The Quantum Information group at the Scuola Normale has published a new study in Nature Physics that fills a gap in the existing literature.
PISA, December 16, 2026. The Quantum Information group at the Scuola Normale, led by Vittorio Giovannetti, Ludovico Lami, Salvatore Oliviero, and Francesco Mele, has published a study in Nature Physics that, for the first time, defines the fundamental limits of quantum tomography for continuous-variable systems—those that model bosonic systems and quantum optical platforms, which are ubiquitous in nature and widely used in quantum technologies.
We know that quantum tomography—that is, the technique used to fully reconstruct an unknown quantum state using many repeated measurements—is very inefficient when measurements are performed on such systems. Compared to systems with discrete states, such as the qubits used in quantum computers by Google or IBM, which require a “limited” number of measurements over a long time span, continuous-variable systems require an enormous number of measurements within a limited time. This is because continuous-variable systems, such as light in optical circuits, do not have two levels (0 and 1), but infinitely many possible levels.
What, then, are the ultimate limits of measurements for this type of system? The Nature Physics study provides a complete answer to this question, establishing fundamental performance limits for any photonic quantum device. The work has also been presented at QIP 2025, the edition of the QIP conference held in January this year in Raleigh, North Carolina (USA).
“Despite the crucial role of continuous-variable systems in quantum technologies, no previous work had systematically investigated the optimal performance of quantum tomography for states of continuous-variable systems,” the authors say. “At a high level, we show that tomography of continuous-variable systems is extremely inefficient in terms of time resources—much more so than tomography of qubit-based systems.”
To illustrate the extreme inefficiency of tomography for continuous-variable states, they show that achieving a target estimation error of 10% for a 10-mode continuous-variable state with approximately one photon per mode would require about 3,000 years of data acquisition. In contrast, tomography of a 10-qubit state can be completed in just a few milliseconds. This dramatic difference highlights the substantial gap in efficiency between tomography of qudit-based systems and continuous-variable systems.
“Overall, our work initiates a new line of research at the interface between quantum learning theory and continuous-variable systems. It has already inspired several subsequent research works and has opened up a number of promising research directions, some of which we have begun to explore in our recent publications.”
