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Journal of Xinjiang Normal University

Another Discussion about Maximum Entangled—state ofSpin Quantities in Two—Particle System

Fan Fifi

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

a complete set of the spin quantities have three basic form in two-body operator which developed by ZEN Jin Yan.according to the local unitary transformation,we give the class of 1/2 spin quantities' entangled-state in two-particle system.the result show that a complete set of the spin quantities have for basic form,and the degree of entanglement is not changing in the same entangled-superposition -state form.

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a complete set of the spin quantities have three basic form in two-body operator which developed by ZEN Jin Yan.according to the local unitary transformation,we give the class of 1/2 spin quantities' entangled-state in two-particle system.the result show that a complete set of the spin quantities have for basic form,and the degree of entanglement is not changing in the same entangled-superposition -state form.
As the simultaneous eigenstates of a complete set of commuting observables (CSCO) consisting of threebody operators of the form σ1ασ2βσrsγ, the construction of entangled states for a three-particle system is investigated. It is shown that there exist 54 different sets of operators (each containing four commuting three-body operators with their product being -1) and any three members of each set constitute a CSCO. It is found that 54 different sets of maximally entangled states can be constructed, including the usual GHZ (Greenberg-Horne-Zeilinger) state as a special case. Once a preferential representation is adopted, all of them can be expressed as a GHZ-like form. Moreover, there also exist 18sets of partially entangled states, where only two particles are entangled.
As the simultaneous eigenstates of a complete set of commuting observables (CSCO) consisting of three-body operators of the form , the construction of entangled states for a three-particle system is investigated. It is shown that there exist 54 different sets of operators (each containing four commuting three-body operators with their product being -1) and any three members of each set constitute a CSCO. It is found that 54 different sets of maximally entangled states can be constructed, including the usual GHZ (Greenberg-Horne-Zeilinger) state as a special case. Once a preferential representation is adopted, all of them can be expressed as a GHZ-like form. Moreover, there also exist 18 sets of partially entangled states, where only two particles are entangled.
Firstly，we discuss a scheme for teleportation of a three-particle entangled W state via a two-particle and a three-particle entangled state. Then，in accordance with the principle of superposition and transformation operators，the three-particle entangled W state is expanded by Bell bases and the teleportation can be realized. The relation of transformation operators with unitary operation is discussed. The necessary condition for realizing the teleportation is that the transformation operators have inverse operators.
In accordance with the principle of superposition，for the teleportation of an arbitrary three-particle state via three pair nonmaximally entangled particles, the system state of particles can be expanded by Bell bases and transformation operator, and the teleportation can be realized only by performing a inverse transformation. The relation of transformation operators with unitary operation is discussed. The necessary condition to realize the teleportation is that the transformation operators have inverse operators.
By properties of independence state vector in quantum mechanics, a theory to produce entanglement is put forward for the first time and the definition of entangled state and the basic forms of entangledment for multiparticle system are given. Finally the definition is given of entangled degree for basic form entangled state and the formula is derived of entangled degree for two and three_particles system. Furthermore, the criterion of disentangled state for three particles system is described.
We characterize and classify the quantum states of a pair of spin-½ particles in terms of the entanglement of the pair. We describe a general strategy for classifying the quantum states of entangled systems, and apply it to the simplest entangled system available - a pair of spin-½ particles. The method is based on local unitary transformations. We give a set of six parameters that describe an arbitrary pure state of a pair of spins, one of which is the entanglement of the pair. We discuss visual representations of the state of this system, and propose a visualization using a Bloch sphere for each subsystem and a disc to record the `shared' information.