Some notes on the robustness of k-coherence and k-entanglement

Abstract

We show that two related measures of k-coherence, called the standard and generalized robustness of k-coherence, are equal to each other when restricted to pure states. As a direct application of the result, we establish an equivalence between two analogous measures of Schmidt rank k-entanglement for all pure states. This answers conjectures raised in the literature regarding the evaluation of the quantifiers, and facilitates an efficient quantification of pure-state resources by introducing computable closed-form expressions for the two measures.

arXiv comment8 pages

References in corpus (19)

• Quantifying Coherence
• Operational Resource Theory of Coherence
• Robustness of entanglement
• Robustness of coherence: An operational and observable measure of quantum coherence
• A Schmidt number for density matrices
• Further results on the cross norm criterion for separability
• Converting Nonclassicality into Entanglement
• A resource theory of superposition
• Convex geometry of quantum resource quantification
• Certification and Quantification of Multilevel Quantum Coherence
• A separability criterion for density operators
• Convex ordering and quantification of quantumness
• Converting multilevel nonclassicality into genuine multipartite entanglement
• Coherence number as a discrete quantum resource
• Quantifying the coherence of pure quantum states
• A new class of entanglement measures
• Generalized Coherence Concurrence and Path distinguishability
• Schmidt balls around the identity
• The modified trace distance of coherence is constant on most pure states

Cited by in corpus (15)

• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• One-Shot Operational Quantum Resource Theory
• Benchmarking one-shot distillation in general quantum resource theories
• Probabilistic transformations of quantum resources
• Characterizing Quantum Networks: Insights from Coherence Theory
• Fisher information universally identifies quantum resources
• One-Shot Manipulation of Dynamical Quantum Resources
• Tight constraints on probabilistic convertibility of quantum states
• Completing the Grand Tour of asymptotic quantum coherence manipulation
• Monotones in General Resource Theories
• Virtual quantum resource distillation: General framework and applications
• Deterministic transformations of multilevel coherent states under incoherence-preserving operations
• Quantum coherence between subspaces: State transformation, Cohering Power, $k$-coherence and other properties
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Exact Quantum Capacity of Decohering Channels in Arbitrary Dimensions