Hierarchy of quantum operations in manipulating coherence and entanglement

Abstract

Quantum resource theory under different classes of quantum operations advances multiperspective understandings of inherent quantum-mechanical properties, such as quantum coherence and quantum entanglement. We establish hierarchies of different operations for manipulating coherence and entanglement in distributed settings, where at least one of the two spatially separated parties are restricted from generating coherence. In these settings, we introduce new classes of operations and also characterize those maximal, i.e., the resource-non-generating operations, progressing beyond existing studies on incoherent versions of local operations and classical communication and those of separable operations. The maximal operations admit a semidefinite-programming formulation useful for numerical algorithms, whereas the existing operations not. To establish the hierarchies, we prove a sequence of inclusion relations among the operations by clarifying tasks where separation of the operations appears. We also demonstrate an asymptotically non-surviving separation of the operations in the hierarchy in terms of performance of the task of assisted coherence distillation, where a separation in a one-shot scenario vanishes in the asymptotic limit. Our results serve as fundamental analytical and numerical tools to investigate interplay between coherence and entanglement under different operations in the resource theory.

19 pages, 2 figures

References in corpus (16)

• Advances in Quantum Cryptography
• Quantum information can be negative
• Entanglement of assistance and multipartite state distillation
• Quantifying Superposition
• Cost of quantum entanglement simplified
• Quantum coherence and state conversion: theory and experiment
• One-shot entanglement distillation beyond local operations and classical communication
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
• Subspace preserving completely positive maps
• Gluing of completely positive maps
• Subspace local quantum channels
• Assisted concentration of Gaussian resources
• Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
• Entanglement theory in distributed quantum information processing
• Necessary and Sufficient Condition for the Equivalence of Two Pure Multipartite States under Stochastic Local Incoherent Operations and Classical Communications
• Spread quantum information in one-shot quantum state merging

Cited by in corpus (4)

• Experimental progress on quantum coherence: detection, quantification, and manipulation
• Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction
• Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics