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The observing strategy of a galaxy survey influences the degree to which itsresulting data can be used to accomplish any science goal. LSST is thus seekingmetrics of observing strategies for multiple science cases in order tooptimally choose a cadence. Photometric redshifts are essential for manyextragalactic science applications of LSST's data, including but not limited tocosmology, but there are few metrics available, and they are notstraightforwardly integrated with metrics of other cadence-dependent quantitiesthat may influence any given use case. We propose a metric for observingstrategy optimization based on the potentially recoverable mutual informationabout redshift from a photometric sample under the constraints of a realisticobserving strategy. We demonstrate a tractable estimation of a variationallower bound of this mutual information implemented in a public code usingconditional normalizing flows. By comparing the recoverable redshiftinformation across observing strategies, we can distinguish between those thatpreclude robust redshift constraints and those whose data will preserve moreredshift information, to be generically utilized in a downstream analysis. Werecommend the use of this versatile metric to observing strategy optimizationfor redshift-dependent extragalactic use cases, including but not limited tocosmology, as well as any other science applications for which photometry maybe modeled from true parameter values beyond redshift.

An information-based metric for observing strategy optimization, demonstrated in the context of photometric redshifts with applications to cosmology