On the role of a priori knowledge in the optimization of quantum information processing

TL;DR

This paper investigates how different types of prior knowledge influence the optimization of quantum state discrimination, revealing that the choice of discriminator depends primarily on classical knowledge of the states rather than preparation probabilities.

Contribution

It clarifies the distinct roles of a priori knowledge types in designing optimal quantum discriminators for qubit and qutrit states.

Findings

Discriminator design depends mainly on knowledge of the states.

A priori probabilities influence parameter choices but not the discriminator type.

Different knowledge types enhance optimization performance in distinct ways.

Abstract

This paper explores the role of a priori knowledge in the optimization of quantum information processing by investigating optimum unambiguous discrimination problems for both the qubit and qutrit states. In general, a priori knowledge in optimum unambiguous discrimination problems can be classed into two types: a priori knowledge of discriminated states themselves and a priori probabilities of preparing the states. It is clarified that whether a priori probabilities of preparing discriminated states are available or not, what type of discriminators one should design just depends on what kind of the classical knowledge of discriminated states. This is in contrast to the observation that choosing the parameters of discriminators not only relies on the a priori knowledge of discriminated states, but also depends on a priori probabilities of preparing the states. Two types of a priori knowledge can be utilized to improve optimum performance but play the different roles in the optimization from the view point of decision theory.