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Chinese Physics Letters

Quantum Discord-Breaking Channels

Chunmei Yao, Zhi He, Zhihua Chen, Jianjun Nie

Published Sep 1, 2013• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0256-307x/30/9/090302

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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.
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.
We identify and characterize all the local quantum channels that preserves the set of classical states, i.e., does not create any quantum correlations. At first we show that the quantum correlations cannot be created from without if and only if the local quantum channel preserves the commutativity, i.e., the images of any two commuting states also commute. And then we provide an operational necessary and sufficient criterion for a known quantum channel to preserve the commutativity as well as a single observable to witness an arbitrary unknown commutativity-preserving channel. All the distance-based measures for quantum correlations, e.g., the geometric measure, are non-increasing while the quantum discord defined by von Neumann measurements can be increasing or decreasing under local commutativity-preserving channels.
Quantum discord (QD) is one of the main quantum correlations in quantum information theory. In this paper, we show that a local channel cannot create QD for zero QD states of size d ⩾ 3 if and only if either it is a completely decohering channel or it is a nontrivial isotropic channel. For the qubit case this property is an additional characteristic of 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 Hu et al for the case of d ⩾ 3 and improve the result proposed by Streltsov et al for the qubit case.
A typical bipartite quantum protocol, such as EPR-steering, relies on two quantum features, entanglement of states and incompatibility of measurements. Noise can delete both of these quantum features. In this work we study the behavior of incompatibility under noisy quantum channels. The starting point for our investigation is the observation that compatible measurements cannot become incompatible by the action of any channel. We focus our attention to channels which completely destroy the incompatibility of various relevant sets of measurements. We call such channels incompatibility breaking , in analogy to the concept of entanglement breaking channels. This notion is relevant especially for the understanding of noise-robustness of the local measurement resources for steering.
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 inevitable interaction between quantum systems and environment induces effects of decoherence which may be so strong as to destroy any initial entanglement between the systems, a phenomenon known as "entanglement breaking". Here we show the simplest examples where the combination of two entanglement-breaking channels into a joint correlated-noise environment reactivates the distribution of entanglement, with classes of entangled states which are perfectly transmitted from a middle station (Charlie) to two remote stations (Alice and Bob). Surprisingly, this reactivation is induced by the presence of purely-classical correlations in the joint environment, whose state is separable with zero discord. This paradoxical effect is proven for quantum systems with Hilbert spaces of any dimension, both finite and infinite.