Coherent preorder of quantum states

Abstract

As an important quantum resource, quantum coherence play key role in quantum information processing. It is often concerned with manipulation of families of quantum states rather than individual states in isolation. Given two pairs of coherent states $({\rho }_1,{\rho }_2)$ and $({\sigma }_1,{\sigma }_2)$, we are aimed to study how can we determine if there exists a strictly incoherent operation $\Phi$ such that $\Phi ({\rho }_i)={\sigma }_i,i=1,2$. This is also a classic question in quantum hypothesis testing. In this note, structural characterization of coherent preorder under strongly incoherent operations is provided. Basing on the characterization, we propose an approach to realize coherence distillation from rank-two mixed coherent states to $q$-level maximally coherent states. In addition, one scheme of coherence manipulation between rank-two mixed states is also presented.

arXiv comment14 pages,73 references, to appear in Quantum Information & Computation 2020

References in corpus (27)

• Decoherence, einselection, and the quantum origins of the classical
• Fundamental limitations for quantum and nano thermodynamics
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• Frozen Quantum Coherence
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
• Truly work-like work extraction
• Reversible transformations from pure to mixed states, and the unique measure of information
• Max- relative entropy of coherence: an operational coherence measure
• Quantifying Superposition
• Genuine quantum coherence
• Stable macroscopic quantum superpositions
• Structure of the resource theory of quantum coherence
• Using and reusing coherence to realize quantum processes
• Probabilistic distillation of quantum coherence
• Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes
• Interferometric visibility and coherence
• One-Shot Coherence Dilution
• Comparison of quantum statistical models: equivalent conditions for sufficiency
• Generic bound coherence under strictly incoherent operations
• Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources
• Enhancing coherence of a state by stochastic strictly incoherent operations
• Optimal distillation of quantum coherence with reduced waste of resources
• Quantum state redistribution with local coherence