The phenomenon of upconversion, in which a system sequentially absorbs two or more photons and emits a photon of a higher frequency, has been used in numerous applications. These include high-resolution non-destructive bioimaging, deep-penetrating photodynamic therapy, and photovoltaic devices. Due to the multi-photon mechanism of upconversion, its quantum yield cannot exceed 50%. We propose a new mechanism of upconversion, which is based on single-photon absorption; in this process, unlike in multiple-photon upconversion, the quantum yield can be higher than 50%. We show that in a system of two atoms interacting with a reservoir, a low-frequency excitation of one atom can be upconverted into a high-frequency excitation of another atom. The energy required for such an upconversion is drawn from the reservoir, which destroys coherence. Decoherence leads to the transition of the system from the pure state with a small energy dispersion to the mixed state with greater dispersion of energy, while the system entropy increases. The phenomenon of single-photon upconversion can be used to increase the efficacy of devices utilizing upconversion.