One-shot coherence distillation

Abstract

We characterize the distillation of quantum coherence in the one-shot setting, that is, the conversion of general quantum states into maximally coherent states under different classes of quantum operations. We show that the maximally incoherent operations (MIO) and the dephasing-covariant incoherent operations (DIO) have the same power in the task of one-shot coherence distillation. We establish that the one-shot distillable coherence under MIO and DIO is efficiently computable with a semidefinite program, which we show to correspond to a quantum hypothesis testing problem. Further, we introduce a family of coherence monotones generalizing the robustness of coherence as well as the modified trace distance of coherence, and show that they admit an operational interpretation in characterizing the fidelity of distillation under different classes of operations. By providing an explicit formula for these quantities for pure states, we show that the one-shot distillable coherence under MIO, DIO, strictly incoherent operations (SIO), and incoherent operations (IO) is equal for all pure states.

arXiv comment6+5 pages; v3: accepted version

References in corpus (55)

• Quantum entanglement
• The Security of Practical Quantum Key Distribution
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Quantifying Coherence
• Quantum Coherence as a Resource
• Conditions for a class of entanglement transformations
• Operational Resource Theory of Coherence
• Measuring Quantum Coherence with Entanglement
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Robustness of coherence: An operational and observable measure of quantum coherence
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• From Classical to Quantum Shannon Theory
• The resource theory of quantum reference frames: manipulations and monotones
• Intrinsic randomness as a measure of quantum coherence
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• Trace-distance measure of coherence
• Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
• A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
• Robustness of asymmetry and coherence of quantum states
• Relating the Resource Theories of Entanglement and Quantum Coherence
• Assisted distillation of quantum coherence
• Quantifying Entanglement with Witness Operators
• A rigorous treatment of distillable entanglement
• Max- relative entropy of coherence: an operational coherence measure
• A quantitative theory of coherent delocalization
• Converting Nonclassicality into Entanglement
• Entanglement Theory and the Second Law of Thermodynamics
• Alternative framework for quantifying coherence
• The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
• Unified quantification of nonclassicality and entanglement
• Numerical approach for unstructured quantum key distribution
• Entanglement cost of mixed states
• Operational one-to-one mapping between coherence and entanglement measures
• Entanglement and coherence in quantum state merging
• Genuine quantum coherence
• Approximate transformations and robust manipulation of bipartite pure state entanglement
• Irreversibility in asymptotic manipulations of entanglement
• Convex geometry of quantum resource quantification
• Noisy channel coding via privacy amplification and information reconciliation
• On the power of PPT-preserving and non-signalling codes
• Quantum resource theories in the single-shot regime
• One-Shot Coherence Dilution
• Convex ordering and quantification of quantumness
• Semidefinite programming strong converse bounds for classical capacity
• Distilling entanglement from arbitrary resources
• One-shot entanglement-assisted quantum and classical communication
• Axiomatic and operational connections between the $l_1$-norm of coherence and negativity
• Logarithmic coherence: Operational interpretation of ${\ell }_1$-norm coherence
• Converting multilevel nonclassicality into genuine multipartite entanglement
• Irreversibility of Asymptotic Entanglement Manipulation Under Quantum Operations Completely Preserving Positivity of Partial Transpose
• Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources
• General theory of environment-assisted entanglement distillation

Cited by in corpus (87)

• Quantum Resource Theories
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• Operational Resource Theory of Quantum Channels
• Gaussian quantum resource theories
• One-Shot Operational Quantum Resource Theory
• No-Go Theorems for Quantum Resource Purification
• Probabilistic distillation of quantum coherence
• Experimental progress on quantum coherence: detection, quantification, and manipulation
• Benchmarking one-shot distillation in general quantum resource theories
• Deterministic Coherence Distillation
• Dynamical Resource Theory of Quantum Coherence
• Catalysis of entanglement and other quantum resources
• Non-asymptotic entanglement distillation
• Coherence distillation machines are impossible in quantum thermodynamics
• Probabilistic transformations of quantum resources
• Generic bound coherence under strictly incoherent operations
• Quantum coherence and state conversion: theory and experiment
• One-Shot Coherence Distillation: Towards Completing the Picture
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Operational interpretation of coherence in quantum key distribution
• Quantum NETwork: from theory to practice
• Quantifying coherence with respect to general quantum measurements
• Extreme dimensionality reduction with quantum modelling
• No-go theorems for quantum resource purification II: new approach and channel theory
• Non-asymptotic assisted distillation of quantum coherence
• Maximal steered coherence and its conversion to entanglement in multiple bosonic reservoirs
• Resource Theory of Imaginarity: New Distributed Scenarios
• An information-theoretic treatment of quantum dichotomies
• One-Shot Manipulation of Dynamical Quantum Resources
• One-shot entanglement distillation beyond local operations and classical communication
• Catalyst-Assisted Probabilistic Coherence Distillation for Mixed States
• Quantum Coherence and Intrinsic Randomness
• Completing the Grand Tour of asymptotic quantum coherence manipulation
• Optimal distillation of quantum coherence with reduced waste of resources
• Detecting coherence via spectrum estimation
• On converse bounds for classical communication over quantum channels
• Virtual quantum resource distillation
• $\alpha$-Logarithmic negativity
• Coherence measure: Logarithmic coherence number
• Quantum Coherence Witness with Untrusted Measurement Devices
• One-shot Coherence Distillation with Catalysts
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• One-shot assisted concentration of coherence
• Coherence manipulation with dephasing-covariant operations
• Quantum coherence fraction
• Epsilon-smooth measure of coherence
• Pseudorandom density matrices
• Quantifying coherence in terms of Fisher information
• Skew information-based coherence generating power of quantum channels
• Optimal probabilistic distillation of quantum coherence
• Examining the validity of Schatten-$p$-norm-based functionals as coherence measures
• Average skew information-based coherence and its typicality for random quantum states
• Experimental demonstration of one-shot coherence distillation: High-dimensional state conversions
• Impossibility of Cloning of Quantum Coherence
• Geometry of skew information-based quantum coherence
• Simple Bounds for One-shot Pure-State Distillation in General Resource Theories
• The block-coherence measures and the coherence measures based on positive-operator-valued measures
• Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction
• Conversion of Gaussian states under incoherent Gaussian operations
• Unveiling quantum steering by quantum-classical uncertainty complementarity
• Cutting a Wire with Non-Maximally Entangled States
• Hierarchy of quantum operations in manipulating coherence and entanglement
• Approximate distillation of quantum coherence
• Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound
• One-shot quantum state exchange
• Faithful coherent states
• No-go theorems for deterministic purification and probabilistic enhancement of coherence
• Criterion for a state to be distillable via stochastic incoherent operations
• Experimental demonstration of optimal probabilistic enhancement of quantum coherence
• Coherence filtration under strictly incoherent operations
• Symmetry-Based Quantum Circuit Mapping
• Quantum Speed Limit for Change of Basis
• Fundamental limits on concentrating and preserving tensorized quantum resources
• The Complementary Information Principle of Quantum Mechanics
• Coherence, superposition, and Löwdin symmetric orthogonalization
• Coherence via reiterated beam splitting
• Quantifying Coherence with Untrusted Devices
• Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
• Single-shot entanglement manipulation of states and channels revisited
• Golden states in resource theory of superposition
• Coordinately Assisted Distillation of Quantum Coherence in Multipartite System
• Impact of quadrature measurement on quantum coherence
• Incoherent Operations Enable State Transformations Impossible under Dephasing-covariant Incoherent Operations
• Direct estimation of quantum coherence by collective measurements
• Closed expressions for one-qubit states of convex roof coherence measures
• Distance-based measures and Epsilon-measures for measurement-based quantum resources