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Entanglement and nonclassicality for multimode radiation-field states

Ivan, Solomon J and Chaturvedi, S and Ercolessi, E and Marmo, G and Morandi, G and Mukunda, N and Simon, R (2011) Entanglement and nonclassicality for multimode radiation-field states. In: Physical Review A, 83 (3).

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Official URL: http://pra.aps.org/abstract/PRA/v83/i3/e032118


Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multimode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beam splitters, in a transparent manner. For single-mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beam splitter, these conditions turn exactly into signatures of negativity under partial transpose (NPT) entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two-mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beam-splitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three-mode beam-splitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.

Item Type: Journal Article
Publication: Physical Review A
Publisher: The American Physical Society
Additional Information: Copyright of this article belongs to The American Physical Society.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 19 Apr 2011 05:30
Last Modified: 19 Apr 2011 05:30
URI: http://eprints.iisc.ac.in/id/eprint/36944

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