Necessary and sufficient conditions for local creation of quantum discord

Abstract

We show that a local channel cannot create quantum discord (QD) for zero QD states of size $d\ge 3$ if and only if either it is a completely decohering channel or it is a nontrivial isotropic channel. For the qubit case this propertiy is additionally characteristic to the completely decohering channel or the commutativity-preserving unital channel. In particular, the exact forms of the completely decohering channel and the commutativity-preserving unital qubit channel are proposed. Consequently, our results confirm and improve the conjecture proposed by X. Hu et al. for the case of $d\ge 3$ and improve the result proposed by A. Streltsov et al. for the qubit case. Furthermore, it is shown that a local channel nullifies QD in any state if and only if it is a completely decohering channel. Based on our results, some protocols of quantum information processing issues associated with QD, especially for the qubit case, would be experimentally accessible.

arXiv comment8 pages

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Cited by in corpus (8)

• Resource Destroying Maps
• Quantum processes which do not use coherence
• Discordlike correlation of bipartite coherence
• There is more to quantum interferometry than entanglement
• Coherence and quantum correlations measure sensitivity to dephasing channels
• Non-commutative measure of quantum correlations under local operations
• Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations
• When quantum channel preserves product states