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

We present a general framework in which both Krylov state and operatorcomplexities can be put on the same footing. In our formalism, the Krylovcomplexity is defined in terms of the density matrix of the associated statewhich, for the operator complexity, lives on a doubled Hilbert space obtainedthrough the channel-state map. This unified definition of complexity in termsof the density matrices enables us to extend the notion of Krylov complexity,to subregion or mixed state complexities and also naturally to the Krylovmutual complexity. We show that this framework also encompasses nicely theholographic notions of complexity.

A universal approach to Krylov State and Operator complexities