Collective Operations Can Exponentially Enhance Quantum State Verification

TL;DR

This paper introduces collective verification strategies for entangled states that significantly reduce measurement requirements and enable direct certification, improving efficiency in quantum state verification processes.

Contribution

It presents novel collective methods for local verification of Bell pairs that transfer noise to fewer copies, reducing measurement needs and enabling direct certification.

Findings

Reduces the number of measurements needed for state verification

Enables direct certification of remaining entangled states

Extends to multipartite states and other quantum verification problems

Abstract

Maximally entangled states are a key resource in many quantum communication and computation tasks, and their certification is a crucial element to guarantee the desired functionality. We introduce collective strategies for the efficient, local verification of ensembles of Bell pairs that make use of an initial information and noise transfer to few copies prior to their measurement. In this way the number of entangled pairs that need to be measured and hence destroyed is significantly reduced as compared to previous, even optimal, approaches that operate on individual copies. Moreover the remaining states are directly certified. We show that our tools can be extended to other problems and larger classes of multipartite states.