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The Entanglement Measure of Multiqubit Pure State in Quantum Errorcorrecting Code
Author: HuLiJuan
Tutor: GaoTing
School: Hebei Normal
Course: Applied Mathematics
Keywords: quantum state quantum entanglement concurrence reduced density matrix
CLC: O413.1
Type: Master's thesis
Year: 2010
Downloads: 55
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Abstract
The entanglement measure of the three common multiqubit pure states in the quantumerrorcorrecting codes is started. Quantum entanglement is not only a key resource in quantum information processing and quantum computation, but also one of the most fascinatingfeatures of quantum theory. It is a most valuable research content. There are three commonquantum errorcorrecting codes, fivequbit quantum errorcorrecting code, sevenqubit quantumerrorcorrecting codeSteane and ninequbit quantum errorcorrecting codeShor. The fivequbitquantum errorcorrecting code is the smallest code that is capable of protecting against a singleerror. So it’s a much useful code.First, we introduce some useful background knowledge. Specifically, we describe the successfully entanglement measures, which we obtained the entanglement characterization of thetwobody quantum systems and the threebody quantum systems. And it also explain the definition of entanglement degree of multiqubit pure state.In the second chapter, we calculate the multibody entanglement degree of the previousthree common multiqubit pure states of the quantum errorcorrecting code states. We givethe concurrences of the fivequbit quantum errorcorrecting code, sevenqubit quantum errorcorrecting codeSteane and ninequbit quantum errorcorrecting codeShor. Dure to the largenumber of the reduceddensity operators, it causes great difficulty for us to calculate. So, wefirst started with a useful conclusion of Schmidt decomposition, which makes the calculationreduce the double. In the multibody entanglement of the three multiqubit pure states, the multibody entanglement of the ninequbit quantum errorcorrecting code is the most complicated.Because the number of the classification of the reduceddensity operators is so many, we muststudy carefully with the special composed structure of the ninequbit quantum errorcorrectingcode and make sure that the classification is accurate.In the three chapter, we give the highertangle of the three multiqubit pure states, i.e.In the last chapter, we made the classification for highdimensional twobody entanglementof the fivequbit quantum errorcorrecting code state, sevenqubit quantum errorcorrectingcodeSteane and ninequbit quantum errorcorrecting codeShor respectively. In this chapter,we must note the coefficient matrix of the quantum state and classification. These are the keysto success. Although the two subsystems carried out classification according to the numberof particles contained, different sequencing of two subsystems cause different coefficient ma trixes. Luckily, it don’t impact the final result. So, we only note the impact that caused differentparticles selecting in the subsystems. Because the number of the selected particles is large, wemust carefully analyse to find out the laws. Among of them, the number of the classification ofninequbit quantum errorcorrecting code state is large. And the coefficient matrix is the mostcomplex. So, the writing of coefficient matrixe must be careful.The main conclusions of this paper are that the three multiqubit pure states don’t havetwoqubit entanglement of the real twobody. But they all have highdimensional twobody entanglement, as well as truly multibody entanglement. And threebody tangle of these threemultiqubit pure states is one. But the degree of the multibody entanglement don’t increasewith the number of particle increasing. The highdimensional twobody entanglement of thefivequbit quantum pure state has two classes. The highdimensional twobody entanglementof the sevenqubit quantum pure state has three classes. And the highdimensional twobodyentanglement of the ninequbit quantum pure state has four classes. In which there is a kindof entanglement, the degree is zero. That is to say, in such combination, there is no entanglement between the two subsystems. So we can know the ninequbit quantum pure state issemiseparable.

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Quantum theory > Quantum mechanics ( wave mechanics,matrix mechanics )
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