Local quantum state marking

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 (LOs) 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 we report intriguing entanglement-assisted catalytic LSM phenomena.

Automated summary

We propose the task of local state marking (LSM), where randomly chosen multipartite quantum states are distributed among separated parties, and the identities of the states are to be marked through local quantum operations and classical communication. We show that LSM is different from local state distinguishability (LSD) and investigate the use of entanglement in assisting the marking of otherwise unmarkable states.