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Journal of sciences, Islamic Republic of Iran

An Entanglement Study of Superposition of Qutrit Spin-Coherent States

Mojtaba Jafarpour

Published Jun 1, 2011• 5 citations
OpenAlex

Abstract

Considering generalized concurrence as the criterion of entanglement, we study entanglement properties of superposition of two qutrit coherent states, as a function of their amplitudes. These states may attain maximum entanglement or no entanglement at all, depending on the choice of the parameters involved. The states revealing maximum entanglement also display the maximum violations of the Bell-CHSH inequalities.

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Considering generalized concurrence as the criterion of entanglement, we study entanglement properties of superposition of two qutrit coherent states, as a function of their amplitudes. These states may attain maximum entanglement or no entanglement at all, depending on the choice of the parameters involved. The states revealing maximum entanglement also display the maximum violations of the Bell-CHSH inequalities.
We study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality for two-spin systems, of arbitrary spins j1{j}_{1}j1​ and j2{j}_{2}j2​, prepared in an entanglement of spin-coherent states of each of the spins. We show that the Bell-CHSH inequality is quite robustly violated for a wide range of values of the parameters that specify the spin-coherent states, and, for a particular choice of these parameters, maximal violations are obtained. That is, the violations can reach the Tsirelson bound, 222\sqrt{2}22​, for any choices of the spins.
Abstract In this paper, we investigate quantum correlations in a qutrit-like superposition of spin coherent states. In particular, the quantum entanglement, the lower bound of the geometric measure of quantum discord, and the lower bound of local quantum uncertainty for the superposition of spin coherent states are examined, and their properties are characterized and compared. The specific dependence of these different correlation quantities on the spin of the system, the coefficient parameters, and the involved coherence parameters is found. As a part of this analysis, conditions for enhanced quantum correlations of qutrit-like superposition states have been identified, which exposes the characteristics of the states based on which the quantum correlations can be controlled and improved.
Abstract In the present paper, based on the general analytical expression [arXiv:2412.03470] for the maximum of the CHSH expectation under local Alice and Bob spin-s measurements in a two-qudit state of dimension d = 2s + 1, s≥1/2, we analyze whether or not, under spin-1 measurements in an arbitrary two-qutrit state, the CHSH inequality is violated. We find analytically for a variety of pure nonseparable two-qutrit states and also, numerically for 1, 000, 000 randomly generated pure nonseparable two-qutrit states, that, under local Alice and Bob spin-1 measurements in each of these nonseparable states, including maximally entangled, the CHSH inequality is not violated. These results together with the spectral decomposition of a mixed state lead us to the Conjecture that, under local Alice and Bob spin-1 measurements, every nonseparable two-qutrit state, pure or mixed, does not violate the CHSH inequality. For a variety of pure two-qutrit states, we further find the values of their concurrence and compare them with the values of their spin-1 CHSH parameter, which determines violation or nonviolation by a two-qutrit state of the CHSH inequality under spin-1 measurements. This comparison indicates that, in contrast to spin- 1 2 measurements, where the spin- 1 2 CHSH parameter of a pure two-qubit state is increasing monotonically with a growth of its entanglement, for a pure two-qutrit state, this is not the case. In particular, for the two-qutrit GHZ state, which is maximally entangled, the spin-1 CHSH parameter is equal to 8 9 , while, for some separable pure two-qutrit states, this parameter can be equal to unity. Moreover, for the two-qutrit Horodecki state, the spin-1 CHSH parameter is equal to 4 2 / 21 < 1 regardless of the entanglement type of this mixed state.