On Quantum Capacity and Quantum Communication Gate (Mathematical Study of Quantum Dynamical Systems and Its Application to Quantum Computer)

昇 渡邉

Kei Inoue

Wen-Ling Xu, Tie-Jun Wang, Cong Cao +1 more

Quantum information science has extensive applications in various research fields, such as information, physics and computer science. It is well known that the quantum properties of a system exhibit many unique advantages in the security of information transmission and processing, computation, and the improvement of channel capacity. Quantum information includes several research fields, for example, quantum communication, quantum computing and so on. In the past 30 years, the development of quantum communication, quantum computing and quantum information processing has made great progress in both theory and experiments. As a fundamental resource for quantum information processing, entanglement is a key element for many applications, such as quantum key distribution, quantum teleportation, quantum dense coding, quantum secure direct communication and quantum metrology. Because of the weak interaction with the environment and the degrees of freedom, entangled photons are the excellent candidates as the quantum-information carrier. Several remarkable experiments have been performed with the photonic entanglement. However, it is necessary to share a pair of entangled photons between the communicating parties in advance in these quantum information processes. Furthermore, the application of hyperentanglement, the entanglement of photon pairs simultaneously existing in more than one degree of freedom, has been widely studied for the reason that it can improve the channel capacity of quantum communications and implement hyperparallel computing, such as the quantum error-correcting code, quantum repeater and deterministic entanglement purification. Moreover, the quantum logic gates play an essential role in quantum information processing which attracts much attention on the designing of the quantum logic gates. Depending on the coherent dynamics of the cavity quantum electrodynamical system, deterministic quantum gate operations between the quantum systems can be realized. Here in this review, by considering high-dimensional quantum systems, several high-dimensional quantum protocols are presented. They can greatly improve the capacity of quantum channel and noise immunity, which exhibits potential applications in quantum information processing. This review describes the development of quantum computing and quantum information processing using hyperentanglement. And the entangled photons in single degree of freedom and multi-degrees of freedom are used to illustrate the two-dimensional and high-dimensional quantum information processing schemes. Finally, the latest progress and further applications of quantum computing and quantum information processing are introduced.

Wolfgang Freudenberg, Masanori Ohya, Noboru Watanabe

R. Pike

S. Andrew Lanham

The engineering problem of building scalable quantum computers has prompted the development of a rich theory modeling the evolution of quantum systems as well as techniques to preserve quantum information in the presence of noise. Such techniques offer systems-level approaches to the problem of robustly encoding and preserving information and, as a result, see applicability in a wide variety of architectures for computing systems. In this thesis, we visit the mathematical underpinnings of quantum information and apply strategies inspired by quantum information processing to two non-quantum systems to demonstrate advantage. We first describe the construction of a quantum emulation device, an analog electronic system with the same mathematical structure as a gate-based quantum computer, and introduce novel time-domain information encoding methods to increase the computational capacity of the device. We confirm the sustained performance of the improved system by successfully transforming emulated states by randomly selected quantum gates. We then visit similarities between quantum information processing and signal processing in the noncoherent wireless communication setting, the latter being an environment characterized by a lack of instantaneous channel knowledge. We describe the theoretical underpinnings of the noncoherent communication environment from both an information theoretic and signal processing perspective. This leads us to propose a multi-antenna space-time code construction based on a family of quantum error correcting codes known as stabilizer codes. For this code, we derive the optimal decoder in Rayleigh and Ricean fading and benchmark the its performance against coherent and differential coding at comparable rates.