Speaker
Milan Mosonyi, Budapest University of Technology and Economics
Abstract
The trade-off relations between the two types of error probabilities in binary i.i.d. quantum state discrimination can be expressed by single-copy formulas in terms of the Petz-type and the sandwiched Rényi divergences of the two states representing the two hypotheses. In the non-i.i.d. setting, the error exponents can usually be expressed in terms of regularized Rényi divergences, which do not admit explicit formulas in general. Here, we consider a class of states, quasifree states on fermionic lattices, and give explicit formulas for a wide range of regularized Rényi divergences, including alpha-z, log-Euclidean, maximal, measured, and the recently introduced integral Rényi divergences. We show that the case where there is a single mode at each lattice site becomes asymptotically classical, with all the different types of regularized Rényi-divergences being equal, while in the case of multiple modes per site, non-commutativity persists under regularization, and all the different types of Rényi divergences give different regularized values in general.
Milan Mosonyi, Budapest University of Technology and Economics
Abstract
The trade-off relations between the two types of error probabilities in binary i.i.d. quantum state discrimination can be expressed by single-copy formulas in terms of the Petz-type and the sandwiched Rényi divergences of the two states representing the two hypotheses. In the non-i.i.d. setting, the error exponents can usually be expressed in terms of regularized Rényi divergences, which do not admit explicit formulas in general. Here, we consider a class of states, quasifree states on fermionic lattices, and give explicit formulas for a wide range of regularized Rényi divergences, including alpha-z, log-Euclidean, maximal, measured, and the recently introduced integral Rényi divergences. We show that the case where there is a single mode at each lattice site becomes asymptotically classical, with all the different types of regularized Rényi-divergences being equal, while in the case of multiple modes per site, non-commutativity persists under regularization, and all the different types of Rényi divergences give different regularized values in general.