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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Uhlmann's fidelity function is one of the most widely used similaritymeasures in quantum theory. One definition of this function is that it is theminimum classical fidelity associated with a quantum-to-classical measurementprocedure of two quantum states. In 2010, Matsumoto introduced another fidelityfunction which is dual to Uhlmann's in the sense that it is the maximimumclassical fidelity associated with a classical-to-quantum preparation procedurefor two quantum states. Matsumoto's fidelity can also be defined using thewell-established notion definition of the matrix geometric mean. In this work,we examine Matsumoto's fidelity through the lens of semidefinite programming togive simple proofs that it possesses many desirable properties for a similaritymeasure, including monotonicity under quantum channels, joint concavity, andunitary invariance. Finally, we provide a geometric interpretation of thisfidelity in terms of the Riemannian space of positive definite matrices, andshow how this picture can be useful in understanding some of its peculiarproperties.

A fidelity measure for quantum states based on the matrix geometric mean