How well can you know the edge of a quantum pyramid?

TL;DR

This paper analyzes the limits of quantum communication using symmetric quantum pyramids, identifying optimal measurement strategies for different decoding goals and highlighting cases where standard methods are suboptimal.

Contribution

It provides the optimal measurement schemes for various decoding strategies in symmetric quantum pyramid communication, revealing limitations of standard measurements.

Findings

Optimal measurement schemes are derived for error minimization, unambiguous discrimination, and information extraction.

Standard square-root measurement is suboptimal in large parameter regimes.

The study advances understanding of quantum measurement strategies in complex state geometries.

Abstract

We consider a symmetric quantum communication scenario in which the signal states are edges of a quantum pyramid of arbitrary dimension and arbitrary shape, and all edge states are transmitted with the same probability. The receiver could employ different decoding strategies: he could minimize the error probability, or discriminate without ambiguity, or extract the accessible information. We state the optimal measurement scheme for each strategy. For large parameter ranges, the standard square-root measurement does not extract the information optimally.