Conservation Laws and Quantum Measurement

Jacques Mallah

For some ideal quantum measurements, conservation laws would seem to be violated systematically. It is argued that the intrinsically non-"ideal" nature of quantum measurements rescues the conservation laws.

Niels Henrik David Bohr

L.D. LANDAU, Efrat Lifshitz

Stanisław Sołtan, Mateusz Frączak, Wolfgang Belzig +1 more

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.

David E. Weeks

Gen Kimura, Bernhard K. Meister, Masanao Ozawa

The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws limit the accuracy of measurements. Recently, various quantitative expressions have been found for quantum limits on measurements induced by additive conservation laws, and have been applied to the study of fundamental limits on quantum-information processing. Here, we investigate generalizations of the WAY theorem to multiplicative conservation laws. The WAY theorem is extended to show that an observable not commuting with the modulus of, or equivalently the square of, a multiplicatively conserved quantity cannot be precisely measured. We also obtain a lower bound for the mean-square noise of a measurement in the presence of a multiplicatively conserved quantity. To overcome this noise it is necessary to make large the coefficient of variation (the so-called relative fluctuation), instead of the variance as is the case for additive conservation laws, of the conserved quantity in the apparatus.