Quantum Measurement And Its Applications In Quantum Information Processing

As a basic postulate, quantum measurement is one of the most important conceptions in quantum mechanics. In the field of quantum information science, quantum measurement plays an irreplaceable role as a bridge between classical world and quantum world. On one hand, via quantum measurement, we can extract information encoded in quantum states, distinguish different quantum states and quantum operations. In this aspect, typical applications include quantum cryptograph, quantum states discrimination, quantum tomography, and quantum error correcting code, etc. On the other hand, noticing that quantum measurement and the unitary evolution are the two basic forms of quantum evolution, hence quantum measurement is also related to quantum manipulation. Through quantum measurement, one can project the system into specific states to accomplish some quantum information processing tasks. Typical applications in this area include one-way quantum computing, quantum teleportation, entanglement swapping, quantum repeater, remote quantum state preparation, etc.The main content of this dissertation is the author's investigation of quantum measurement and its applications in quantum information processing. Here is the outline:1. We present two schemes for realizing arbitrary n-operator generalized quantum measurement (GQM) on single atomic qubit and single photonic qubit, respectively. For the atomic qubit, we propose a scheme where one 2-dimension ancillary atomic qubit is enough to realize arbitrary n-operator GQM, hence avoiding quantum operations in high-dimensional Hilbert space and significantly reducing the complicacy of the ancilla system. For single photonic polarization qubit, using path degrees of freedom as ancilla system, we present a scheme for implementing arbitrary n-operator GQM, which is simpler than previous schemes. Based on this scheme, we demonstrate a set of 2-operator GQMs on single photonic polarization qubit, and combining with entangled photon source, we realize a kind of deterministic entanglement transformations of bipartite pure states.2. Based on Rydberg blockade effect and post-selective measurement of photonic polarization states, we propose a theoretical scheme of preparing arbitrary four-qubit W class of entangled states with atomic ensembles in a single step. The success of the entanglement preparation can be heralded by photon measurement event.3. Based on ion measurement and Rydberg blockade effect in atomic ensembles, we propose a novel quantum repeater scheme. In our scheme, the muli-photon noise is suppressed and the efficiency of the entanglemet swapping procedures is increased. The entanglement distribution rate is higher by orders of magnitude than the previous ones. At the same time, the fidelity of the final entanglement is also relatively enhanced.4. Optical quantum memory is one of the key elements of quantum repeater. Based on direct control of specific transition dipole moment in atomic ensemble, we present a novel kind of optical quantum memory. An analytical treatment of the equation of motion is performed and concrete calculation is done based on realistic parameter of a magneto-dependent transition dipole moment in Tm³⁺:YAG crystal. This kind of quantum memory has high efficiency and the advantages of simple physical picture and experimental feasibility.5. Through non-projective which-way measurement, one can partially extract which-way information from double-slit interferometer, which allows us to quantificationally study the complementarity between which-way information and interference pattern. An inequality concerning wave-particle duality is derived, which is more stringent and has a relatively clear physical meaning.