Quantum coherence fraction

Abstract

As an analogy of fully entangled fraction in the framework of entanglement theory, we have introduced the notion of quantum coherence fraction $C_{\mathcal{F}}$, which quantifies the closeness between a given state and the set of maximally coherent states. By providing an alternative formulation of the robustness of coherence $C_{\mathcal{R}}$, we have elucidated the relationship between quantum coherence fraction and the normalized version of $C_{\mathcal{R}}$ (i.e., ${\overline{C}}_{\mathcal{R}}$), where the role of genuinely incoherent operations (GIO) is highlighted. Numerical simulation shows that though as expected $C_{\mathcal{F}}$ is upper bounded by ${\overline{C}}_{\mathcal{R}}$, $C_{\mathcal{F}}$ constitutes a good approximation to ${\overline{C}}_{\mathcal{R}}$ especially in low-dimensional Hilbert spaces. Even more intriguingly, we can analytically prove that $C_{\mathcal{F}}$ is exactly equivalent to ${\overline{C}}_{\mathcal{R}}$ for qubit and qutrit states. Moreover, some intuitive properties and implications of $C_{\mathcal{F}}$ are also indicated.

9pages, 3 figures. Comments are welcome

References in corpus (43)

• Quantum entanglement
• Mixed State Entanglement and Quantum Error Correction
• Quantifying Coherence
• Quantifying Entanglement
• Quantum Coherence as a Resource
• Entanglement Measures and Purification Procedures
• Quantum Resource Theories
• Operational Resource Theory of Coherence
• Measuring Quantum Coherence with Entanglement
• On mutually unbiased bases
• Robustness of coherence: An operational and observable measure of quantum coherence
• A new proof for the existence of mutually unbiased bases
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• A Schmidt number for density matrices
• Quantum coherence in multipartite systems
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Quantum coherence and geometric quantum discord
• Robustness of asymmetry and coherence of quantum states
• Schmidt number witnesses and bound entanglement
• Converting Nonclassicality into Entanglement
• Local environment can enhance fidelity of quantum teleportation
• Maximal Coherence and the Resource Theory of Purity
• Maximally coherent mixed states: Complementarity between maximal coherence and mixedness
• Operational one-to-one mapping between coherence and entanglement measures
• Genuine quantum coherence
• Optimal Teleportation Based on Bell Measurement
• Quantum processes which do not use coherence
• One-shot coherence distillation
• Device independent state estimation based on Bell's inequalities
• Maximally coherent states and coherence-preserving operations
• All quantum states useful for teleportation are nonlocal resources
• Certification and Quantification of Multilevel Quantum Coherence
• The fully entangled fraction as an inclusive measure of entanglement applications
• Maximal coherence in generic basis
• Converting multilevel nonclassicality into genuine multipartite entanglement
• Quantum steerability: characterization, quantification, superactivation and unbounded amplification
• Super-Activation of Quantum Steering
• Coherence number as a discrete quantum resource
• Subspace preserving completely positive maps
• Gluing of completely positive maps
• Subspace local quantum channels
• Interpreting quantum coherence through a quantum measurement process
• Work extraction and fully entangled fraction

Cited by in corpus (7)

• Quantum Discord for multiqubit Systems
• Coherence Fraction in Grover Search Algorithm
• No-go theorems for deterministic purification and probabilistic enhancement of coherence
• Resource theory of dephasing estimation in multiqubit systems
• Decoding Quantum Search Advantage: The Critical Role of State Properties in Random Walks
• State convertibility under genuinely incoherent operations
• Static and dynamic coherence fraction in the Bernstein-Vazirani algorithm