Optimism and Pessimism in Games

This paper considers the impact of ambiguity in strategic situations. It extends the earlier literature by allowing for optimistic responses to ambiguity. Ambiguity is modelled by CEU preferences. We propose a new solution concept for players who may express ambiguity- preference. Then we study comparative statics of changes in ambiguity-attitude in games with strategic complements. This gives a precise statement of the impact of ambiguity on economic behaviour.Ambiguity in games, support, strategic complementarity, optimism, multiple equilibria.

The Uniqueness Theorem for Entanglement Measures

We explore and develop the mathematics of the theory of entanglement measures. After a careful review and analysis of definitions, of preliminary results, and of connections between conditions on entanglement measures, we prove a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to coincide with the reduced von Neumann entropy on pure states. We also prove several versions of a theorem on extreme entanglement measures in the case of mixed states. We analyse properties of the asymptotic regularization of entanglement measures proving, for example, convexity for the entanglement cost and for the regularized relative entropy of entanglement.Comment: 22 pages, LaTeX, version accepted by J. Math. Phy

Average output entropy for quantum channels

We study the regularized average Renyi output entropy \bar{S}_{r}^{\reg} of quantum channels. This quantity gives information about the average noisiness of the channel output arising from a typical, highly entangled input state in the limit of infinite dimensions. We find a closed expression for \beta_{r}^{\reg}, a quantity which we conjecture to be equal to \Srreg. We find an explicit form for \beta_{r}^{\reg} for some entanglement-breaking channels, and also for the qubit depolarizing channel $\Delta_{\lambda}$ as a function of the parameter $\lambda$. We prove equality of the two quantities in some cases, in particular we conclude that for $\Delta_{\lambda}$ both are non-analytic functions of the variable $\lambda$.Comment: 32 pages, several plots and figures; positivity condition added for Theorem on entanglement breaking channels; new result for entrywise positive channel

Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions

We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region is comprised of the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. For each region, we give an example of a channel for which the corresponding region has a single-letter description. One of our examples relies on a new result proved here, perhaps of independent interest, stating that the coherent information over any degradable channel is concave in the input density operator. We conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information.Comment: 38 pages, 1 figure. Fixed typos, added new example. Submitted to IEEE Tranactions on Information Theor