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 Schr{ö}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.

Published version

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Cited by in corpus (18)

• Quantum Coherence as a Resource
• Quantum coherence and geometric quantum discord
• Non-Local Advantage of Quantum Coherence
• Entanglement and coherence in quantum state merging
• Relative quantum coherence, incompatibility, and quantum correlations of states
• Evolution equation for quantum coherence
• Hierarchy of the nonlocal advantage of quantum coherence and Bell nonlocality
• Steered quantum coherence as a signature of quantum phase transitions in spin chains
• Nonlocal advantage of quantum coherence in high-dimensional states
• Quantum coherence of multiqubit states in correlated noisy channels
• Extracting quantum coherence via steering
• Finite-size scaling of coherence and steered coherence in the Lipkin-Meshkov-Glick model
• How the relativistic motion affects Einstein-Podolsky-Rosen steering
• Of Local Operations and Physical Wires
• Environment-induced quantum coherence spreading of a qubit
• The power of a control qubit in weak measurements
• Weak measurement effect on optimal estimation with lower and upper bound on relativistic metrology
• Frozen condition of quantum coherence