March 03, 2026 -- In classical physics, the concept of memory is well understood. If the future evolution of a system depends only on its present state, the process is said to be memoryless. On the other hand, if past states continue to influence future outcomes, the system has memory.

In quantum physics, however, this clarity has long been missing. Quantum systems can store and transmit information in ways that have no classical analogue, and the act of measurement plays a fundamental role in the dynamics.

In a new study published in the journal PRX Quantum, researchers from the University of Turku in Finland, University of Milan in Italy, and Nicolaus Copernicus University in Toruń in Poland address this long-standing problem by revisiting what “memory” means in a quantum context.

“Our work shows that memory is not a single concept but can manifest in different ways depending on how the evolution of a system is described,” says first author, Doctoral Researcher Federico Settimo from the University of Turku.

Memory effects have been extensively studied over the past years and are well characterised in the evolution of quantum states, an approach originally formulated by Erwin Schrödinger. Quantum mechanics, however, also admits an equally fundamental and historically distinct perspective, developed by Werner Heisenberg: instead of evolving states, what is described is the time evolution of observables, meaning the physical quantities that are directly measured in experiments.

The two pictures, although giving equal values for any experimental result, are not equivalent when describing memory effects, as the new study shows.

The researchers demonstrated that this difference has direct consequences for how memory can be witnessed. Some memory effects can be detected only by following the evolution of quantum states, while others appear exclusively when considering the evolution of observables. A quantum process may therefore look memoryless from one point of view, while exhibiting memory from the other. This result shows that quantum memory is richer than previously thought and cannot be fully captured by focusing on quantum states alone.

“Our findings open up new research avenues into the dynamics of quantum systems. Moreover, our work has implications beyond its foundational significance for quantum technologies, where the external environment induces noise and memory effects. Knowing how memory can be witnessed is essential for developing strategies to mitigate noise or exploit environmental effects in realistic quantum devices,” says Professor of Theoretical Physics Jyrki Piilo from the University of Turku.

Overall, the study clarifies a fundamental aspect of quantum dynamics and highlights how the uniquely quantum nature of time evolution reshapes even basic concepts such as memory.