Toward computability of trace distance discord

Ciccarello, F.; Tufarelli, T.; Giovannetti, V.

Abstract

It is known that a reliable geometric quantifier of discord-like correlations can be built by employing the so-called trace distance, which is used to measure how far the state under investigation is from the closest 'classical-quantum' state. To date, the explicit calculation of this indicator for two qubits has only been accomplished for states where the reduced density matrix of the measured party is maximally mixed, a class that includes Bell-diagonal states. Here, we first reduce the required optimization for a general two-qubit state to the minimization of an explicit two-variable function. Using this framework, we show that the minimum can be analytically worked out in a number of relevant cases, including quantum-classical and X states. This provides an explicit and compact expression for the trace distance discord of an arbitrary state belonging to either of these important classes of density matrices.

• Journal Article Type: Article
• Acceptance Date: Dec 9, 2013
• Online Publication Date: Jan 21, 2014
• Publication Date: Jan 21, 2014
• Deposit Date: Mar 13, 2018
• Publicly Available Date: Dec 3, 2018
• Journal: New Journal of Physics
• Electronic ISSN: 1367-2630
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 16
• Article Number: 013038
• DOI: https://doi.org/10.1088/1367-2630/16/1/013038
• Public URL: https://nottingham-repository.worktribe.com/output/1113857
• Publisher URL: http://iopscience.iop.org/article/10.1088/1367-2630/16/1/013038/meta