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

Single Qutrit Entanglement

Sinem Binicioǧlu, Alexander A. Klyachko, A.S. Shumovsky

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We discussed a recent approach to quantum entanglement. The approach is based on presetting of basic observables of quantum system. Entangled states are interpreted as states with maximal amount of uncertainty of all basic observables.
DOI
10.1364/cqo.2007.cmi50

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Abstract The absolute values of polynomial SLOCC invariants (which always vanish on separable states) can be seen as entanglement measures. We study the case of real 3-qutrit systems and discover a new set of maximally entangled states (from the point of view of maximizing the hyperdeterminant). We also study the basic fundamental invariants and find real 3-qutrit states that maximize their absolute values. It is notable that the Aharonov state is a simultaneous maximizer for all three fundamental invariants. We also study the evaluation of these invariants on random real 3-qutrit systems and analyze their behavior using histograms and level-set plots. Finally, we show how to evaluate these invariants on any 3-qutrit state using basic matrix operations.
In this brief report we show the new Bell-Clauser-Horne inequality for two entangled three dimensional quantum systems (so called qutrits). This inequality is violated by a maximally entangled state of two qutrits observed via symmetric three input and three output port beamsplitter only if the amount of noise in the system equals 11−632≈0.308{11-6\sqrt3 \over 2}\approx 0.308211−63​​≈0.308. This is in perfect agreement with the previous numerical calculations presented in Kaszlikowski {\it et. al.} Phys. Rev. Lett. {\bf 85}, 4418 (2000).