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Research on the Structure of Mutually Unbiased Based and Their Applications

Author: YanFei
Tutor: YangMingï¼›CaoZhuoLiang
School: Anhui University
Course: Physical Electronics
Keywords: The quantum No partial base Quantum state reconstruction of Entangled structure Quantum logic gates
CLC: O413.1
Type: PhD thesis
Year: 2011
Downloads: 38
Quote: 0
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1980s, quantum mechanics is applied to the field of information generated and developed an emerging interdisciplinary science - quantum information science. In quantum information science, the state of motion of microscopic particles called quantum state, it is a concrete manifestation of the quantum information, the core unit to play the role in quantum information science. With a trace of a Hermitian matrix to describe the state of the quantum system. Informed unknown quantum state information, it is necessary to determine the quantum state, that a lot of the same quantum state backup several different base measurement. Then based on the measurement results to determine the matrix elements of the density matrix. For a quantum system, the measurement base, therefore, is the best measurement of how measurement-based group (ie, measurement results without waste) has important practical significance. People only find primes dimensional system and primes power-dimensional system is the best measurement of the base, ie no partial measurement base, while the non-prime numbers and non-prime number of power-dimensional system, no partial base exist problems, currently also no clear conclusion. Therefore, based on the characteristics of the partial-its application, the doctoral thesis conducted a study of the following aspects: a proposed state based on the unbiased measurement-Victoria optimal quantum particle system to reconstruct the physical program. Unbiased base applied to quantum state reconstruction process to achieve optimal quantum state reconstruction. Existing quantum state reconstruction process, there is a lot of information about waste, the reason is there is a certain degree of overlap between the quantum measurement results in the reconstruction process. Unbiased based measurements in the reconstruction process, we can see the information in the existing quantum state reconstruction process based on the definition of partial-overlap or waste will be completely eliminated, and therefore heavier unbiased based measurement-based quantum states Frame must be optimal. Use of the prime power dimensional system based on finite field theory Unbiased base solution method, we obtain the specific form of single and multiple three-level systems (qutrits) all Unbiased base of, and designed to achieve these unbiased base The sequence of measurements of quantum logic gates (that is easy to implement a single and two-qutrits logic gates), which proposed to achieve the optimal solution for single and multiple three-level system quantum state reconstruction. The advantage of this program is to eliminate the existing state of the information of the reconfiguration scheme waste, thus greatly reducing the number of measurements required and the operation time, so that the quantum state reconstruction process more simple. Second, multiple three-state system Unbiased base the entanglement structure and achieve unbiased measurement of physical complexity. It can be seen from the the three qutrits system without partial group form the entangled structure (i.e., the association between the various subsystems) is more complicated, but also depending on the entangled structure, surprisingly found that the above method without partial yl not only in the form of the unbiased base. For three qutrits System, there are five groups of different entangled structure unbiasedness group form. Free migraine-based measurements of physical complexity (physical complexity proportional to the entanglement unbiased basis decomposition as a direct product of the basis for calculating the required joint operation number) bound to partial-entangled structure, so in order to optimal state reconstruction of a real sense, it is necessary to select from this the five groups Unbiased base in a set of physical complexity lowest measurement-based as the optimal state reconstruction process. Through a lot of detailed analytical calculation, we find the optimal unbiased measurement base, and gives the group an unbiased basis decomposition as a direct product of the calculation base sequence of operations for all quantum logic gates. The single qutrit logic gates and two qutrits these logic gates can be realized as we know it and experiment, so the sequence of these logic gates proposed would undoubtedly optimal quantum state reconstruction experiments provide important reference. Three, three three-dimensional systems of different the entangled structure Unbiased base form of the conversion. We take advantage of the joint unitary operation to achieve the conversion between the different high-dimensional system the entangled structure Unbiased base form of which reveals the relationship between the a different structure Unbiased base form of. Which will have a particular unbiased measurement-based laboratory has practical significance.

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