In energy harvesting communication systems, the energy required for message transmission is maintained by an exogenous energy arrival process independent of the message. This links the problem of communication with an energy harvesting transmitter to the problem of communication over state-dependent channels. In particular, if the transmitter has no battery, the available energy can be viewed as a state and the resulting channel is a state-dependent channel with causal state information at the transmitter only. In general, information transmission blurs the state information that the receiver can get from the received signal. In this paper, we explore the trade-off between the information rate R and the entropy reduction of the energy arrival process Δ at the receiver side over an AWGN channel with an energy harvesting transmitter. If the transmitter has no battery, the trade-off points are achieved by Shannon strategies and we show that the optimal input distributions are discrete. Next, we consider the state amplification problem for an energy harvesting transmitter with an unlimited battery. We show that the optimal trade-off region in this extreme case is expressed explicitly in a simple form and its boundary is achieved by a combination of best-effort-transmit and random binning schemes with an i.i.d. Gaussian codebook of average power equal to the average recharge rate. Finally, we propose an uncoded state amplification scheme that splits the energy between message transmission and entropy reduction and study its performance in a numerical example.