Local Distinguishability of Any Three Quantum States

Abstract

We prove that any three linearly independent pure quantum states can always be locally distinguished with nonzero probability regardless of their dimension, entanglement, or multipartite structure. Almost always, all three states can be unambiguously identified. The only exceptional case, where one state is locally knowable but the other two are not, is found among multi-qubit states.

4 Pages, v2 - second corollory corrected, reference added; v3- abstract expanded, proofs elaborated, reference added

References in corpus (2)

• Generic local distinguishability and completely entangled subspaces
• Optimal conclusive discrimination of two states can be achieved locally

Cited by in corpus (33)

• Several nonlocal sets of multipartite pure orthogonal product states
• LOCC distinguishability of unilaterally transformable quantum states
• Limitations on separable measurements by convex optimization
• Genuinely Nonlocal Product Bases: Classification and Entanglement Assisted Discrimination
• Three maximally entangled states can require two-way LOCC for local discrimination
• More nonlocality with less purity
• When do Local Operations and Classical Communication Suffice for Two-Qubit State Discrimination?
• Entanglement Cost of Nonlocal Measurements
• Entanglement, mixedness and perfect local discrimination of orthogonal quantum states
• Entanglement in channel discrimination with restricted measurements
• Distinguishability classes, resource sharing, and bound entanglement distribution
• Indistinguishability of bipartite states by positive-partial-transpose operations in the many-copy scenario
• Nonlocality of tripartite orthogonal product states
• Nonlocality without entanglement: Party asymmetric case
• Separability and entanglement in superpositions of quantum states
• Local hypothesis testing between a pure bipartite state and the white noise state
• Unextendible entangled bases and more nonlocality with less entanglement
• Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
• Entangled state distillation from single copy mixed states beyond LOCC
• Locally unidentifiable subset of quantum states and its resourcefulness in secret password distribution
• Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination
• More assistance of entanglement, less rounds of classical communication
• Exploring strong locality : Quantum state discrimination regime and beyond
• Local indistinguishability and incompleteness of entangled orthogonal bases: Method to generate two-element locally indistinguishable ensembles
• LOCC distinguishable orthogonal product states with least entanglement resource
• Locality of Orthogonal Product States via Multiplied Copies
• Local Unambiguous Discrimination with Remaining Entanglement
• Extended necessary condition for local operations and classical communication: Tight bound for all measurements
• The Independence of Distinguishability and the Dimension of the System
• Multi-partite subspaces containing no locally inaccessible information
• Classifying locally distinguishable sets: No activation across bipartitions
• Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
• Unconditionally superposition-robust entangled state in all multiparty quantum systems