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Abstract: We extend the holographic construction of [1] from AdS3 to higher dimen-sions. In particular, we show that the Bekenstein-Hawking entropy of codimension-two surfaces in the bulk with planar symmetry can be evaluated in terms of the ‘differential entropy ’ in the boundary theory. The differential entropy is a certain quantity con-structed from the entanglement entropies associated with a family of regions covering a Cauchy surface in the boundary geometry. We demonstrate that a similar construc-tion based on causal holographic information fails in higher dimensions, as it typically yields divergent results. We also show that our construction extends to holographic backgrounds other than AdS spacetime and can accommodate Lovelock theories of higher curvature gravity. ArXiv ePrint: 1403.xxxx a