Catalytic coherence transformations

Abstract

Catalytic coherence transformations allow the otherwise impossible state transformations using only incoherent operations with the aid of an auxiliary system with finite coherence which is not being consumed in anyway. Here we find the necessary and sufficient conditions for the deterministic and stochastic catalytic coherence transformations between pair of pure quantum states. In particular, we show that the simultaneous decrease of a family of Rényi entropies of the diagonal parts of the states under consideration are necessary and sufficient conditions for the deterministic catalytic coherence transformations. Similarly, for stochastic catalytic coherence transformations we find the necessary and sufficient conditions for achieving higher optimal probability of conversion. We, thus, completely characterize the coherence transformations amongst pure quantum states under incoherent operations. We give numerous examples to elaborate our results. We also explore the possibility of the same system acting as a catalyst for itself and find that indeed {\it self catalysis} is possible. Further, for the cases where no catalytic coherence transformation is possible we provide entanglement assisted coherence transformations and find the necessary and sufficient conditions for such transformations.

8 pages, 2 figures, 1 table, close to published version

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• Measuring Quantum Coherence with Entanglement
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Cited by in corpus (42)

• Quantum Coherence as a Resource
• Quantum Resource Theories
• Operational one-to-one mapping between coherence and entanglement measures
• Entanglement and coherence in quantum state merging
• A resource theory of superposition
• Genuine quantum coherence
• Energy Cost of Creating Quantum Coherence
• Probabilistic distillation of quantum coherence
• Catalytic quantum teleportation and beyond
• Coherence and asymmetry cannot be broadcast
• Catalytic Transformations of Pure Entangled States
• Catalysis of entanglement and other quantum resources
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Quantum coherence quantifiers based on the Rényi $\alpha$-relative entropy
• Coherence breaking channels and coherence sudden death
• Catalyst-Assisted Probabilistic Coherence Distillation for Mixed States
• Enhancing coherence of a state by stochastic strictly incoherent operations
• Coherence of quantum channels
• Relative Entropy and Catalytic Relative Majorization
• Amplifying asymmetry with correlated catalysts
• Resource theory of superposition: State transformations
• One-shot Coherence Distillation with Catalysts
• Complementary relation of quantum coherence and quantum correlations in multiple measurements
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Remote Creation of Quantum Coherence
• Catalytic Transformations in Coherence Theory
• Quantum coherence fluctuation relations
• Catalysis in Action via Elementary Thermal Operations
• Entanglement catalysis for quantum states and noisy channels
• Partial coherence versus entanglement
• Increasing the dimension of the maximal pure coherent subspace of a state via incoherent operations
• A hierarchy of thermal processes collapses under catalysis
• Resource engines
• Teleportation with Embezzling Catalysts
• No-go theorems for deterministic purification and probabilistic enhancement of coherence
• Communication with Quantum Catalysts
• Coherence, superposition, and Löwdin symmetric orthogonalization
• Quantifying imaginarity of quantum operations
• Catalytic transformations with finite-size environments: applications to cooling and thermometry
• Experimental demonstration of robustness of Gaussian quantum coherence
• Statistics of Entanglement Transformation with Hierarchies among Catalysts
• A finite sufficient set of conditions for catalytic majorization