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arXiv:1211.4805 · Physical Review A

Power of quantum channels for creating quantum correlations

Tahereh Abad, Vahid Karimipour, Laleh Memarzadeh

Published Dec 18, 2012• 19 citations
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Abstract

Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semiclassical channel [Phys. Rev. Lett. 107, 170502 (2011)]. We find the power of any given local channel for producing quantum correlations on an initially classically correlated state. We introduce a computable measure for quantifying the quantum correlations in quantum-classical states, which is based on the noncommutativity of ensemble states in one party of the composite system. Using this measure we show that the amount of quantum correlations produced is proportional to the classical correlations in the initial state. The power of an arbitrary channel for producing quantum correlations is found by averaging over all possible initial states. Finally, we compare our measure with the geometrical measure of quantumness for a subclass of quantum-classical sates, for which we have been able to find a closed analytical expression.

DOI
10.1103/physreva.86.062316

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Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semiclassical channel [Phys. Rev. Lett. 107, 170502 (2011)]. We find the power of any given local channel for producing quantum correlations on an initially classically correlated state. We introduce a computable measure for quantifying the quantum correlations in quantum-classical states, which is based on the noncommutativity of ensemble states in one party of the composite system. Using this measure we show that the amount of quantum correlations produced is proportional to the classical correlations in the initial state. The power of an arbitrary channel for producing quantum correlations is found by averaging over all possible initial states. Finally, we compare our measure with the geometrical measure of quantumness for a subclass of quantum-classical sates, for which we have been able to find a closed analytical expression.
We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channels this is indeed the case: The amount of quantum correlations can only decrease under the action of unital channels. However, nonunital channels (e.g., such as dissipation) can create quantum correlations for some initially classical states. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintuitively, local decoherence can generate quantum correlations.
We define quantum-correlating power (QCP) of a local quantum channel acting on the left part of a bipartite quantum system as the maximum amount of left quantum correlation that can be created by this channel. We prove that for any local channel, the optimal input state, which corresponds to the maximum quantum correlation in the output state, must be a classical-classical state. Further, the single-qubit channels with maximum QCP can be found in the class of channels which take their optimal input states to rank-two quantum-classical states. A superactivation property of QCP, that is, two zero-QCP channels can constitute a positive-QCP channel, is observed and discussed for single-qubit phase damping channels. The analytic expression for QCP of single-qubit amplitude damping channel is obtained.
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.
We prove the condition for local trace-preserving channels to create quantum correlation from initially classical states. For two-qubit states, the necessary and sufficient condition for a channel that cannot create quantum correlation in any initially classical state is that it is either a completely decohering channel or a mixing channel. For states in higher dimensions, we show that even a mixing channel can create quantum correlation from a classically correlated state. Our results reveal that mixedness is important for creation of quantum correlation in high-dimension quantum systems.
This thesis explores ways in which quantum channels and correlations (of both classical and quantum types) manifest themselves, and also studies the interplay between these two aspects in various physical settings. Quantum channels represent all possible evolutions of states allowed by quantum mechanics while correlations are intrinsic (nonlocal) properties of composite systems. There are four main problems that are addressed (i) the role played by initial system-bath correlations on the subsystem dynamics of an open quantum system, (ii) computation of correlations for two-qubit X-states, (iii) the robustness of non-Gaussian entanglement under symmetric local noisy attenuator and amplifier channels, and finally, (iv) the connection between nonclassicality breaking and entanglement breaking for single-mode bosonic Gaussian channels.
Quantum correlations typically decrease with increasing noise, although classical correlators (CCors) may rise for a particular class of states with noise. To analyse the behavior of classical correlation (CC) in the presence of local noise, we scrutinize the set of classical correlators, axiomatic CC measures like classical discord, and local work for Haar uniformly generated states. Like quantum correlation measures, we illustrate that when noise levels rise, the average value of the CC measures for noisy output states obtained from random input states decreases for most of the channels. We also demonstrate a connection between the CCors of the noise-affected multipartite states that are produced and the CCors of the initial states that exhibit exponential, polynomial, and constant behavior as the noise level changes. Moreover, based on CCors of the generalised N-qubit W state as input, we determine a method to discriminate between the quantum channels, namely phase damping, depolarizing, and amplitude damping channels. We also relate classical, quantum, and total correlation measures that exhibit a comparable reaction to decoherence for generic states.