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We study correlations of observables in energy eigenstates of chaotic systemsof a large size $N$. We show that the bipartite entanglement of two subsystemsis quite strong, whereas macroscopic entanglement of the total system isabsent. It is also found that correlations, either quantum or classical, amongless than $N/2$ points are quite small. These results imply that chaotic statesare stable. Invariance of these properties under local operations is alsoshown.Comment: 5 pages, 2 figure

Correlations of Observables in Chaotic States of Macroscopic Quantum Systems