Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction
arXiv:2002.12004 · doi:10.1109/TIT.2021.3064009
Abstract
We give the first systematic study on the second order asymptotics of the operational task of coherence distillation with and without assistance. In the unassisted setting, we introduce a variant of randomness extraction framework where free incoherent operations are allowed before the incoherent measurement and the randomness extractors. We then show that the maximum number of random bits extractable from a given quantum state is precisely equal to the maximum number of coherent bits that can be distilled from the same state. This relation enables us to derive tight second order expansions of both tasks in the independent and identically distributed setting. Remarkably, the incoherent operation classes that can empower coherence distillation for generic states all admit the same second order expansions, indicating their operational equivalence for coherence distillation in both asymptotic and large block length regime. We then generalize the above line of research to the assisted setting, arising naturally in bipartite quantum systems where Bob distills coherence from the state at hand, aided by the benevolent Alice possessing the other system. More precisely, we introduce a new assisted incoherent randomness extraction task and establish an exact relation between this task and the assisted coherence distillation. This strengthens the one-shot relation in the unassisted setting and confirms that this cryptographic framework indeed offers a new perspective to the study of quantum coherence distillation. Likewise, this relation yields second order characterizations to the assisted tasks. As by-products, we show the strong converse property of the aforementioned tasks from their second order expansions.
arXiv commentv2 added the second order analysis on the assisted coherence distillation, one author is added; comments are welcome
References in corpus (56)
- Quantum entanglement
- Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
- 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
- Tight Finite-Key Analysis for Quantum Cryptography
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- 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
- Quantum Information Processing with Finite Resources -- Mathematical Foundations
- One-Shot Classical-Quantum Capacity and Hypothesis Testing
- 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
- Relating the Resource Theories of Entanglement and Quantum Coherence
- Assisted distillation of quantum coherence
- A quantitative theory of coherent delocalization
- The Chernoff lower bound for symmetric quantum hypothesis testing
- The quantum capacity of channels with arbitrarily correlated noise
- Entanglement of assistance and multipartite state distillation
- Quantifying Superposition
- Second-order asymptotics for quantum hypothesis testing
- Numerical approach for unstructured quantum key distribution
- Entanglement and coherence in quantum state merging
- Genuine quantum coherence
- One-shot coherence distillation
- Quantum Lost and Found
- Stable macroscopic quantum superpositions
- The private capacity of quantum channels is not additive
- Towards resource theory of coherence in distributed scenarios
- Using and reusing coherence to realize quantum processes
- Probabilistic distillation of quantum coherence
- One-Shot Coherence Dilution
- Quantum Coding with Finite Resources
- Inverting quantum decoherence by classical feedback from the environment
- Experimental cyclic inter-conversion between Coherence and Quantum Correlations
- Practical Evaluation of Security for Quantum Key Distribution
- Second-order asymptotics for source coding, dense coding and pure-state entanglement conversions
- Experimentally Obtaining Maximal Coherence Via Assisted Distillation Pro cess
- Generic bound coherence under strictly incoherent operations
- One-Shot Coherence Distillation: Towards Completing the Picture
- Non-asymptotic assisted distillation of quantum coherence
- The l1 Norm of Coherence of Assistance
- Classical capacities of quantum channels with environment assistance
- On environment-assisted capacities of quantum channels
- Channel correction via quantum erasure
- General theory of environment-assisted entanglement distillation
- Distributed Private Randomness Distillation
- Secure uniform random number extraction via incoherent strategies
- Assisted concentration of Gaussian resources
- Correcting quantum channels by measuring the environment
- Quantum state redistribution with local coherence
- Hierarchy of quantum operations in manipulating coherence and entanglement
- Coherence of assistance and regularized coherence of assistance