly based on superposition-basis and entanglement measurements This requires high- delity implementation to be effective in the laboratory Unfortunately, quantum measurements are invasive in the sense that little or no re nement is achieved by further observation of an already measured system Some of the dif culties in implementing communication in quantum information stems from the fragility of Schr dinger-cat-like superpositions Even with transmission of orthogonal codewords, decoherence, energy dissipation, and other imperfections deteriorate orthogonality If the states in the sender s alphabet are not orthogonal, no measurement can distinguish between overlapping quantum states without some ambiguity [21, 35 38] Then errors seem unavoidable: there exists a nonzero probability that the receiver will misinterpret the transmitted codeword However, this impossibility of discriminating between nonorthogonal quantum states presents an advantage for quantum key distribution [39] Indeed, nonorthogonality prevents an eavesdropper from acquiring information without disturbing the state Also, in some cases it has been shown by Fuchs [36] that the classical information capacity of a noisy channel is actually maximized by a nonorthogonal alphabet Mathematically, the question of distinguishing between nonorthogonal states [36, 37] is addressed by optimizing a state-determining measurement over all posCoherent States in Quantum Physics Jean-Pierre Gazeau Copyright 2009 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 978-3-527-40709-5.

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itive-operator-valued measures (POVM) [38] But arbitrary POVMs are not easy to manipulate! In a recent work, Cook, Martin, and Geremia [40] demonstrated that real-time quantum feedback can be used in place of a quantum superposition of the type Schr dinger cat state to implement an optimal quantum measurement for discriminating between optical coherent states This work gives us an excellent opportunity of presenting standard coherent states as they are produced and used in realistic conditions As a preliminary to the description of the experiment, we will also give an account of the theoretical background needed

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Resolving channel con ict If a seller is a click-and-mortar company, such as Levi s or GM, it may face a con ict with its regular distributors when it sells directly online Known as channel con ict, this situation can alienate the regular distributors Channel con ict has forced some companies (eg, Legocom) to limit their B2C efforts; others (eg, some automotive companies) have decided not to sell direct online An alternative approach is to try to collaborate in some way with the existing distributors whose services may be restructured For example, an auto company could allow customers to con gure a car online, but require that the car be picked up from a dealer, where customers would arrange nancing, warranties, and service IT tools can facilitate resolution of channel con ict, for example by using a group DSS ( 12).

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