0 Ju n 20 09 RANDOM QUANTUM CHANNELS II : ENTANGLEMENT OF RANDOM SUBSPACES , RÉNYI ENTROPY ESTIMATES AND ADDITIVITY PROBLEMS
نویسندگان
چکیده
In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and Winter to get violations of the additivity equalities for minimum output Rényi entropies. We show that random channels obtained by randomly coupling the input to a qubit violate the additivity of the p-Rényi entropy. For some sequences of random quantum channels, we compute almost surely the limit of their Schatten S1 → Sp norms.
منابع مشابه
Random Quantum Channels Ii: Entanglement of Random Subspaces, Rényi Entropy Estimates and Additivity Problems
In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and Winter to get violations of the additivity equalities for minimum output Rényi entropies. We show that random channels obtained by randomly coupling the inpu...
متن کاملComments on Hastings’ Additivity Counterexamples
3 Background on random states and channels 7 3.1 Probability distributions for states . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Probability distributions on the simplex ∆d . . . . . . . . . . . . . . . . . . . . . . 8 3.3 Estimates for μd,n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Probability distribution for random unitary channels . ....
متن کاملPerspectives in High Dimensions Schedule
s David Alonso-Gutiérrez On a different proof of Junge’s estimate for the isotropy constant of polytopes Tuesday 4:30–4:55 p.m. Abstract: It was proved by M. Junge that the isotropy constant of any symmetric polytope with 2N vertices is bounded by C logN . We give a different proof of this result, which shows that the same estimate is true when the polytope is nonsymmetric with N vertices. It w...
متن کاملDynamical Entropy for the Quantized CAT Map
We estimate the dynamical entropy for the quantized CAT map. It turns out that the result depends on the rotation parameter and positivity of the dynamical entropy demands asymptotic abelianness. Further the estimates ooer a counterexample to the additivity of the dynamical entropy for tensor products.
متن کاملTesting for additivity in partially linear regression with possibly missing responses
We consider a partially linear regression model with multivariate covariates and with responses that are allowed to be missing at random. This covers the usual settings with fully observed data and the nonparametric regression model as special cases. We first develop a test for additivity of the nonparametric part in the complete data model. The test statistic is based on the difference between...
متن کامل