Ergodic quantum dynamics, via a non-demolition coupling, generates EPR states with lower purity and higher operator-transfer capacity than infinite-temperature scramblers, with a parametric advantage when initial states are smooth in energy.
Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice
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abstract
We prove non-asymptotic lower bounds on the expectation of the maximum of $d$ independent Gaussian variables and the expectation of the maximum of $d$ independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (asymptotically optimal) non-asymptotic lower bound on the minimax regret of online learning with expert advice.
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Enhanced entanglement from quantum ergodicity
Ergodic quantum dynamics, via a non-demolition coupling, generates EPR states with lower purity and higher operator-transfer capacity than infinite-temperature scramblers, with a parametric advantage when initial states are smooth in energy.