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Based on the AdS/CFT correspondence, we study how to reconstruct bulkspacetime metrics by various quantum information measures on the boundary fieldtheories, which include entanglement entropy, mutual information, entanglementof purification, and computational complexity according to the proposals ofcomplexity=volume 2.0 and complexity=generalized volume. We present severalreconstruction methods, all of which are free of UV divergence and most ofwhich are driven by the derivatives of the measures with respect to theboundary scales. We illustrate that the exterior and interior of a black holecan be reconstructed using the measures of spatial entanglement andtime-evolved complexity, respectively. We find that these measures always probethe spacetime in a local way: reconstructing the bulk metric in differentradial positions requires the information at different boundary scales. We alsoshow that the reconstruction method using complexity=volume 2.0 is the simplestand has a certain strong locality.

Reconstructing black hole exteriors and interiors using entanglement and complexity