Quantum coherence of steered states

TL;DR

This paper introduces a measure called maximal steered coherence to quantify how quantum steering can remotely generate coherence in a shared quantum system, revealing its relation to entanglement and discord.

Contribution

The paper defines and analyzes maximal steered coherence as a new measure for quantifying coherence generated through quantum steering, highlighting its properties and relation to other quantum correlations.

Findings

Maximal steered coherence vanishes for quantum-classical states.

It reaches a maximum for pure entangled states with full Schmidt rank.

Bob's channel can increase maximal steered coherence if and only if it is neither unital nor semi-classical.

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 Schr{\"o}dinger, 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.