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In 1927, Heisenberg heuristically disclosed the tradeoff between the error inthe measurement and the caused disturbance on another complementary observable.In the quantum theory, most of uncertainty relations are proposed to reveal theamount of unavoidable uncertainty in the measuring process. In this paper, westudy the error-disturbance relation from the information viewpoint. We ask howmuch information, rather than how much uncertainty, can be obtained during thetwo sequential measurements. To achieve optimal information gain, we argue thatthe strategy for the "intelligent" prior apparatus is to clone the unknownstate, and for the posterior one is to perform the swapping operation. Wepropose the coarse-grained random access code, and therein informationcausality as a physical principle can be exploited for deriving the upper-boundof information gain. Finally, we conjecture the information gain of measuringthe position and momentum of a quantum object in the coarse-grained way.

Informatic error-disturbance relation in the qubit case