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We present a general formalism for charecterizing 2-time quantum states,describing pre- and post-selected quantum systems. The most general 2-timestate is characterized by a `density vector' that is independent ofmeasurements performed between the preparation and post-selection. We provide amethod for performing tomography of an unknown 2-time density vector. Thisprocedure, which cannot be implemented by weak or projective measurements,brings new insight to the fundamental role played by Kraus operators in quantummeasurements. Finally, after showing that general states and measurements areisomorphic, we show that any measurement on a 2-time state can be mapped to ameasurement on a preselected bipartite state.

Pre- and post-selected quantum states: density matrices, tomography, and Kraus operators