# Conservation laws in quantum noninvasive measurements

## TL;DR

This paper explores how quantum measurements, even weak ones, can appear to violate conservation laws like energy and angular momentum, emphasizing the importance of measurement context in quantum physics.

## Contribution

It demonstrates that quantum conservation laws depend on the measurement context and provides feasible experimental examples of apparent nonconservation.

## Key findings

- Weak measurements can show nonconservation of energy and angular momentum.
- Noncommuting observables affect the apparent conservation in quantum measurements.
- Conservation laws in quantum mechanics are context-dependent.

## Abstract

Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation (measurement). In quantum mechanics, however, invasive observations change quantities drastically, irrespective of any classical conservation law. One may hope to overcome this nonconservation by performing a weak, almost noninvasive measurement. Interestingly, we find that the nonconservation is manifest even in weakly measured correlations if some of the other observables do not commute with the conserved quantity. Our observations show that conservation laws in quantum mechanics should be considered in their specific measurement context. We provide experimentally feasible examples to observe the apparent nonconservation of energy and angular momentum.