Local Quantum State Marking

TL;DR

This paper introduces local state marking (LSM), a task where parties identify quantum states using only local operations and classical communication, highlighting differences from local state distinguishability and exploring entanglement-assisted marking.

Contribution

The paper defines the LSM task, distinguishes it from LSD, and investigates entanglement-assisted and catalytic LSM phenomena, advancing understanding of local quantum state identification.

Findings

Perfect LSD implies perfect LSM, but not vice versa.

LSM can be enhanced with entanglement assistance.

Entanglement-assisted catalytic LSM shows intriguing phenomena.

Abstract

We propose the task of local state marking (LSM), where some multipartite quantum states chosen randomly from a known set of states are distributed among spatially separated parties without revealing the identities of the individual states. The collaborative aim of the parties is to correctly mark the identities of states under the restriction that they can perform only local quantum operations (LO) on their respective subsystems and can communicate with each other classically (CC) -- popularly known as the operational paradigm of LOCC. While mutually orthogonal states can always be marked exactly under global operations, this is in general not the case under LOCC. We show that the LSM task is distinct from the vastly explored task of local state distinguishability (LSD) -- perfect LSD always implies perfect LSM, whereas we establish that the converse does not hold in general. We also explore entanglement assisted marking of states that are otherwise locally unmarkable and report intriguing entanglement assisted catalytic LSM phenomenon.