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We consider the transmission of classical information over a quantum channel. The channel is de ned by an \alphabet" of quantum states, e.g. certain photon polarizations, together with a speci ed set of probabilities with which these states must be sent. The Levitin-Kholevo theorem implies that the amount of information transmitted per \letter" cannot be greater than the von Neumann entropy H of the letter ensemble. In fact the actual amount of transmitted information will usually be signi cantly less than H if the receiver is restricted to making separate measurements on the individual signals. We show, however, that if the sender uses block coding and the receiver distinguishes whole code words rather than individual letters, the information transmitted per letter can be made arbitrarily close to H. We apply this result to \superdense" coding, and we consider its extension to noisy channels.

A new and exciting approach to the basics of quantum theory, this undergraduate textbook contains extensive discussions of conceptual puzzles and over 800 exercises and problems. Beginning with three elementary 'qubit' systems, the book develops the formalism of quantum theory, addresses questions of measurement and distinguishability, and explores the dynamics of quantum systems. In addition to the standard topics covered in other textbooks, it also covers communication and measurement, quantum entanglement, entropy and thermodynamics, and quantum information processing. This textbook gives a broad view of quantum theory by emphasizing dynamical evolution, and exploring conceptual and foundational issues. It focuses on contemporary topics, including measurement, time evolution, open systems, quantum entanglement, and the role of information.

SummaryBackgroundBullous pemphigoid is a blistering skin disorder with increased mortality. We tested whether a strategy of starting treatment with doxycycline gives acceptable short-term blister control while conferring long-term safety advantages over starting treatment with oral corticosteroids.MethodsWe did a pragmatic, multicentre, parallel-group randomised controlled trial of adults with bullous pemphigoid (three or more blisters at two or more sites and linear basement membrane IgG or C3). Participants were randomly assigned to doxycycline (200 mg per day) or prednisolone (0·5 mg/kg per day) using random permuted blocks of randomly varying size, and stratified by baseline severity (3–9, 10–30, and >30 blisters for mild, moderate, and severe disease, respectively). Localised adjuvant potent topical corticosteroids (<30 g per week) were permitted during weeks 1–3. The non-inferiority primary effectiveness outcome was the proportion of participants with three or fewer blisters at 6 weeks. We assumed that doxycycline would be 25% less effective than corticosteroids with a 37% acceptable margin of non-inferiority. The primary safety outcome was the proportion with severe, life-threatening, or fatal (grade 3–5) treatment-related adverse events by 52 weeks. Analysis (modified intention to treat [mITT] for the superiority safety analysis and mITT and per protocol for non-inferiority effectiveness analysis) used a regression model adjusting for baseline disease severity, age, and Karnofsky score, with missing data imputed. The trial is registered at ISRCTN, number ISRCTN13704604.FindingsBetween March 1, 2009, and Oct 31, 2013, 132 patients were randomly assigned to doxycycline and 121 to prednisolone from 54 UK and seven German dermatology centres. Mean age was 77·7 years (SD 9·7) and 173 (68%) of 253 patients had moderate-to-severe baseline disease. For those starting doxycycline, 83 (74%) of 112 patients had three or fewer blisters at 6 weeks compared with 92 (91%) of 101 patients on prednisolone, an adjusted difference of 18·6% (90% CI 11·1–26·1) favouring prednisolone (upper limit of 90% CI, 26·1%, within the predefined 37% margin). Related severe, life-threatening, and fatal events at 52 weeks were 18% (22 of 121) for those starting doxycycline and 36% (41 of 113) for prednisolone (mITT), an adjusted difference of 19·0% (95% CI 7·9–30·1), p=0·001.InterpretationStarting patients on doxycycline is non-inferior to standard treatment with oral prednisolone for short-term blister control in bullous pemphigoid and significantly safer in the long-term.FundingNIHR Health Technology Assessment Programme.

Classical messages can be sent via a noisy quantum channel in various ways, corresponding to various choices of ensembles of signal states of the channel. Previous work by Holevo and by Schumacher and Westmoreland relates the capacity of the channel to the properties of the signal ensemble. Here we describe some properties characterizing the ensemble that maximizes the capcity, using the relative entropy "distance" between density operators to give the results a geometric flavor.