English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The minimum probability of error (MPE) measurement discriminates between aset of candidate quantum states with the minimum average error probabilityallowed by quantum mechanics. Conditions for a measurement to be MPE werederived by Yuen, Kennedy and Lax (YKL). MPE measurements have been found forstates that form a single orbit under a group action, i.e., there is atransitive group action on the states in the set. For such state sets, termedgeometrically uniform (GU) by Forney, it was shown that the `pretty goodmeasurement' (PGM) attains the MPE. Even so, evaluating the actual probabilityof error (and other performance metrics) attained by the PGM on a GU setinvolves inverting large matrices, and is not easy in general. Our firstcontribution is a formula for the MPE and conditional probabilities of GU sets,using group representation theory. Next, we consider sets of pure states thathave multiple orbits under the group action. Such states are termed compoundgeometrically uniform (CGU). MPE measurements for general CGU sets are notknown. In this paper, we show how our representation-theoretic description ofoptimal measurements for GU sets naturally generalizes to the CGU case. We showhow to compute the MPE measurement for CGU sets by reducing the problem tosolving a few simultaneous equations. The number of equations depends on thesizes of the multiplicity space of irreducible representations. For many commongroup representations (such as those of several practical good linear codes),this is much more tractable than solving large semi-definite programs---whichis what is needed to solve the YKL conditions numerically for arbitrary statesets. We show how to evaluate MPE measurements for CGU states for some examplesrelevant to quantum-limited classical optical communication.

Optimal Measurements for Symmetric Quantum States with Applications to Optical Communication