Quantum Measurements, Energy Conservation and Quantum Clocks

TL;DR

This paper investigates energy conservation and signaling in quantum measurements on a spin chain, revealing that the projection postulate may not always hold and that non-local interactions can lead to signaling.

Contribution

It demonstrates that energy conservation in quantum measurements can be violated or signaling can occur due to non-local Hamiltonians, challenging traditional assumptions.

Findings

Energy is conserved but not supplied by measurement devices.

The projection postulate does not always apply in non-local interactions.

Signaling occurs due to non-local interaction Hamiltonians.

Abstract

We consider a spin chain extending from Alice to Bob with next neighbors interactions, initially in its ground state. Assuming that Bob measures the last spin of the chain, the energy of the spin chain has to increase, at least on average, due to the measurement disturbance. Presumably, the energy is provided by Bob's measurement apparatus. Assuming now that, simultaneously to Bob's measurement, Alice measures the first spin, we show that either energy is not conserved, - implausible - or the projection postulate doesn't apply, and that there is signalling. An explicit measurement model shows that energy is conserved (as expected), but that the spin chain energy increase is not provided by the measurement apparatus(es), that the projection postulate is not always valid - illustrating the Wigner-Araki-Yanase (WAY) theorem - and that there is signalling, indeed. The signalling is due to the non-local interaction Hamiltonian. This raises the question of a suitable quantum information inspired model of such non-local Hamiltonians.