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One-Shot Coherence Distillation.

Bartosz Regula¹, Kun Fang², Xin Wang²

¹School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.

Physical Review Letters

|July 21, 2018

Summary

This summary is machine-generated.

This study shows maximally incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO) equally distill quantum coherence in a single shot. Distillable coherence under MIO and DIO is efficiently computable and equals that of other operations for pure states.

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Area of Science:

Quantum Information Theory
Quantum Thermodynamics

Background:

Quantum coherence is a key resource in quantum information processing.
Understanding coherence distillation is crucial for quantum technologies.

Purpose of the Study:

To characterize one-shot quantum coherence distillation under different quantum operations.
To establish efficient computation methods for distillable coherence.
To introduce and analyze new coherence monotones.

Main Methods:

Analysis of one-shot coherence distillation.
Semidefinite programming for efficient computation.
Quantum hypothesis testing formulation.
Introduction of generalized coherence monotones.

Main Results:

Maximally incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO) exhibit equal power in one-shot coherence distillation.
One-shot distillable coherence under MIO and DIO is efficiently computable via semidefinite programming.
A family of coherence monotones is introduced, generalizing robustness and modified trace distance.
For pure states, one-shot distillable coherence is equal across MIO, DIO, strictly incoherent, and general incoherent operations.

Conclusions:

The study provides a comprehensive characterization of one-shot coherence distillation.
Efficient computational tools and new monotones are established for quantifying coherence.
The findings reveal fundamental equalities in coherence distillation for pure states across various operational frameworks.