Study Of The Binegativity Of Quantum States In 2(?)2 And 2(?)3 Systems

In quantum entanglement theory,finding a good entanglement measure and studying the evolution of entanglement of quantum states in quantum noise environment are very helpful for us to better understand and use quantum entanglement.It was argued that binegativity is might be a good quantifier of entanglement.This thesis is the research on the binegativity of quantum states in 2(?)2 and 2(?)3 systems.Firstly,we give the analytic formula of the binegativity of arbitrary X-type quantum state in 2 (?)2 system.Next,we study the evolution of concurrence,negativity and binegativity of two kinds of X-type quantum states in 2 (?) 2 system under three kinds of 2 (?) 2 quantum noise channels.Then,we study the properties of the binegativity and the relationship between the binegativity and the negativity of quantum states in 2 (?) 3 system.Finally,we study the evolution of negativity and binegativity of a class of quantum states in 2 (?) 3 system under three kinds of 2 (?) 3 quantum noise channels.Our results support the hypothesis that binegativity is a good entanglement measure.In the first chapter,we briefly introduce the basic knowledge related to this thesis,including quantum states,density operators and entanglement measure,etc.In the second chapter,we introduce the definition,properties of binegativity and the relationship between the binegativity and the negativity.In the third chapter,we calculate the binegativity of several kinds of mixed states in 2 (?) 2 system and compare them with their concurrence and negativity.We find that compared with concurrence of these 2-qubit mixed states,their binegativity and negativity are more similar with the change of parameters.In the fourth chapter,we give the analytic formula of the binegativity of arbitrary X-type quantum state in 2 (?) 2 system and give the analytic formula of the concurrence,negativity and binegativity of the final state under three kinds of 2 (?) 2 quantum noise channels.In the fifth chapter,we study the evolution of the binegativity of two kinds of X-type quantum states in 2 (?) 2 system under three kinds of 2 (?) 2 quantum noise channels and compare them with the evolution of their concurrence and negativity.We find that with the increase of the noise parameters of the channels,concurrence,negativity and binegativity of the final states decrease gradually,and compared with concurrence of these two kinds of initial states,the evolution of their binegativity and negativity under noise channels is more similar.In the sixth chapter,firstly,we study the binegativity of quantum states in 2 (?) 3 systems,give and prove several properties of the binegativity of quantum states in 2 (?) 3 system,the relationship between the binegativity and the negativity.Then,we calculate the binegativity of a class of quantum states in 2 (?) 3 system and compare it with its negativity.We find that the binegativity and the negativity of such 2 (?) 3 quantum state are very similar with the change of parameters.In the seventh chapter,we study the evolution of the binegativity of a class of quan-tum states in 2(?)3 system undre three kinds of 2(?)3 quantum noise channels and compare it with the evolution of its negativity.We find that the binegativity and the negativi-ty of the final state decrease gradually with the increase of the noise parameters of the channels,the evolution of the binegativity and the negativity of the initial state under the quantum noise channels is very similar.