EAPSI: Analysis of SLOCC Convertibility and Quantum Transformations on Higher Order N-Partite Greenberger-Horne-Zeilinger States

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Computers and information systems are built on bits, which can be anything that represents a binary value such as off/on, or 0/1. We may use quantum objects as bits, such as photons, because two possible states of polarization can be measured. However, quantum objects are especially unique because they can be in a superposition of both states, and they can also be entangled in a way such that the measurement of one system affects the other, which cannot be done with non-quantum (classical) bits. So quantum computing systems allow for calculations that cannot be done classically, and it is useful to know of systems that perform computations that classical computers cannot. One particularly interesting quantum state is the Greenberger-Horne-Zeilinger (GHZ) state because of its non-classical properties, and the focus of this project is to do extensive research on this state and its properties. This project will be done in collaboration with Dr. Kae Nemoto, the leading professor in the Quantum Information Sciences research group at the National Institute of Informatics in Tokyo, Japan.GHZ states are non-biseparable states even for the simplest GHZ state. Therefore, it is useful to study its entanglement in terms of Stochastic Local Operations and Classical Communication (SLOCC) convertibility to apply those states in quantum information systems. It is also useful to study quantum operations on the state that do not result in simply entangled (Bell) states. This project will study both those properties in the n-partite GHZ state for few qubits and work its way up to make general statements for n-partite states for large number of qubits.This award, under the East Asia and Pacific Summer Institutes program, supports summer research by a U.S. graduate student and is jointly funded by NSF and the Japanese Society for the Promotion of Science.