No-go theorems for deterministic purification and probabilistic enhancement of coherence
arXiv:2203.15238 · doi:10.1088/1751-8121/ac4ecd
Abstract
The manipulation of quantum coherence is one of the principal issues in the resource theory of coherence, with two critical topics being the purification and enhancement of coherence. Here, we present two no-go theorems for the deterministic purification of coherence and the probabilistic enhancement of coherence, respectively. Specifically, we prove that a quantum state cannot be deterministically purified if it can be expressed as a convex combination of an incoherent state and a coherent state. Besides, we give an easy-to-verified sufficient and necessary condition to determine whether a state can be probabilistically enhanced via a stochastic strictly incoherent operation (sSIO). Our findings provide two feasibility criteria for the deterministic purification and the probabilistic enhancement of coherence, respectively. These results have repercussions on the understanding of quantum coherence in real quantum systems.
References in corpus (56)
- Advances in Quantum Metrology
- Quantifying Coherence
- Quantum Coherence as a Resource
- Quantum Resource Theories
- Operational Resource Theory of Coherence
- Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
- Robustness of coherence: An operational and observable measure of quantum coherence
- Vibrations, Quanta and Biology
- Quantum coherence, time-translation symmetry and thermodynamics
- Intrinsic randomness as a measure of quantum coherence
- Using entanglement against noise in quantum metrology
- Frozen Quantum Coherence
- Low-temperature thermodynamics with quantum coherence
- Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences
- Quantum coherence and geometric quantum discord
- Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
- Assisted distillation of quantum coherence
- Max- relative entropy of coherence: an operational coherence measure
- Conditions for coherence transformations under incoherent operations
- Alternative framework for quantifying coherence
- Coherence depletion in the Grover quantum search algorithm
- Measuring Coherence with Entanglement Concurrence
- Entanglement and coherence in quantum state merging
- Genuine quantum coherence
- Quantum processes which do not use coherence
- One-shot coherence distillation
- Measure-Independent Freezing of Quantum Coherence
- Structure of the resource theory of quantum coherence
- No-Go Theorems for Quantum Resource Purification
- Maximally coherent states and coherence-preserving operations
- Probabilistic distillation of quantum coherence
- Asymmetry and coherence weight of quantum states
- Experimental progress on quantum coherence: detection, quantification, and manipulation
- Deterministic Coherence Distillation
- Catalytic coherence transformations
- A new coherence measure based on fidelity
- Experimentally Obtaining Maximal Coherence Via Assisted Distillation Pro cess
- Estimating coherence measures from limited experimental data available
- One-Shot Coherence Distillation: Towards Completing the Picture
- Quantum coherence and state conversion: theory and experiment
- Operational interpretation of coherence in quantum key distribution
- Catalyst-Assisted Probabilistic Coherence Distillation for Mixed States
- Completing the Grand Tour of asymptotic quantum coherence manipulation
- Enhancing coherence of a state by stochastic strictly incoherent operations
- Optimal distillation of quantum coherence with reduced waste of resources
- Detecting coherence via spectrum estimation
- Coherence as a resource for source-independent quantum random-number generation
- Quantifying coherence in terms of the pure-state coherence
- One-shot Coherence Distillation with Catalysts
- Efficient estimation of multipartite quantum coherence
- Quantum coherence fraction
- Epsilon-smooth measure of coherence
- Quantum state targeting
- Experimental demonstration of one-shot coherence distillation: High-dimensional state conversions
- Anomalies of weight-based coherence measure and mixed maximally coherent states
- Polynomial measure of coherence