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

计算机和信息系统是建立在比特的基础上的，比特可以是任何表示二进制值的东西，比如off/on或0/1。我们可以使用量子物体作为比特，比如光子，因为可以测量两种可能的极化状态。然而，量子物体是特别独特的，因为它们可以处于两种状态的叠加，它们也可以以一种方式纠缠在一起，这样一个系统的测量就会影响另一个系统，这在非量子（经典）比特中是做不到的。因此，量子计算系统允许进行经典计算机无法完成的计算，并且了解执行经典计算机无法完成的计算的系统是有用的。一个特别有趣的量子态是greenberger - horn - zeilinger （GHZ）态，因为它的非经典性质，这个项目的重点是对这种状态及其性质进行广泛的研究。该项目将与Kae Nemoto博士合作完成，他是日本东京国立信息研究所量子信息科学研究小组的首席教授。即使对于最简单的GHZ状态，GHZ状态也是不可分的。因此，从随机局部操作和经典通信（SLOCC）可转换性的角度来研究量子纠缠态对量子信息系统的应用是有用的。研究不产生简单纠缠态（贝尔态）的态上的量子操作也是有用的。该项目将研究少量量子比特的n-部GHZ状态的这些特性，并努力为大量量子比特的n-部状态做出一般陈述。该奖项由美国国家科学基金会和日本科学促进会共同资助，隶属于东亚和太平洋暑期研究所项目，支持一名美国研究生进行暑期研究。

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.