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Quantum measurement and its applications in photonic quantum information

Quantum measurement and its applications in photonic quantum information
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The discovery of quantum physics in the early 20th century suggested a new paradigm for physical phenomena and new understanding of Nature. The new understanding of nature has been a good playground for scientists and there has been a large ‘quantum leap’ of human knowledge. Quantum physics affects not only the human knowledge but also the real life. For instance, many basic devices in present industrial society such as lasers and semiconductors were invented with understanding of quantum physics.Recently, a new information science that combines quantum physics and classical information science, quantum information science has been widely researched. Quantum information science can relatively easily compute things that are known very difficult or even impossible to compute with classical computation. For instance, factoring a large number can be done in reasonable time with Shor’s algorithm in which it takes a tremendous time with classical computation. The most distinguished features of quantum information science are that the usage of a qubit (quantum bit) for a fundamental unit of information and concepts of measurement in quantum physics is adopted. In this thesis, I introduce how quantum measurement is applied in quantum information science and what can be practical uses quantum information science.First, I report the experimental verification of commutation relation of Pauli operators. Commutation relation introduces a concept of ‘non-commutating observables’ that is connected to a very fundamental concept of quantum physics, the uncertainty principle. The uncertainty principle says ‘uncertainty’ in ‘quantum measurement’, thus understanding of uncertainty principle is very important to understand quantum physics as well as quantum measurement. Although commutation relation is well studied theoretically, experimental verifications have been started to report only lately. In this thesis, I experimentally show the commutation relation of Pauli operators which form a complete set of unitary operations in two-dimensional quantum system, qubit with the identity operation.Next, I report how a typical non-projective quantum measurement, weak measurement, affects a qubit system. While a projective measurement causes a complete state collapse towards the eigenstate of the measurement basis, a weak measurement only causes a partial collapse. With this property, a weak measurement has its mathematical inverse operations, so it is possible to nullify the weak measurement. In the thesis, I report the partial state collapse due to the weak measurement as well as the state recovery from the reversing measurement.Furthermore, a practical application of quantum measurement reversal in quantum information science is also studied. Specifically, entanglement protection protocol via weak measurement and quantum measurement reversal under amplitude damping decoherence is suggested and experimentally demonstrated. This entanglement protection protocol is an important example of a direct application of quantum measurement in quantum information science. Especially, the suggested protocol works even under the entanglement sudden death causing decoherence environment where entanglement distillation protocol does not work. Thus it is expected that the entanglement protection protocol will become an important way to cope with decoherence.Finally, a generation of three-photon N00N state and its double-slit spatial interference is reported. Because of the effective wavelength reduction of 1/N, N00N state is considered as an important resource for quantum imaging and quantum metrology. In particular, since the effective wavelength reduction in spatial domain can be directly applied to quantum imaging, quantum lithography, and quantum metrology, it is evaluated as a vital technique. The reported spatial interference of three-photon N00N state is the first spatial interference for N>2, N00N state.
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