Three Approximate Entropies

Details Three Approximate Entropies Three Approximate Entropies

Apr 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aps..apro12001l&link_type=abstract

American Physical Society, April Meeting, Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American As

Astronomy and Astrophysics

Astrophysics

Scientific paper

In 1993,(E. & T. Lubkin, Int.J.Theor.Phys. 32), 993 (1993) we gave exact mean trace of squared density matrix P for 3 models of an n-dimensional part of an nK-dimensional pure state. Models named: random nK ket (Haar); pure-pure driven by random Hamiltonian (Gauss); Gauss with n,K coupling reset small (weak). Neglecting higher powers of P gives the approximation: ln(n)- defines deficit = (n - 1)/2 which yields deficits, Haar: n((n+K)/(nK+1) - 1)/2 = ( n - 1/n - 1/K + 1/nnK )/2K + Order(f[n] / KKK); Gauss: (n/2)( (n+K)/(nK+1) + 2(nK+1-n-K)/nK(nK+1)(nK+3)) - 1/2 = ( n - 1/n - 1/K + 2/nK - 1/nnK )/2K + Order( f[n]/KKK ); weak: (n/2)(2(K+n)/((K+1)(n+1))) - 1/2 = (n/(n+1))(1 + (n-1)/K - (n-1)/KK + Order(f[n]/KKK)) - 1/2 [unreliable]. These would stay poor even as Karrow∞ unless deficit << 1 bit. Haar and Gauss come out good, but weak has too large a deficit. Though many authors (beginning with Don Page(D.N.Page, PRL 71), 1291 (1993)) have found the exact for Haar, I haven't yet seen exact for Gauss or for weak.

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