Local Quantum State Marking

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.

Closed to published version

References in corpus (8)

• Quantum Circuits Architecture
• A generalized no-broadcasting theorem
• Multipartite Nonlocality without Entanglement in Many Dimensions
• All entangled states are useful for channel discrimination
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Local discrimination of mixed states
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Cited by in corpus (4)

• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Genuine Activation of Quantum Nonlocality: Stronger Than Local Indistinguishability
• Locally unidentifiable subset of quantum states and its resourcefulness in secret password distribution
• Any four orthogonal ququad-ququad maximally entangled states are locally markable