Local certification of unitary operations
arXiv:2312.17037 · doi:10.1038/s41598-024-75148-z
Abstract
In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the probability of the type II error, given a specified maximum probability of the type I error, considering assistance through entanglement with auxiliary systems. Our result indicates connection of the local certification problem with a product numerical range of unitary matrices. We show that the optimal local strategy does not need usage of auxiliary systems and requires only single round of one-way classical communication. Moreover, we compare local and global certification strategies and show that typically local strategies are optimal, yet in some extremal cases, where global strategies make no errors, local ones may fail miserably. Finally, some application for local certification of von Neumann measurements are discussed as well.
References in corpus (19)
- Quantum Resource Theories
- Local Distinguishability of Multipartite Orthogonal Quantum States
- Distinguishability and indistinguishability by LOCC
- Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
- Truncations of random unitary matrices
- Distinguishability of maximally entangled states
- Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations
- A framework for bounding nonlocality of state discrimination
- Distinguishability of Quantum States by Separable Operations
- Local indistinguishability of orthogonal product states
- Local discrimination of mixed states
- Local Distinguishability of Multipartite Unitary Operations
- Numerical shadow and geometry of quantum states
- Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras
- Almost all quantum channels are equidistant
- Entanglement in channel discrimination with restricted measurements
- Product numerical range in a space with tensor product structure
- Discrimination of two-qubit unitaries via local operations and classical communication
- On the optimal certification of von Neumann measurements