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arXiv:1907.05440

Quantum discord-breaking and discord-annihilating channels

Thao P. Le

Published Jul 11, 2019• 0 citations
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Abstract

Quantum discord-breaking channels were previously defined as the local channels that act on subsystem $A$ to produce classical-quantum states across system $AB$. However, unlike entanglement, discord is asymmetric. Here, we characterise the discord-breaking channels that act on subsystem $B$, thus completing the overall description of discord-breaking channels. We then introduce the notion of discord-annihilating channels, which act globally on system $AB$ to destroy quantum discord, and find their closed form. Discord-annihilating channels have clear operational description, involving subspace projections on subsystem $A$ and conditional preparation of fixed states on subsystem $B$.

DOI
10.48550/arxiv.1907.05440

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Quantum discord-breaking channels were previously defined as the local channels that act on subsystem AAA to produce classical-quantum states across system ABABAB. However, unlike entanglement, discord is asymmetric. Here, we characterise the discord-breaking channels that act on subsystem BBB, thus completing the overall description of discord-breaking channels. We then introduce the notion of discord-annihilating channels, which act globally on system ABABAB to destroy quantum discord, and find their closed form. Discord-annihilating channels have clear operational description, involving subspace projections on subsystem AAA and conditional preparation of fixed states on subsystem BBB.
Through comparisons with an entanglement breaking (EB) channel, we characterize the local quantum channels that destroy quantum correlations, especially for quantum discord, and give a detailed description of a discord-breaking (DB) channel. We prove that the quantum discord can be broken if and only if the local quantum channel is a commutativity-creating (CoC) channel. Then we show which kind of channels is a CoC channel, and address the relation between EB and DB channels. Furthermore we apply our results to three typical noise channels.
We introduce and investigate a family of entanglement-annihilating channels. These channels are capable of destroying any quantum entanglement within the system they act on. We show that they are not necessarily entanglement breaking. In order to achieve this result we analyze the subset of locally entanglement-annihilating channels. In this case, the same local noise applied on each subsystem individually is less entanglement annihilating (with respect to multi-partite entanglement) as the number of subsystems is increasing. Therefore, the bipartite case provides restrictions on the set of local entanglement-annihilating channels for the multipartite case. The introduced concepts are illustrated on the family of single-qubit depolarizing channels.
The role played by quantum discord in mixed-state computation is widely debated since, in spite of evidence of its importance in creating quantum advantages, even in the absence of entanglement, there are not direct proofs of its necessity in these computational tasks. Recently, the presence of discord was shown to be necessary and sufficient for remote state preparation for a broad class of quantum channels [Daki\ifmmode \acute{c}\else \'{c}\fi{} et al., Nat. Phys. 8, 666 (2012)]. Here, we show that this property is not universal. There are states whose discord cannot be considered as a quantum resource since it has been produced locally that are useful for remote state preparation, and there are bona fide discordant states that are of no help.
A generalization of quantum discord to multipartite systems is proposed. A key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems. It is by construction zero only for systems with classically correlated subsystems and is a non-negative quantity, giving a measure of the total nonclassical correlations in the multipartite system with respect to a fixed measurement ordering. For the tripartite case, we show that the discord can be decomposed into contributions resulting from changes induced by nonclassical correlation breaking measurements in the conditional mutual information and tripartite mutual information. The former gives a measure of the bipartite nonclassical correlations and is a non-negative quantity, while the latter is related to the monogamy of the nonclassical correlations.
Abstract. In an initially uncorrelated mixed separable bi-partite system, quantum correlations can emerge under the action of a local measurement or local noise [1]. We analyze this counter-intuitive phenomenon using quantum discord as a quantifier. We then relate changes in quantum discord to system-environment correlations between the system in a mixed state and some purifying environmental mode using the Koashi-Winter inequality. On this basis, we suggest an interpretation of discord as a byproduct of transferring entanglement and correlations around the different subsystems of a global pure state.
In an initially uncorrelated mixed separable bi-partite system, quantum correlations can emerge under the action of a local measurement or local noise [ 1 ]. We analyse this counter-intuitive phenomenon using quantum discord as a quantifier. We then relate changes in quantum discord to system–environment correlations between the system in a mixed state and some purifying environmental mode using the Koashi–Winter inequality. On this basis, we suggest an interpretation of discord as a byproduct of transferring entanglement and correlations around the different subsystems of a global pure state.