Postponing the choice: advantage of deferred measurements in quantum information processing
C. Carmeli, T. Heinosaari, A. Toigo
TL;DR
This work analyzes whether deferring the choice of a second quantum measurement can outperform fixed joint measurements or universal cloning. It develops a unified framework for three strategies—fixed joint meters, approximate cloning, and sequential measurements with deferred choices—under depolarizing noise and, in extended form, allows negative noise parameters. The authors derive exact compatibility regions (CR) for nonnegative noise and extended regions (ECR) for negative noise, showing that equivalences between strategies hold under certain conditions (e.g., MU bases or unbiasedness) but can fail for overnoisy devices, with explicit optimal joint devices provided at boundary points. The methodology relies on Weyl-Heisenberg covariance and symmetrization to obtain covariant joint instruments, yielding insights into the structure and limitations of deferred-measurement approaches with practical implications for quantum information processing where measurement freedom is constrained.
Abstract
Simultaneously implementing two arbitrary quantum measurements on the same system is impossible. The consequence of this limitation is that selecting one measurement actively excludes other possibilities. Two incompatible choices can then be forced together only at the cost of adding enough noise to the measurements. An intriguing alternative is to postpone the choice, or part of it, until a later stage. We explore the advantages of this deferred decision-making and discover that the benefits critically depends on the assumptions about the forthcoming choice. In certain scenarios postponing the choice introduces no additional cost, while in others partial postponement can be effectively the same as full postponement.