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Physica Scripta

A study of correlation properties of multiqubit states by using a characteristic function

O. V. Belyaeva, A. S. Chirkin

Published Feb 11, 2013• 3 citations
Publisher

Abstract

We present calculations of the normally ordered characteristic function (NOCF) of Bose operators for the Greenberger–Horne–Zeilinger states and the Dicke ones. The NOCF is shown to contain information about two types of photon correlations: pseudoclassical and quantum ones. Quantum correlations are connected with interference terms of the NOCF, whereas pseudoclassical photon correlations and their cumulants satisfy the relations for classical random variables. We introduce a measure of the quantumness for entangled multimode states not related to the entropy approach. The maximum of the measure of quantumness is demonstrated to explain an intuitive choice of numeric values for the coefficients in a multiqubit state vector.

DOI
10.1088/0031-8949/87/03/038101

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We present calculations of the normally ordered characteristic function (NOCF) of Bose operators for the Greenberger–Horne–Zeilinger states and the Dicke ones. The NOCF is shown to contain information about two types of photon correlations: pseudoclassical and quantum ones. Quantum correlations are connected with interference terms of the NOCF, whereas pseudoclassical photon correlations and their cumulants satisfy the relations for classical random variables. We introduce a measure of the quantumness for entangled multimode states not related to the entropy approach. The maximum of the measure of quantumness is demonstrated to explain an intuitive choice of numeric values for the coefficients in a multiqubit state vector.
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Abstract Quantum correlations are central to the foundations of quantum physics and form the basis of quantum technologies. Here, our goal is to connect quantum correlations and computation: using quantum correlations as a resource for computation—and vice versa, using computation to test quantum correlations. We derive Bell-type inequalities that test the capacity of quantum states for computing Boolean functions within a specific model of computation and experimentally investigate them using 4-photon Greenberger–Horne–Zeilinger (GHZ) states. Furthermore, we show how the resource states can be used to specifically compute Boolean functions—which can be used to test and verify the non-classicality of the underlying quantum states. The connection between quantum correlation and computability shown here has applications in quantum technologies, and is important for networked computing being performed by measurements on distributed multipartite quantum states.
We measure high-order correlation functions of detected-photon numbers in the mesoscopic regime by means of hybrid photodetectors. The analytical expressions for correlations are evaluated in terms of quantities that can be experimentally accessed by a selfconsistent analysis of the detectors' outputs. We demonstrate that high-order correlations can be used to characterize the nature of the optical states, for instance by better discriminating between classical and quantum behavior even in critical situations, such as multimode twin-beam state. The results are in very good agreement with the theory, both for classical states and quantum states.
The entanglement quantification and classification of multipartite quantum states are two important research fields in quantum information. In this work, we study the entanglement of arbitrary-dimensional multipartite pure states by looking at the averaged partial entropies of various bipartite partitions of the system, namely, the so-called Manhattan distance (l1{l}_{1}l1​ norm) of averaged partial entropies (MAPE), and it is proved to be an entanglement measure for pure states. We connected the MAPE with the coefficient matrices, which are important tools in entanglement classification and reexpressed the MAPE for arbitrary-dimensional multipartite pure states by the nonzero singular values of the coefficient matrices. The entanglement properties of the nnn-qubit Dicke states, arbitrary-dimensional Greenberger-Horne-Zeilinger states, and D3n{D}_{3}^{n}D3n​ states are investigated in terms of the MAPE, and the relation between the rank of the coefficient matrix and the degree of entanglement is demonstrated for symmetric states by two examples.
Coherent states are the quantum states, which give the closest description to classical states. Since their superpositions show quantum properties, research on these states has been of great interest. In addition, having nonclassical properties is necessary for quantum correlations. In this paper, we focus on two-mode entangled coherent states which are out of phase, and study the nonclassical properties such as squeezing of quadrature operators, antibunching and oscillatory photon statistics. Then we discuss about their entanglement, which is a quantum correlation in different conditions and compare the results.