Multiparty orthogonal product states with minimal genuine nonlocality

Abstract

Nonlocality without entanglement and its subsequent generalizations offer deep information-theoretic insights and subsequently find several useful applications. Concept of genuinely nonlocal set of product states emerges as a natural multipartite generalization of this phenomenon. Existence of such sets eventually motivates the problem concerning their entanglement-assisted discrimination. Here, we construct examples of genuinely nonlocal product states for arbitrary number of parties. Strength of genuine nonlocality of these sets can be considered minimal as their perfect discrimination is possible with entangled resources residing in Hilbert spaces having the smallest possible dimensions. Our constructions lead to fully separable measurements that are impossible to implement even if all but one party come together. Furthermore, they also provide the opportunity to compare different multipartite states that otherwise are incomparable under single copy local manipulation.

Accepted in Physical Review A

References in corpus (14)

• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Multipartite Nonlocality without Entanglement in Many Dimensions
• All entangled states are useful for channel discrimination
• Device-independent randomness expansion against quantum side information
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Local discrimination of mixed states
• Strong Quantum Nonlocality without Entanglement in Multipartite Quantum Systems
• Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system
• Strong quantum nonlocality with entanglement
• Nonlocality Without Entanglement: Quantum Theory and Beyond
• Random-Receiver Quantum Communication
• Multi-copy adaptive local discrimination: Strongest possible two-qubit nonlocal bases

Cited by in corpus (7)

• Thermodynamic Signatures of Genuinely Multipartite Entanglement
• Strong quantum nonlocality without entanglement in $n$-partite system with even $n$
• Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
• Local Quantum State Marking
• Genuine Activation of Quantum Nonlocality: Stronger Than Local Indistinguishability
• Locally unidentifiable subset of quantum states and its resourcefulness in secret password distribution
• Information locking and its resource efficient extraction