Quantum mechanics is a probabilistic theory that does not describe individual events. Yet when we perform a single measurement, we find a well-defined outcome. This apparent contradiction, known as the measurement problem, has a long history going back to the early days of quantum mechanics. A research collaboration involving the Institute of Physics proposes a new approach to this problem.

The collaboration consists of Armen Allahverdyan (Yerevan Physics Institute, Armenia), Roger Balian (CEA Saclay, France) and Theo Nieuwenhuizen (IoP Amsterdam and International Institute of Physics, Natal, Brazil). In a paper published in Annals of Physics in January, the researchers propose two main ingredients that are sufficient to account for all properties of quantum measurements, including the uniqueness of the outcome of each individual run.

*Relaxation of sub-ensembles*

Understanding the quantum measurement process requires describing the measured system and the measurement apparatus as a compound quantum system governed by the rules of quantum statistical mechanics. The dynamical process that this system undergoes appears to be a relaxation to thermodynamic equilibrium. The final state thus reached yields information about a large statistical ensemble of runs but does not describe individual runs of the measurement. The authors note that decompositions of this final state may generate states which are candidates to describe sub-ensembles of runs. Next, they employ a new mechanism called ‘poly-microcanonical relaxation’ to prove that over a very short time scale all such states reach the form that agrees with the expected properties of ideal quantum measurements. This result is a step towards understanding individual runs, but it is still formal.

*Postulate at the macroscopic level*

The formalism of quantum mechanics assigns numbers called ‘q-probabilities’ to each possible outcome of an arbitrary measurement. Due to the specific features of quantum theory, this set of numbers cannot in general be interpreted as actual probabilities. However, the authors postulate such an interpretation for the specific q-probabilities pertaining to the indications of the pointer of the measurement device. The consistency of this interpretation relies on the macroscopic size of the pointer and on the properties of the final states associated with sub-ensembles. The new postulate relates quantum theory to observational facts but does not directly concern the tested microscopic system. It allows to describe properties of individual runs, and provides a justification to all properties usually attributed to ideal measurements. These results contribute to a deeper insight in the measurement problem.

*Open Access Publication: A sub-ensemble theory of ideal quantum measurement processes *

*Featured Image: Credit: Scott Akerman*

Provided by: University of Amsterdam