Locally distinguishing a maximally entangled basis using shared entanglement

Abstract

We consider the problem of distinguishing between the elements of a bipartite maximally entangled orthonormal basis using local operations and classical communication (LOCC) and a partially entangled state acting as a resource. We derive an exact formula for the optimum success probability and find that it corresponds to the fully entangled fraction of the resource state. The derivation consists of two steps: First, we consider a relaxation of the problem by replacing LOCC with positive-partial-transpose (PPT) measurements and establish an upper bound on the success probability as the solution of a semidefinite program, and then show that this upper bound is achieved by a teleportation-based LOCC protocol. This further implies that separable and PPT measurements provide no advantage over LOCC for this task. We also present lower and upper bounds on the success probability for distinguishing the elements of an incomplete orthonormal maximally entangled basis in the same setup.

arXiv comment15 pages; v2: 24 pages, published version - title and abstract slightly modified, a new section discussing the case of an incomplete basis, and other edits for clarity

References in corpus (44)

• Quantum entanglement
• A computable measure of entanglement
• Quantum Nonlocality without Entanglement
• Unextendible Product Bases and Bound Entanglement
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Graph States for Quantum Secret Sharing
• Quantum State Discrimination
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Quantum Data Hiding
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Quantum state discrimination and its applications
• Multipartite Nonlocality without Entanglement in Many Dimensions
• Nonlocality, Asymmetry, and Distinguishing Bipartite States
• Distinguishability of the Bell states
• Hiding bits in Bell states
• Distinguishability and indistinguishability by LOCC
• Local indistinguishability: more nonlocality with less entanglement
• Local indistinguishability and LOCC monotones
• Hiding classical data in multi-partite quantum states
• Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication
• Optimal local discrimination of two multipartite pure states
• Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
• Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding
• Strong Quantum Nonlocality without Entanglement
• Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
• Distinguishability of maximally entangled states
• Bipartite subspaces having no LOCC-distinguishable bases
• Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication
• Understanding entanglement as resource: locally distinguishing unextendible product bases
• Distinguishability of Quantum States by Separable Operations
• Several nonlocal sets of multipartite pure orthogonal product states
• LOCC distinguishability of unilaterally transformable quantum states
• PPT-indistinguishable states via semidefinite programming
• Local discrimination of mixed states
• Limitations on separable measurements by convex optimization
• Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose
• More nonlocality with less purity
• Entanglement as a resource for local state discrimination in multipartite systems
• Entanglement Cost of Nonlocal Measurements
• Optimal resource states for local state discrimination
• Entanglement cost of two-qubit orthogonal measurements
• Tight bounds on the distinguishability of quantum states under separable measurements
• Pure state estimation and the characterization of entanglement
• Entanglement cost of discriminating noisy Bell states by local operations and classical communication