Information-disturbance tradeoff in quantum measurements

We present a simple information-disturbance tradeoff relation valid for any general measurement apparatus: The disturbance between input and output states is lower bounded by the information the apparatus provides in distinguishing these two states.

Figure 1

Indirect measurement model. The system, initially in a state $\varrho$ impinges in the measuring apparatus (dashed line) which is initially prepared in the state $\sigma$. A unitary $U$ correlates the system and the apparatus. A projective measurement $M$ is then performed on the apparatus and yields the classical result $k$, which conditions the output state of the system ${\varrho }^{\prime }$.