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arXiv:0911.3460 · Physical Review A

Single-experiment-detectable nonclassical correlation witness

Robabeh Rahimi, Akira SaiToh

Published Aug 11, 2010• 38 citations
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Abstract

Recent progress in theories of quantum information has determined nonclassical correlation defined differently from the widely used entanglement as an important property to evaluate computation and communication with mixed quantum states. We introduce an operational method to detect nonclassical correlation of bipartite systems. In this method, we use particular maps analogous to the well-established entanglement witnesses. Thus, the maps are called nonclassical correlation witness maps. Furthermore, it is proved that such a map can be generally decomposed so that a single-run experiment is feasible for implementation in bulk-ensemble systems.

DOI
10.1103/physreva.82.022314

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Recent progress in theories of quantum information has determined nonclassical correlation defined differently from the widely used entanglement as an important property to evaluate computation and communication with mixed quantum states. We introduce an operational method to detect nonclassical correlation of bipartite systems. In this method, we use particular maps analogous to the well-established entanglement witnesses. Thus, the maps are called nonclassical correlation witness maps. Furthermore, it is proved that such a map can be generally decomposed so that a single-run experiment is feasible for implementation in bulk-ensemble systems.
A bipartite quantum system in a mixed state can exhibit nonclassical correlations which can go beyond quantum entanglement. While quantum discord is the standard measure of quantifying such general quantum correlations, the nonclassicality can be determined by simpler means via the measurement of witness operators. We experimentally construct a positive map to witness nonclassicality of two qubits in an NMR system. The map can be decomposed in terms of measurable spin magnetizations so that a single run of an experiment on an ensemble of spins suffices to detect the nonclassicality in the state, if present. We let the state evolve in time and use the map to detect nonclassicality as a function of time. To evaluate the efficacy of the witness operator as a means to detect nonclassicality, we measure quantum discord by performing full quantum-state tomography at each time instant and obtain a fairly good match between the two methods.
In this paper we provide an operational method to detect multipartite entanglement in ensemble-based quantum computing. This method is based on the concept of the entanglement witness. We decompose the entanglement witness for each class of multipartite entanglement into nonlocal operations in addition to local measurements. Individual single-qubit measurements are performed simultaneously; hence complete detection of entanglement is performed in a single-run experiment. In this sense, our scheme is superior to the generally used entanglement witnesses that require a number of experiments and preparation of copies of quantum state for detection of entanglement.
We develop a general strategy for the detection of nonclassical system-environment correlations in the initial states of an open quantum system. The method employs a dephasing map which operates locally on the open system and leads to an experimentally accessible witness for genuine quantum correlations, measuring the Hilbert-Schmidt distance between pairs of open system states. We further derive the expectation value of the witness for various random matrix ensembles modeling generic features of complex quantum systems. This expectation value is shown to be proportional to a measure for the quantum discord which reduces to the concurrence for pure initial states.
Several definitions of classicality are considered, such as P-representability, generalized coherent states and separable states. These notions are treated under a simple and general definition based on convex sets, which enables the use of the Hahn-Banach theorem to separate classical states from nonclassical ones. Nonclassicality linear witnesses are constructed, based on the observables available in a given physical situation. Some examples of nonclassical states are considered, with detection schemes available nowadays. Reviewing the concept of entanglement potential from a different perspective, it is shown that in some contexts an arbitrary single-system nonclassical state can be converted into a bipartite entangled state, provided a generalized controlled-displacement (e.g., beam-splitter, CNOT gate) is available. Also, this entanglement can be detected in a simple way using the nonclassicality witness of the original single-system state. Finally, we extend the discussion to multipartite states, proposing alternative ways to generate and classify multipartite entanglement.
We report on an experiment to detect nonclassical correlations in a highly mixed state. The correlations are characterized by the quantum discord and are observed using four qubits in a liquid-state nuclear magnetic resonance quantum information processor. The state analyzed is the output of a DQC1 computation, whose input is a single quantum bit accompanied by nnn maximally mixed qubits. This model of computation outperforms the best known classical algorithms and, although it contains vanishing entanglement, it is known to have quantum correlations characterized by the quantum discord. This experiment detects nonvanishing quantum discord, ensuring the existence of nonclassical correlations as measured by the quantum discord.
Quantum mechanics predicts the existence of correlations between composite systems that, although puzzling to our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect entanglement of many qubits. Here we propose to detect entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. We witness entanglement without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. To illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables.