Random path intersections generated by collision and meeting of stable processes in thin time sets are characterized in terms of Hausdorff dimension and capacity.
Using the symbol calculus developed by Berezin, Kree and Raczka, it is shown that the algebra generated by the canonical commutation relation (CCR) is splitted into creation part and annhilation part with holomorphic ...Using the symbol calculus developed by Berezin, Kree and Raczka, it is shown that the algebra generated by the canonical commutation relation (CCR) is splitted into creation part and annhilation part with holomorphic and anti-bolomorphic symbols respectively. Further. in the Weyl representation of CCR, three Weyl operators will constitute an irreducible set of the fall CCR-algebra if some number theoretic conditions are satisfied.展开更多
A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces p...A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.展开更多
We illustrate the dichotomy of classical/quantum correlations by virtue of monogamy. More precisely, we show that correlations in a bipartite state are classical if and only it each party ot the state can be perfectly...We illustrate the dichotomy of classical/quantum correlations by virtue of monogamy. More precisely, we show that correlations in a bipartite state are classical if and only it each party ot the state can be perfectly correlated with other ancillary systems. In particular, this means that if there are quantum correlations between two parties, then the classical （as well as quantum） correlating capabilities of the two parties with other systems have to be strictly reduced.展开更多
文摘Random path intersections generated by collision and meeting of stable processes in thin time sets are characterized in terms of Hausdorff dimension and capacity.
文摘Using the symbol calculus developed by Berezin, Kree and Raczka, it is shown that the algebra generated by the canonical commutation relation (CCR) is splitted into creation part and annhilation part with holomorphic and anti-bolomorphic symbols respectively. Further. in the Weyl representation of CCR, three Weyl operators will constitute an irreducible set of the fall CCR-algebra if some number theoretic conditions are satisfied.
基金Supported by the National Natural Science Foundation of China under Grant No 10571166.
文摘A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.
基金Supported by the National Natural Science Foundation of China under Grant No 10771208, the Science Fund for Creative Research Groups under Grant No 10721101, and the Key Lab of Random Complex Structures and Data Science of Chinese Academy of Sciences under Grant No 2008DP173182.
文摘We illustrate the dichotomy of classical/quantum correlations by virtue of monogamy. More precisely, we show that correlations in a bipartite state are classical if and only it each party ot the state can be perfectly correlated with other ancillary systems. In particular, this means that if there are quantum correlations between two parties, then the classical （as well as quantum） correlating capabilities of the two parties with other systems have to be strictly reduced.
