title: Quantum coherence of steered states.
abstract: Lying at the heart of quantum mechanics, coherence has recently been studied as a key resource in quantum information theory. Quantum steering, a fundamental notion originally considered by Schödinger, has also recently received much attention. When Alice and Bob share a correlated quantum system, Alice can perform a local measurement to 'steer' Bob's reduced state. We introduce the maximal steered coherence as a measure describing the extent to which steering can remotely create coherence; more precisely, we find the maximal coherence of Bob's steered state in the eigenbasis of his original reduced state, where maximization is performed over all positive-operator valued measurements for Alice. We prove that maximal steered coherence vanishes for quantum-classical states whilst reaching a maximum for pure entangled states with full Schmidt rank. Although invariant under local unitary operations, maximal steered coherence may be increased when Bob performs a channel. For a two-qubit state we find that Bob's channel can increase maximal steered coherence if and only if it is neither unital nor semi-classical, which coincides with the condition for increasing discord. Our results show that the power of steering for coherence generation, though related to discord, is distinct from existing measures of quantum correlation.
authors.affiliation: School of Information Science and Engineering, and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Jinan, 250100, P. R. China.
authors.forename: Xueyuan
authors.initials: X
authors.lastname: Hu
authors.affiliation: Controlled Quantum Dynamics Theory, Department of Physics, Imperial College London, London SW7 2AZ, UK.
authors.forename: Antony
authors.initials: A
authors.lastname: Milne
authors.affiliation: School of Information Science and Engineering, and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Jinan, 250100, P. R. China.
authors.forename: Boyang
authors.initials: B
authors.lastname: Zhang
authors.affiliation: Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Heng
authors.initials: H
authors.lastname: Fan