In current and future complex quantum processes and devices, quantum information is not only shared but processed and transmitted, leading to quantum effects in both space and time. While the structure of entanglement – spatial quantum correlations – is understood and its certification from experimental data is a well developed field of research, the study of genuinely spatio-temporal quantum correlations is still in its early stages. More in-depth investigation, both at the theoretical and the experimental level, is necessary to obtain a comprehensive understanding of quantum resources in space and time as well as robust means to certify and exploit them.
The TaQC project has provided significant foundational, platform agnostic advances in all of these areas. The exploration of correlation structures in the presence of noise has yielded, for the first time, a stratification of the space of quantum processes with classical memory and offered new insights into their practical capabilities. Given the ubiquitousness of detrimental noise, memory of this type will be dominantly present and controllable in near-term quantum devices, making this categorisation an important tool for further explorations. Analogously, the provided higher-order resource theory of athermality enables the analysis of thermodynamic properties of entire quantum devices and processes, rather than their individual building blocks, as was previously the state-of-the art.
The results of the TaQC project on the influence of memory size on observable correlations introduces a powerful tool to certify the properties of quantum processes from limited experimental control. This, in turn, opens up a novel avenue towards the efficient learning and characterisation of complex quantum devices. In addition, the algorithm developed for the numerical evaluation of the corresponding memory size witnesses is designed to automatically compress the number of free variables. Beyond the case of memory witnesses, this technique offers a feasible approach to the numerical optimsation of heretofore computationally intractable problems in quantum information theory. Similarly, the developed techniques to deduce the structural properties of general quantum processes now enable their optimisation under physical constraints and and provide the theoretical underpinnings for the systematic study of general quantum devices.
Furthermore, the TaQC project has conceptualised the important class of stationary processes in the quantum realm, and developed a roadmap of previously unknown quantum effects that these processes can display beyond their classical counterparts. Together with the developed resource monotones these insights provide a novel lens into the capabilities and complexity of stationary quantum processes. The developed protocol for the reconstruction of generative models offers, for the first time, an efficient way to predict the behaviour of stationary quantum processes with memory from continuous experimental data. By accounting for long-term correlations, this approach extends beyond the case of independent and identically distributed data previously considered in tomographic setups, enabling the study of strongly correlated natural and engineered quantum processes.
Overall, our work has resulted in a multitude of novel theoretical tools for the characterisation, certification and reconstruction of general quantum processes, paving a way for the systematic control and exploitation of genuinely quantum spatio-temporal correlations in the next generation of quantum experiments and devices.
