K. R. W. Jones, "Quantum limits to information about states for finite dimensional Hilbert space," Journal of Physics A, vol. 24, pp. 121--130, 1991. Home/Search Document Not in Database Summary Related Articles Check |
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Quantum Information Theory - Barnum, III (1998) (Correct)
....with U b unitary and U b jbi = j b i: With a uniform prior, the average disturbance by measurement becomes D = 1 Gamma Z d Omega X b p(bj )jh j b ij 2 = 1 Gamma X b g b Z d Omega jh jbij 2 jh j b ij 2 : 4.11) The integral on the RHS is easily done using Eq. 12) of Jones [39]; its value is: 1 jhbj b ij 2 d(d 1) 4.12) Hence D = 1 Gamma X b g b 1 jhbj b ij 2 d(d 1) 1 Gamma d P b g b jhbj b ij 2 d(d 1) 4.13) Each term in the sum is maximized where j b i = e iOE b jbi, giving F max = 2 d 1 ; D min = d Gamma 1 d 1 : ....
....the Scrooge ensemble (which is the ensemble for which the accessible information is minimal, among the ensembles for a given density operator) 38] the uniform ensemble being the Scrooge ensemble for the unit density operator. I will present a different derivation using the methods of Jones [39]. The information gain from measurement is the mutual information between the 95 prior distribution and the measurement outcome, denoted H ( Psi : B) I will use this in the form: H(B : Psi) H(B) Gamma H(Bj Psi) 4.39) The fundamental probabilities from which this can be calculated are the ....
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K. R. W. Jones, "Quantum limits to information about states for finite dimensional Hilbert space," Journal of Physics A, vol. 24, pp. 121--130, 1991.
Information-Disturbance Tradeoff in Quantum Measurement on the.. - Barnum (2000) (Correct)
....except in three cases, for which the matrix elements in (28) are as follows: 1. i=j, l=m, i 6= l R d Omega jhij ij 2 jhlj ij 2 2. i=m, j=l, i 6= j R d Omega jhij ij 2 jhjj ij 2 3. i=j=l=m : R d Omega jhij ij 4 : 30) The integrals are easily done using Eq. 12) of Jones [18], which yields: Z d Omega jh jaij 2 jh jbij 2 = 1 jhajbij 2 d(d 1) 31) where jai ; jbi are any normalized, but not necessarily orthogonal or identical, vectors. For our cases 1 and 2; the matrix elements are 1=d(d 1) case 3 gives 2=d(d 1) We combine 1=2 times the case 3 ....
....accessible information is minimal [12] The uniform ensemble is the Scrooge ensemble for the uniform density operator I=d. Here I present a different derivation of the information gained by a finegrained measurement, which applies to the the uniform ensemble only and uses the methods of Jones [18]. The information gain from measurement is the mutual information between the prior distribution and the measurement outcome, denoted H ( Psi : B) I will use this in the form: H(B : Psi) H(B) Gamma H(Bj Psi) 37) This can be calculaated form the prior probability measure on states p(j i) ....
[Article contains additional citation context not shown here]
K. R. W. Jones, "Quantum limits to information about states for finite dimensional Hilbert space," Journal of Physics A, vol. 24, pp. 121--130, 1991.
Mean Dynamical Entropy of Quantum System Tends to.. - Slomczynski, Zyczkowski (Correct)
....Z Omega Z Omega jhjT y Gamma1 x jij 2 N ln jhjT y Gamma1 x jij 2 N dx dy = Gamma Z Omega jhjT z jij 2 N ln jhjT z jij 2 N dz: 4. 2) We can now apply the formula for the overlap of two SU(d) coherent states (see above) which enables us to use the result from Jones [17,18] who calculated generalized mean entropy of pure quantum state in d dimensional complex Hilbert space. Proceeding in this way we get H I = Gamma ln N M [ Psi (M d) Gamma Psi (M 1) 4.3) where N = dim(HM ) M d Gamma1 M ) and Psi is the digamma function, satisfying Psi(x 1) ....
....jhjT Gamma1 y UT x jij 2 N d (U) 1 C A dxdy = Gamma Z U(N) jhjV jij 2 N ln jhjV jij 2 N d (V ) 5. 7) We can calculate the last quantity utilizing the formulae for the distribution of hjU ji given by Ku s et al. 23] Otherwise, we can use the already mentioned result of Jones [18]. Applying one of these methods we get the following formula: hHU i U(N) Gamma ln N Psi (N 1) Gamma Psi (2) 5.8) Finally from (4.3) 5.5) and (5.8) we obtain the main result of this work: a lower and an upper bound for the mean dynamical entropy l b D H SU(d) dyn E u b ; 5.9) ....
K. R. W. Jones, Quantum limits to information about states for finite dimensional Hilbert space. J. Phys. A24, 121 (1991).
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