$d$ locally indistinguishable maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$

Abstract

We give a explicit construction of $d$ locally indistinguishable orthogonal maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ for any $d\ge 4$. This gives an answer to the conjecture proposed by S. Bandyopadhyay in 2009. Thus it reflects the nonlocality of the fundamental feature of quantum mechanics.

arXiv commentThe paper is rewrited, especally the introduction. 5 pages, no figures

References in corpus (16)

• Quantum Nonlocality without Entanglement
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Graph States for Quantum Secret Sharing
• Quantum Data Hiding
• Nonlocality, Asymmetry, and Distinguishing Bipartite States
• Distinguishability of the Bell states
• Distinguishability and indistinguishability by LOCC
• Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
• Distinguishability of maximally entangled states
• Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
• Bipartite subspaces having no LOCC-distinguishable bases
• LOCC distinguishability of unilaterally transformable quantum states
• PPT-indistinguishable states via semidefinite programming
• Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose
• Three maximally entangled states can require two-way LOCC for local discrimination
• Any $2\otimes n$ subspace is locally distinguishable

Cited by in corpus (18)

• Quantum gate teleportation between separated qubits in a trapped-ion processor
• Nonlocality of orthogonal product basis quantum states
• Semidefinite programming relaxations for quantum correlations
• Local distinguishability based genuinely quantum nonlocality without entanglement
• Bounds on the smallest sets of quantum states with special quantum nonlocality
• The local distinguishability of any three generalized Bell states
• On small set of one-way LOCC indistinguishability of maximally entangled states
• Locally stable sets with minimum cardinality
• Twist-teleportation based local discrimination of maximally entangled states
• Genuine hidden nonlocality without entanglement: from the perspective of local discrimination
• Strong quantum nonlocality and unextendibility without entanglement in $N$-partite systems with odd $N$
• Alternative method for deriving nonlocal multipartite product states
• Local discrimination of generalized Bell states via commutativity
• Positive-partial-transpose distinguishability for lattice-type maximally entangled states
• Local distinguishability of quantum states in multipartite System
• Graph connectivity based strong quantum nonlocality with genuine entanglement
• Application of Ramsey theory to localization of set of product states via multicopies
• Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States