R\'enyi generalizations of quantum information measures

Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in applications. We prescribe R\'enyi generalizations for any quantum information measure which consists of a linear combination of von Neumann entropies with coefficients chosen from the set {-1,0,1}. As examples, we describe R\'enyi generalizations of the conditional quantum mutual information, some quantum multipartite information measures, and the topological entanglement entropy. Among these, we discuss the various properties of the R\'enyi conditional quantum mutual information and sketch some potential applications. We conjecture that the proposed R\'enyi conditional quantum mutual informations are monotone increasing in the R\'enyi parameter, and we have proofs of this conjecture for some special cases.Comment: 9 pages, related to and extends the results from arXiv:1403.610

Performance measurement and information production

When performance measures are used for evaluation purposes, agents have some incentives to learn how their actions affect these measures. We show that the use of imperfect performance measures can cause an agent to devote too many resources (too much effort) to acquiring information. Doing so can be costly to the principal because the agent can use information to game the performance measure to the detriment of the principal. We analyze the impact of endogenous information acquisition on the optimal incentive strength and the quality of the performance measure used

On a continuous time game with incomplete information

For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, one shows that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some martingale measures. One also characterizes the optimal martingale measures and compute it explicitely in several examples