Necessary and sufficient conditions for local creation of quantum correlation

TL;DR

This paper establishes the precise conditions under which local quantum operations can generate quantum correlations from classical states, providing a complete characterization of such channels in finite-dimensional systems.

Contribution

It proves that a local trace-preserving channel can create quantum correlation if and only if it does not preserve commutativity, and explicitly characterizes these channels for qubits and qutrits.

Findings

Necessary and sufficient condition for quantum correlation creation is non-commutativity preservation.

Explicit forms of commutativity-preserving channels for qubits and qutrits.

Identification of channels that can generate quantum correlations from classical states.

Abstract

Quantum correlation can be created by a local operation from some initially classical states. We prove that the necessary and sufficient condition for a local trace-preserving channel to create quantum correlation is that it is not a commutativity-preserving channel. This condition is valid for arbitrary finite dimension systems. We also derive the explicit form of commutativity-preserving channels. For a qubit, a commutativity-preserving channel is either a completely decohering channel or a mixing channel. For a three-dimensional system (qutrit), a commutativity-preserving channel is either a completely decohering channel or an isotropic channel.