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arXiv:1203.6149 · Physical Review A

Quantum correlating power of local quantum channels

Xueyuan Hu, Heng Fan, Dong Zhou, Wu‐Ming Liu

Published Mar 29, 2013• 67 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.032340

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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 investigate the superadditivity property of quantum-correlating power (QCP), which is the power of generating quantum correlation by a local quantum channel. We prove that, when two local quantum channels are used in parallel, the QCP of the composed channel is no less than the sum of QCP of the two channels. For local channels with zero QCP, the superactivation of QCP is a fairly common effect, and it is proven to exist widely except for the trivial case where both of the channels are completely decohering channels or unitary operators. For general quantum channels, we show that the (not-so-common) additivity of QCP can be observed for the situation where a measuring-and-preparing channel is used together with a completely decohering channel.
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We study two distinct diagnostics of bipartite quantum channels: the average fidelity between a desired state and noisy output across different classes of input states, and generation of entanglement from pure product input states, quantified by well-defined entangling power. These diagnostics are generally independent, but together they provide a more complete description of bipartite channels. We show that the fidelity averaged over any local-unitary orbit with fixed Schmidt coefficients for equal local dimensions is completely determined by the average input-output fidelity and its restriction to product inputs. We also introduce concurrence- and negativity-based entangling power for two-qubit channels, prove their convexity and monotonicity under local postprocessing, and show that, unlike the previously proposed linear-entropy quantity, they vanish for all separable channels. Representative separable and nonseparable channels are investigated. Finally, we generalize our definitions of entangling power to nonproduct inputs, and provide an analytical lower bound for the concurrence-based entanglement variation, showing its effectiveness with specific examples.
We discuss the interconnections between basic correlation measures of a bipartite quantum state and basic information characteristics of a quantum channel, focusing on the benefits of these interconnections for solving specific problems concerning the characteristics of both types. We describe properties of the (unoptimized and optimized) quantum discord in infinite-dimensional bipartite systems. In particular, using the generalized Koashi–Winter relation, a simple condition is obtained that guarantees that a state with zero quantum discord is quantum-classical. Two possible definitions of the quantum discord for states with infinite one-way classical correlation are proposed and analysed. The generalized versions of Koashi–Winter and Xi–Lu–Wang–Li relations are used to obtain advanced continuity bounds for the Holevo information at the outputs of a channel and its complementary channel (as functions of a channel for a given ensemble of input states), for the Holevo capacity and the unregularized private capacity of a quantum channel depending either on the input dimension or on the input energy bound. We also discuss the properties of quantum channels which are “doppelgangers” of the monotonicity of the quantum discord and the entropy reduction of a local measurement under quantum channels acting on an unmeasured subsystem.
We show an experimental procedure to certify the classical capacity for noisy qubit channels. The method makes use of a fixed bipartite entangled state, where the system qubit is sent to the channel input and the set of local measurements, ${\ensuremath{\sigma}}_{x}\ensuremath{\bigotimes}{\ensuremath{\sigma}}_{x}, {\ensuremath{\sigma}}_{y}\ensuremath{\bigotimes}{\ensuremath{\sigma}}_{y}$, and ${\ensuremath{\sigma}}_{z}\ensuremath{\bigotimes}{\ensuremath{\sigma}}_{z}$, is performed at the channel output and the ancilla qubit, thus without resorting to full quantum process tomography. The witness to the classical capacity is then achieved by reconstructing sets of conditional probabilities, noise deconvolution, and classical optimization of the pertaining mutual information. The performance of the method to provide lower bounds to the classical capacity is tested by a two-photon polarization entangled state in Pauli channels and amplitude damping channels. The measured lower bounds to the channels are in high agreement with the simulated data, which take into account both the experimental entanglement fidelity $F=0.979\ifmmode\pm\else\textpm\fi{}0.011$ of the input state and the systematic experimental imperfections.