Explaining policies of Markov Decision Processes (MDPs) is complicated due to their probabilistic and sequential nature. We present a technique to explain policies for factored MDPs by populating a set of domain-independent templates. We also present a mechanism to determine a minimal set of templates that, viewed together, completely justify the policy. These explanations can be generated automatically at run-time with no additional effort required from the MDP designer. We demonstrate this technique using the problems of advising undergraduate students in their course selection and assisting people with dementia in completing the task of handwashing. We also evaluate these automatically generated explanations for course-advising through a user study involving students.

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Abstract. Spatial filtering is an important technique for reducing sky background noise in a satellite quantum key distribution downlink receiver. Atmospheric turbulence limits the extent to which spatial filtering can reduce sky noise without introducing signal losses. Using atmospheric propagation and compensation simulations, the potential benefit of adaptive optics (AO) to secure key generation (SKG) is quantified. Simulations are performed assuming optical propagation from a low-Earth-orbit satellite to a terrestrial receiver that includes AO. Higherorder AO correction is modeled assuming a Shack-Hartmann wavefront sensor and a continuous-face-sheet deformable mirror. The effects of atmospheric turbulence, tracking, and higher-order AO on the photon capture efficiency are simulated using statistical representations of turbulence and a time-domain wave-optics hardware emulator. SKG rates are calculated for a decoy-state protocol as a function of the receiver field of view for various strengths of turbulence, sky radiances, and pointing angles. The results show that at fields of view smaller than those discussed by others, AO technologies can enhance SKG rates in daylight and enable SKG where it would otherwise be prohibited as a consequence of background optical noise and signal loss due to propagation and turbulence effects. Keywords: quantum key distribution; adaptive optics; decoy states; quantum information; cryptography; sky radiance.Paper 151557P received Nov. 5, 2015; accepted for publication Dec. 24, 2015; published online Feb. 2, 2016; corrected Apr. 26, 2016. IntroductionThe threat quantum computing poses to public key cryptography is motivating the development of alternatives to modern key sharing techniques that rely on computational complexity for security.1,2 Presently, there is interest in developing quantum key distribution (QKD), presented by Bennett and Brassard in 1984 (BB84), as a provably secure alternative.2-5 QKD lends itself to mathematical proofs of theoretical security and offers the potential for secure generation of symmetric encryption keys in real time over optical channels.

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