TRACE INEQUALITIES AND QUANTUM ENTROPY: An introductory course

By Eric A. Carlen. 2009

330 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability, Quantum Computing

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Citations in the corpus

Fast and Furious Convergence: Stochastic Second Order Methods under Interpolation (2019, methodology): “Now we have the following expected decrease of the function value for one update, by the convexity of ω and using Jensen’s inequality, apply Jensen’s inequality using the convexity of (cid:107)·(cid:107) H for some H (cid:23) 0 and that ω is monotonically increasing on the positive domain and the fa”
Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance (2016, background): “∗-subalgebra A of Mn(C), there is the conditional expectation EA which is the orthogonal projection in HM n(C) onto HA [71]. This may be written as an average over the unitaries in the commutant of A [9, 70]; the connected component of this group Uthat contains the identity is a Lie subgroup of SU(n”
Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries (2016, background): “9 in [Car10] and the comments following it.”
Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy (2013, neutral): “King’s proof in turn exploits the following LiebThirring trace inequality [45] (see also [12]), which holds for B ≥ 0, any operator C , and for α ≥ 1: Tr{(C BC†)α} ≤ Tr{(C†C)α Bα}.”
An Analog of the 2-Wasserstein Metric in Non-Commutative Probability Under Which the Fermionic Fokker–Planck Equation is Gradient Flow for the Entropy (2012, background): “10) in [6]) that the entropy Tr(B logB), defined for density matrices acting on C for some m ≥ 1, is maximized by B if and only if B is a pure state, i.”