Quantum mechanics is usually formulated with an implicit assumption that "observers" are classical agents who are external to the world. Our own experience of the world is classical, and therefore the measurements defined formally in the theory closely match our (classical) experience. While the classical-quantum divide implied by this process is sufficient for all practical purposes, it is not well defined. There is no a priori reason to rule out observers who do not conform to the standard rules and record measurement results in a quantum memory.  In this work we generalize quantum measurement theory to include observers with a quantum memory and show that such observers have more options when interacting with the world around them  (compared to their external 'classical' counterparts). The results could have implications on  quantum-internet scenarios where quantum computers play the role of observers.

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