Quantum Errors and Disturbances: Response to Busch, Lahti and Werner

TL;DR

This paper defends the operator approach to quantum errors and disturbances, clarifies its physical meaning, and discusses its relevance compared to alternative methods amidst ongoing controversies.

Contribution

It clarifies the physical interpretation of the operator approach and compares its usefulness to Wasserstein-based methods in quantum error analysis.

Findings

Operator approach's physical meaning is clarified.

Situations where operator approach is preferable are identified.

Discussion on the interpretation issues behind error-disturbance controversies.

Abstract

Busch, Lahti and Werner (BLW) have recently criticized the operator approach to the description of quantum errors and disturbances. Their criticisms are justified to the extent that the physical meaning of the operator definitions has not hitherto been adequately explained. We rectify that omission. We then examine BLW's criticisms in the light of our analysis. We argue that, although the approach BLW favour (based on the Wasserstein 2-deviation) has its uses, there are important physical situations where an operator approach is preferable. We also discuss the reason why the error-disturbance relation is still giving rise to controversies almost a century after Heisenberg first stated his microscope argument. We argue that the source of the difficulties is the problem of interpretation, which is not so wholly disconnected from experimental practicalities as is sometimes supposed.