This paper introduces a new framework for quantum simultaneous information and power transfer (QSIPT), enabling the joint use of quantum states for classical information and energy transfer in quantum communication systems. We propose a novel model in which quantum states are simultaneously used to transmit classical information through a quantum channel and transfer energy to an energy harvesting (EH) receiver. The trade-off between communication rate and harvested energy is characterized by the capacity-power function, which is defined and characterized for both discrete-variable (DV) and continuous-variable (CV) quantum channels. For DV channels, we derive the properties of the capacity-power function, providing analytical upper and lower bounds for the amplitude damping channel and an exact closed-form characterization for the quantum erasure channel. For CV channels, we extend the mathematical framework by introducing a generalized beam-splitter (BS) receiver with adjustable transmissivity, jointly optimized with a transmitter mean-photon-number budget, that splits the channel output between the information decoder and the EH receiver. Specifically, we analyze the capacity-power trade-off under various Gaussian encoding schemes including coherent, squeezed, and thermal states for both lossy bosonic and additive Gaussian noise channels. Closed-form expressions are derived for coherent-state encoding under the joint photon-number-budget and adjustable-transmissivity formulation; squeezed-state inputs are evaluated numerically. Our results show that, within the considered displaced Gaussian encoding class, coherent states achieve the best capacity-power trade-off, squeezed states do not outperform coherent-state encoding under the phase-insensitive channel and passive receiver architecture, and thermal states enable energy transfer without supporting reliable communication.