Deterministic Coherence Distillation

Abstract

Coherence distillation is one of the central problems in the resource theory of coherence. In this Letter, we complete the deterministic distillation of quantum coherence for a finite number of coherent states under strictly incoherent operations. Specifically, we find the necessary and sufficient condition for the transformation from a mixed coherent state into a pure state via strictly incoherent operations, which recovers a connection between the resource theory of coherence and the algebraic theory of majorization lattice. With the help of this condition, we present the deterministic coherence distillation scheme and derive the maximum number of maximally coherent states obtained via this scheme.

arXiv comment5 pages, 1 figure

References in corpus (30)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Quantum Mechanics helps in searching for a needle in a haystack
• Quantum cryptography: Public key distribution and coin tossing
• Advances in Quantum Metrology
• Quantum-enhanced measurements: beating the standard quantum limit
• Quantifying Coherence
• Quantum Coherence as a Resource
• Conditions for a class of entanglement transformations
• Operational Resource Theory of Coherence
• Intrinsic randomness as a measure of quantum coherence
• The general structure of quantum resource theories
• Quantum coherence and geometric quantum discord
• Max- relative entropy of coherence: an operational coherence measure
• A quantitative theory of coherent delocalization
• Conditions for coherence transformations under incoherent operations
• Alternative framework for quantifying coherence
• Operational one-to-one mapping between coherence and entanglement measures
• Genuine quantum coherence
• Quantum processes which do not use coherence
• One-shot coherence distillation
• Probabilistic distillation of quantum coherence
• One-Shot Coherence Dilution
• Generic bound coherence under strictly incoherent operations
• Non-asymptotic assisted distillation of quantum coherence
• Deterministic entanglement concentration
• Error exponents for entanglement concentration
• Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources
• Enhancing coherence of a state by stochastic strictly incoherent operations
• Detecting coherence via spectrum estimation
• Flag Additivity in Quantum Resource Theories

Cited by in corpus (37)

• Tunable phonon induced steady state coherence in a double quantum dot
• Experimental progress on quantum coherence: detection, quantification, and manipulation
• Asymmetric twin-field quantum key distribution
• Catalyst-Assisted Probabilistic Coherence Distillation for Mixed States
• Validating and controlling quantum enhancement against noise by motion of a qubit
• One-shot Coherence Distillation with Catalysts
• Efficient estimation of multipartite quantum coherence
• Correlation-induced coherence and its use in detecting quantum phase transitions
• Average skew information-based coherence and its typicality for random quantum states
• Examining the validity of Schatten-$p$-norm-based functionals as coherence measures
• Skew information-based coherence generating power of quantum channels
• Optimal probabilistic distillation of quantum coherence
• Experimental demonstration of one-shot coherence distillation: High-dimensional state conversions
• Geometry of skew information-based quantum coherence
• Increasing the dimension of the maximal pure coherent subspace of a state via incoherent operations
• The block-coherence measures and the coherence measures based on positive-operator-valued measures
• Conversion of Gaussian states under incoherent Gaussian operations
• Approximate distillation of quantum coherence
• Pairwise Measurement Induced Synthesis of Quantum Coherence
• Exploring quantum properties of bipartite mixed states under coherent and incoherent basis
• Entropic Diagram Characterization of Quantum Coherence: Degenerate Distillation and the Maximum Eigenvalue Uncertainty Bound
• No-go theorems for deterministic purification and probabilistic enhancement of coherence
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Extremal elements of a sublattice of the majorization lattice and approximate majorization
• 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
• Beating the repeaterless bound with adaptive measurement-device-independent quantum key distribution
• Coherence, superposition, and Löwdin symmetric orthogonalization
• State convertibility under genuinely incoherent operations
• Golden states in resource theory of superposition
• Incoherent Operations Enable State Transformations Impossible under Dephasing-covariant Incoherent Operations
• Probabilistic Coherence Transformation Under Strictly Incoherent Operation
• Strictly incoherent operations for one-qubit systems
• Closed expressions for one-qubit states of convex roof coherence measures
• Simplest non-additive measures of quantum resources
• Distance-based measures and Epsilon-measures for measurement-based quantum resources