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arXiv:1012.3075 · International Journal of Quantum Information

CLASSICALITY WITNESS FOR TWO-QUBIT STATES

Jonas Maziero, ROBERTO M. SERRA

Published Apr 1, 2012• 24 citations
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Abstract

In the last few years one realized that if the state of a bipartite system can be written as ∑i,j pij|ai〉〈ai| ⊗ |bj〉〈bj|, where {|ai〉} and {|bj〉} form orthonormal basis for the subsystems and {pij} is a probability distribution, then it possesses at most classical correlations. In this article we introduce a nonlinear witness providing a sufficient condition for classicality of correlations (absence of quantum discord) in a broad class of two-qubit systems. Such witness turns out to be necessary and sufficient condition in the case of Bell-diagonal states. We show that the witness introduced here can be readily experimentally implemented in nuclear magnetic resonance setups.

DOI
10.1142/s0219749912500281

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In the last few years one realized that if the state of a bipartite system can be written as ∑i,j pij|ai〉〈ai| ⊗ |bj〉〈bj|, where {|ai〉} and {|bj〉} form orthonormal basis for the subsystems and {pij} is a probability distribution, then it possesses at most classical correlations. In this article we introduce a nonlinear witness providing a sufficient condition for classicality of correlations (absence of quantum discord) in a broad class of two-qubit systems. Such witness turns out to be necessary and sufficient condition in the case of Bell-diagonal states. We show that the witness introduced here can be readily experimentally implemented in nuclear magnetic resonance setups.
Quantum correlations in composite and separable quantum systems are characterized by non-vanishing quantum discord. We demonstrate the necessary and sufficient conditions for existence of hermitian witness operators for quantum discord, bypassing the problem of non-convexity of the set of all classical states. We propose an example of a linear witness which can detect quantum correlations in large classes of separable bipartite systems. Decomposition of the witness in terms of a small number of locally measurable operators as shown here, paves the way for experimental detection of quantum correlations beyond entanglement.
Quantum discord represents a correlation beyond classicality that could be useful for many quantum information tasks, and therefore is viewed as a valuable quantum resource. Theoretically, whether a bipartite quantum state has a non-zero amount of quantum discord or not can be determined once its density matrix is given. Experimentally, however, it is not easy to perform a reliable tomography on the state, especially when considering the imperfection of devices and the high dimensionality of system. Here, inspired by the so-called dimension witness, we propose a new approach using uncharacterized measurements to witness quantum discord of an unknown bipartite state within arbitrary dimension system. Furthermore, 2×22 \times 22×2 measurements are sufficient for any bipartite state of arbitrarily large dimension. For any two-qubit state, we show that the maximum of witness happens when one performs mutually orthogonal basis measurement on each qubit. Our method exhibits high robustness against device imperfections, such as error tolerance, indicating its experimental feasibility.
The threshold between classical and nonclassical two-qubit states is drawn at the place when these states can no longer be described by classical correlations, i.e., quantum discord or entanglement appear. However, to check if the correlations are classical (in terms of quantum discord and entanglement) it is sufficient to witness the lack of quantum discord because its zero value implies the lack of entanglement. We explain how the indicator of quantum discord introduced by Girolami and Adesso [Phys. Rev. Lett. 108, 150403 (2012)] can be practically measured in linear-optical systems using standard beam splitters and photon detectors. We study the efficiency of the setup assuming both ideal and real components and show that the efficiency of the proposed implementation is better than the full two-photon quantum tomography. Thus, we demonstrate that a class of experiments previously available on NMR platform can be implemented in optical systems.
The study of the connections between entanglement and non-classicality has seen an increasing interest in the last few years. Several forms of entanglement witnesses have been proposed to reveal and quantify the entangle ment of a particular state or a particular class of states. Non-classicality indicators have been proposed so as to quantify quantum correlations in two-qubit states. It has been demonstrated that there are interesting situations in which non-entangled states (i.e. separable) can behave in a non-classical way.
"We review the theoretical and the experimental researches aimed at quantifying or identifying quantum correlations in liquid-state nuclear magnetic resonance (NMR) systems at room temperature. We first overview, at the formal level, a method to determine the quantum discord and its classical counterpart in systems described by a deviation matrix. Next, we describe an experimental implementation of that method. Previous theoretical analysis of quantum discord decoherence had predicted the time dependence of the discord to change suddenly under the influence of phase noise. The experiment attests to the robustness of the effect, sufficient to confirm the theoretical prediction even under the additional influence of a thermal environment. Finally, we discuss an observable witness for the quantumness of correlations in two-qubit systems and its first NMR implementation. Should the nature, not the amount, of the correlation be under scrutiny, the witness offers the most attractive alternative."
The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.