Quantum entanglement and coherence are two fundamental resources for quantum information processing. Recent results clearly demonstrate their relevance in quantum technological tasks, including quantum communication and quantum algorithms. In this Letter we study the role of quantum coherence for quantum state redistribution, a fundamental task where two parties aim to relocate a quantum particle by using a limited amount of quantum communication and shared entanglement. We provide general bounds for the resource rates required for this process, and show that these bounds are tight under additional reasonable constraints, including the situation where the receiving party cannot use local coherence. While entanglement cannot be directly converted into local coherence in our setting, we show that entanglement is still useful for local coherence creation if an additional quantum channel is provided, and the optimal protocol for local coherence creation for any given amount of quantum communication and shared entanglement is presented. We also discuss possible extensions of our methods to other scenarios where the receiving party is limited by local constraints, including theories of thermodynamics and asymmetry.Quantum entanglement and coherence are two fundamental resources for quantum information processing. Recent results clearly demonstrate their relevance in quantum technological tasks, including quantum communication and quantum algorithms. In this Letter we study the role of quantum coherence for quantum state redistribution, a fundamental task where two parties aim to relocate a quantum particle by using a limited amount of quantum communication and shared entanglement. We provide general bounds for the resource rates required for this process, and show that these bounds are tight under additional reasonable constraints, including the situation where the receiving party cannot use local coherence. While entanglement cannot be directly converted into local coherence in our setting, we show that entanglement is still useful for local coherence creation if an additional quantum channel is provided, and the optimal protocol for local coherence creation for any given amount of quantum communication and shared entanglement is presented. We also discuss possible extensions of our methods to other scenarios where the receiving party is limited by local constraints, including theories of thermodynamics and asymmetry.

arXiv:1804.04915Apr 13, 20187 citations

Quantum Coherence and Measurement Theory

Daniel F. Walls, Gerard J Milburn

Springer eBooksDec 6, 20072 citations

Coherence measure: Logarithmic coherence number

Zhengjun Xi, Shanshan Yuwen

We introduce a measure of coherence which is extended from the coherence rank via the standard convex roof construction; we call it the logarithmic coherence number. This approach is parallel to the Schmidt measure in entanglement theory. We study some interesting properties of the logarithmic coherence number and show that this quantifier can be considered as a proper coherence measure. We find that the logarithmic coherence number can be calculated exactly for a large class of mixed states. We also discuss the relationships between the logarithmic coherence number and other coherence quantifiers, e.g., the relative entropy of coherence, the ${l}_{1}$ -norm coherence, and average fidelity coherence. We give the relationship between coherence and entanglement in a bipartite system, and our results can be generalized to multipartite settings. Finally, we give that the creation of entanglement with bipartite incoherent operations is bounded by the logarithmic coherence number of the initial system during the process.We introduce a measure of coherence which is extended from the coherence rank via the standard convex roof construction; we call it the logarithmic coherence number. This approach is parallel to the Schmidt measure in entanglement theory. We study some interesting properties of the logarithmic coherence number and show that this quantifier can be considered as a proper coherence measure. We find that the logarithmic coherence number can be calculated exactly for a large class of mixed states. We also discuss the relationships between the logarithmic coherence number and other coherence quantifiers, e.g., the relative entropy of coherence, the ${l}_{1}$-norm coherence, and average fidelity coherence. We give the relationship between coherence and entanglement in a bipartite system, and our results can be generalized to multipartite settings. Finally, we give that the creation of entanglement with bipartite incoherent operations is bounded by the logarithmic coherence number of the initial system during the process.

arXiv:1811.02242Physical Review AFeb 28, 201925 citations

Generalized spectroscopy; coherence, superposition, and loss

Johan Åberg, Daniel K. L. Oi

We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We find that loss channels constructed using linear optics form a special subclass. We suggests a generalized spectroscopy where, in analogy with the absorption spectrum, we measure a "coherence loss spectrum" and a "superposition creation spectrum". The theory is illustrated with examples.We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We find that loss channels constructed using linear optics form a special subclass. We suggests a generalized spectroscopy where, in analogy with the absorption spectrum, we measure a "coherence loss spectrum" and a "superposition creation spectrum". The theory is illustrated with examples.

arXiv:quant-ph/0703203Mar 22, 20071 citation

Detecting coherence with respect to general quantum measurements

Yu‐Cheng Chen, Jiong Cheng, Wen-Zhao Zhang +1 more

arXiv:2208.05133Science China Information SciencesJul 3, 20234 citations

{l}_{1}

-norm coherence, and average fidelity coherence. We give the relationship between coherence and entanglement in a bipartite system, and our results can be generalized to multipartite settings. Finally, we give that the creation of entanglement with bipartite incoherent operations is bounded by the logarithmic coherence number of the initial system during the process.