The rapid development of technology has provided a wealth of resources enabling the trust of everyday interactions to be undermined. Authentication schemes aim to address this challenge by providing proof of identity. This can be achieved by using devices that, when challenged, give unique but reproducible responses. At present, these distinct signatures are commonly generated by physically unclonable functions, or PUFs. These devices provide a straightforward measurement of a physical characteristic of their structure that has inherent randomness, due to imperfections in the manufacturing process. These hard-to-predict physical responses can generate a unique identity that can be used for authentication without relying on the secrecy of stored data. However, the classical design of these devices limits both their size and security. Here we show that the extensively studied problematic fluctuations in the current-voltage measurements of resonant tunnelling diodes (RTDs) provide an uncomplicated, robust measurement that can function as a PUF without conventional resource limitations. This is possible due to quantum tunnelling within the RTD, and on account of these room temperature quantum effects, we term such devices QUFs - quantum unclonable functions. As a result of the current-voltage spectra being dependent on the atomic structure and composition of the nanostructure within the RTD, each device provides a high degree of uniqueness, whilst being impossible to clone or simulate, even with state-of-the-art technology. We have thus created PUF-like devices requiring the fewest resources which make use of quantum phenomena in a highly manufacturable electronic device operating at room temperature. Conventional spectral analysis techniques, when applied to our QUFs, will enable reliable generation of unpredictable unique identities which can be employed in advanced authentication systems.