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How Energy Conservation Limits Our Measurements

Sagnik Chakraborty

IMSc

Observations in quantum mechanics are subject to complex
restrictions arising from the principle of energy conservation. Determining
such restrictions, however, has been so far an elusive task, and only
partial results are known. In this Letter, we discuss how constraints on
the energy spectrum of a measurement device translate into limitations on
the measurements which we can effect on a target system with a nonconstant
energy operator. We provide efficient algorithms to characterize such
limitations and, in case the target is a two-level quantum system, we
quantify them exactly. Our Letter, thus, identifies the boundaries between
what is possible or impossible to measure, i.e., between what we can see or
not, when energy conservation is at stake.

Link: journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.140502