Quantum Error Correction and One-Way LOCC State Distinguishability

Abstract

We explore the intersection of studies in quantum error correction and quantum local operations and classical communication (LOCC). We consider one-way LOCC measurement protocols as quantum channels and investigate their error correction properties, emphasizing an operator theory approach to the subject, and we obtain new applications to one-way LOCC state distinguishability as well as new derivations of some established results. We also derive conditions on when states that arise through the stabilizer formalism for quantum error correction are distinguishable under one-way LOCC.

arXiv comment20 pages

References in corpus (28)

• Mixed State Entanglement and Quantum Error Correction
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Quantum Nonlocality without Entanglement
• General Entanglement Breaking Channels
• Local Distinguishability of Multipartite Orthogonal Quantum States
• A Unified and Generalized Approach to Quantum Error Correction
• Nonlocality, Asymmetry, and Distinguishing Bipartite States
• Hiding bits in Bell states
• Coding Theorems for Quantum Channels
• 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
• 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
• Distinguishability of maximally entangled states
• Zero-error communication via quantum channels, non-commutative graphs and a quantum Lovasz theta function
• Bipartite subspaces having no LOCC-distinguishable bases
• Properties of Conjugate Channels with Applications to Additivity and Multiplicativity
• Generalization of Quantum Error Correction via the Heisenberg Picture
• Distinguishability of Quantum States by Separable Operations
• Condition for unambiguous state discrimination with local operations and classical communication
• Quantum Error Correction of Observables
• Three maximally entangled states can require two-way LOCC for local discrimination
• Any $2\otimes n$ subspace is locally distinguishable
• Quantum error correction on infinite-dimensional Hilbert spaces
• Operator Structures and Quantum One-Way LOCC Conditions
• Small sets of locally indistinguishable orthogonal maximally entangled states

Cited by in corpus (1)

• Vector Representations of Graphs and Distinguishing Quantum Product States with One-way LOCC