Research On Entangling Rates And Mixing Rates

Quantum information theory is a combination of quantum mechanics and information science.This emerging and frontier theory involves the study of information processing.Entanglement is one of the most amazing phenomena in the quantum world.As a unique resource of quantum mechanics,it also plays a vital role in many significant applications of quantum information.Generation of entanglement by experiment provides help for the realization of quantum communication and quantum computers.Therefore,it is an important research direction in quantum information how to generate entanglement more efficiently.Bounding entangling rates and mixing rates is the main issue of this thesis.Entangling rate describes how fast entanglement can be produced and also scales the capability for a nonlocal Hamiltonian to generate entanglement.Mixing rate is a quantity which functions as an useful tool of analyzing entangling rate better.The main innovations and contributions of this thesis are as follows.As for entangling rates in the absence of ancillas,we mainly aim at some situations ignored and append the supplement for the sake of rigor and completeness.After numerical simulations,we also obtain the maximum of entangling rates when auxiliary systems do not exist.When taking into account the auxiliary systems,we derive bounds on mixing rates in a special case when the probabilistic ensemble of states is under certain restrictions.In this case we can prove the small incremental mixing conjecture with a constant c' = 1,which is improved over the previous results of which the tightest is c' = 2.Furthermore,we demonstrate a bound ?(?,H)?2 ||H|| log(d)for the small incremental entangling conjecture if d is sufficiently large.