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Old and New Concepts of Physics

Squeezed and Entangled States of a single Spin

Barış Öztop, Alexander A. Klyachko, A.S. Shumovsky

Published Jul 3, 2007• 0 citations
Publisher

Abstract

We show correspondence between the notions of spin squeezing and spin entanglement. We propose a new measure of spin squeezing. We consider a number of physical examples.
DOI
10.2478/v10005-007-0020-0

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The approach to extend the notion of entanglement for characterizing the properties of quantum correlations in the state of a single qudit is presented. New information and entropic inequalities, such as the subadditivity condition, strong subadditivity condition, and monotonicity of relative entropy for a single qudit corresponding to an arbitrary spin state with spin j are discussed. The idea to employ quantum correlations in the single-qudit state, such as the entanglement, for developing a new quantum technique in quantum computing and quantum communication is proposed. Examples of qutrit and qudit with j = 3/2 are considered.
Particle number fluctuations, no matter how small, are present in experimental setups. One should rigorously take these fluctuations into account, especially for entanglement detection. In this context, we generalize the spin-squeezing inequalities introduced by G. T\'oth et al. [Phys. Rev. Lett. 99, 250405 (2007).]. These new inequalities are fulfilled by all separable states even when the number of particles is not constant and may present quantum fluctuations. These inequalities are useful for detecting entanglement in many-body systems when the superselection rule does not apply or when only a subspace of the total system Hilbert space is considered. We also define general dichotomic observables for which we obtain a coordinate-independent form of the generalized spin-squeezing inequalities. We give an example where our generalized coordinate-independent spin-squeezing inequalities present a clear advantage over the original ones.