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arXiv:0906.4187 · Quantum Information Processing

Tractable measure of nonclassical correlation using density matrix truncations

Akira SaiToh, Robabeh Rahimi, Mikio Nakahara

Published Nov 3, 2010• 3 citations
arXivHTMLPDF
DOI
10.1007/s11128-010-0208-8

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There is a commonly recognized paradigm in which a multipartite quantum system described by a density matrix having no product eigenbasis is considered to possess nonclassical correlation. Supporting this paradigm, we define two entropic measures of nonclassical correlation of a multipartite quantum system. One is defined as the minimum uncertainty about a joint system after we collect outcomes of particular local measurements. The other is defined by taking the maximum over all local systems about the minimum distance between a genuine set and a mimic set of eigenvalues of a reduced density matrix of a local system. The latter measure is based on an artificial game to create mimic eigenvalues of a reduced density matrix of a local system from eigenvalues of a density matrix of a global system. Numerical computation of these measures for several examples is performed.
A legitimate and easily computable measure of nonclassicality for the pure state of the single-mode electromagnetic field based on the standard deviation in the measurement of the homodyne rotated quadrature operator is proposed. The proposed quantity is an effective nonclassical area projected by the optical tomogram of the quantum state of light on to the optical tomographic plane. It is found that if the nonclassical area projected by the optical tomogram of a pure single-mode quantum state is greater than zero the state is strictly a nonclassical state and it is zero for the classical state. Nonclassical area spanned by the optical tomogram of nonclassical states of light such as Fock states, squeezed states, photon-added coherent states, and even and odd coherent states, have been evaluated theoretically. Nonclassical area projected by the optical tomogram of a quantum state of light may be experimentally tractable using the balanced homodyne detection of the quadrature operator of the field avoiding the reconstruction of density matrix or the quasiprobability distribution of the state.