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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Assessing Higher-order Quantum Polarization Correlations using Multipole Expansions

Luis Lorenzo Sánchez-Soto

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We use a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the first one corresponding to the classical picture on the Poincaré sphere. In this way we formulate a whole hierarchy of measures that properly assess higher-order polarization correlations.

DOI
10.1364/cqo.2013.t2a.3

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We use a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the first one corresponding to the classical picture on the Poincaré sphere. In this way we formulate a whole hierarchy of measures that properly assess higher-order polarization correlations.
We advocate for a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the first one corresponding to the classical picture on the Poincare sphere. We employ the particular case of the QQQ function to formulate a whole hierarchy of measures that properly assess higher-order polarization correlations.
We capitalize on a multipolar expansion of the polarization density matrix, in which multipoles appear as successive moments of the Stokes variables. When all the multipoles up to a given order KKK vanish, we can properly say that the state is KthK\mathrm{th}Kth-order unpolarized, as it lacks of polarization information to that order. First-order unpolarized states coincide with the corresponding classical ones, whereas unpolarized to any order tally with the quantum notion of fully invariant states. In between these two extreme cases, there is a rich variety of situations that are explored here. The existence of hidden polarization emerges in a natural way in this context.
We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.