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On Quantum Error-correcting Codes and Quantum Nonlocality

Author: TangWeiDong
Tutor: YuSiXia
School: University of Science and Technology of China
Course: Atomic and Molecular Physics
Keywords: Nonbinary Graph states Quantum Error Correcting Codes Quan-tum nonlocality GHZ nonlocality Bell inequality GHZ Paradoxes Quantumcontextuality Kochen-Specker inequality
CLC: TN911.22
Type: PhD thesis
Year: 2013
Downloads: 54
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Quantum theory is essential for us to understand the behaviors of the micro-scopic scales. The earliest version of it has been formulated in the first decade of last century, but in nowadays many interesting topics in it remain unsettled, such as nonlocality of many-partite systems. Moreover, quantum mechanics led us to reconsider the scope of information processing and computation and its funda-mental principles which brought many new words or new meanings to our lifestyle such as’quantum information’,’qubit’,’entanglement’et.al.In this thesis, we mainly focus on some branches of two topics:nonbina-ry graphical error-correcting codes in quantum error-correcting codes and multi-partite Greenberger-Horne-Zeilinger(GHZ) paradoxes in quantum nonlocality the-ory.In our first topic, we construct quantum error-correcting codes from nonbina-ry graph states. First, we introduce the concept of a coding clique for a weighted graph and show how it is related to the construction of both stabilizer and non-additive QECCs. Then we present some codes found via computer searches. At last we construct analytically four families of optimal stabilizer codes that satu-rate the quantum Singleton bound for any odd dimension as well as a family of nonadditive codes.In our second topic, we study GHZ paradoxes from qudit graph states and multi-setting GHZ paradoxes. First, we review the concepts of quantum nonlocal-ity and quantum contextuality. Then we study GHZ paradoxes for an arbitrary number (greater than3) of particles with the help of qudit graph states on a spe-cial kind of graphs, called GHZ graphs. Furthermore, based on the GHZ paradox arising from a GHZ graph, we derive a Bell inequality with two d-outcome observ-ables for each observer, whose maximal violation attained by the corresponding graph state, and a Kochen-Specker inequality testing the quantum contextuali-ty in a state-independent fashion. In the end we investigate multi-settings GHZ paradoxes for multi-particles and in qubit case we give an experimental testable Bell inequality.

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