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arXiv:1406.2723 · Journal of the Korean Physical Society

Local quantum uncertainty of SU(2) invariant states

E. Faizi, Bahram Ahansaz

Published Dec 1, 2015• 8 citations
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Abstract

In this research, we investigated the quantum correlation in SU (2) invariant quantum spin systems by using the local quantum uncertainty (LQU). The SU (2) invariant quantum spin states are invariant under global rotations of the subsystems, and in real physical systems, such states arise from states of isotropic spin systems in thermal equilibrium. We derive an analytic expression for the LQU of (2 j + 1) ⊗ 2 and (2 j + 1) ⊗ 3 quantum spin systems with SU (2) symmetry.

DOI
10.3938/jkps.67.2033

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Computing the entanglement of formation of a bipartite state is generally difficult, but special symmetries of a state can simplify the problem. For instance, this allows one to determine the entanglement of formation of Werner states and isotropic states. We consider a slightly more general class of states, rotationally symmetric states, also known as SU(2)-invariant states. These states are invariant under global rotations of both subsystems, and one can examine entanglement in cases where the subsystems have different dimensions. We derive an analytic expression for the entanglement of formation of rotationally symmetric states of a spin-jjj particle and a spin-12{1\over2}21​ particle. We also give expressions for the I-concurrence, I-tangle, and convex-roof-extended negativity.
Local quantum uncertainty is defined as the minimum amount of uncertainty in measuring a local observable for a bipartite state. It provides a well-defined measure of pairwise quantum correlations in quantum systems and has operational significance in quantum metrology. In this work, we analytically derive the expression of local quantum uncertainty for two-qubit [Formula: see text] states which are of paramount importance in various fields of quantum information. As an illustration, we consider two-qubit states extracted from even and odd spin coherent states.
We analyze the entanglement of SU(2)-invariant density matrices of two spins S1,{S}_{1},S1​, S2{S}_{2}S2​ using the Peres-Horodecki criterion. Such density matrices arise from thermal equilibrium states of isotropic-spin systems. The partial transpose of such a state has the same multiplet structure and degeneracies as the original matrix with the eigenvalue of largest multiplicity being non-negative. The case S1=S,{S}_{1}=S,S1​=S, S2=1/2{S}_{2}=1/2S2​=1/2 can be solved completely and is discussed in detail with respect to isotropic Heisenberg spin models. Moreover, in this case the Peres-Horodecki criterion turns out to be a sufficient condition for nonseparability. We also characterize SU(2)-invariant states of two spins of length 1.
Abstract Many measures of quantum correlations have been introduced so far, and now their properties are carefully studied both theoretically and experimentally. The most important among them are quantum entanglement and quantum discord. Recently, it was shown that the Wigner–Yanase skew information and quantum Fisher information also can serve as measures of nonclassical correlations. These discordlike measures are called local quantum uncertainty (LQU) and interferometric power or local quantum Fisher information (LQFI), correspondingly. In this paper the behavior of LQU and LQFI is considered at thermal equilibrium of the two-qubit Heisenberg models in the absence and presence of an external magnetic field; these cases correspond to the Bell-diagonal and general X states, respectively.
Computing the entanglement of formation of a bipartite state is generally difficult, but special symmetries of a state can simplify the problem. For instance, this allows one to determine the entanglement of formation of Werner states and isotropic states. We consider a slightly more general class of states, rotationally symmetric states, also known as SU(2)-invariant states. These states are invariant under global rotations of both subsystems, and one can examine entanglement in cases where the subsystems have different dimensions. We derive an analytic expression for the entanglement of formation of rotationally symmetric states of a spin-jjj particle and a spin-1over2{1\\over2}1over2 particle. We also give expressions for the I-concurrence, I-tangle, and convex-roof-extended negativity.