This book presents the basics of quantum information, e.g., foundation
of quantum theory, quantum algorithms, quantum entanglement, quantum
entropies, quantum coding, quantum error correction and quantum
cryptography. The required knowledge is only elementary calculus and
linear algebra. This way the book can be understood by undergraduate
students. In order to study quantum information, one usually has to
study the foundation of quantum theory. This book describes it from more
an operational viewpoint which is suitable for quantum information while
traditional textbooks of quantum theory lack this viewpoint. The current
book bases on Shor's algorithm, Grover's algorithm, Deutsch-Jozsa's
algorithm as basic algorithms. To treat several topics in quantum
information, this book covers several kinds of information quantities in
quantum systems including von Neumann entropy. The limits of several
kinds of quantum information processing are given. As important quantum
protocols, this book contains quantum teleportation, quantum dense
coding, quantum data compression. In particular conversion theory of
entanglement via local operation and classical communication are treated
too. This theory provides the quantification of entanglement, which
coincides with von Neumann entropy. The next part treats the quantum
hypothesis testing. The decision problem of two candidates of the
unknown state are given. The asymptotic performance of this problem is
characterized by information quantities. Using this result, the optimal
performance of classical information transmission via noisy quantum
channel is derived. Quantum information transmission via noisy quantum
channel by quantum error correction are discussed too. Based on this
topic, the secure quantum communication is explained. In particular, the
quantification of quantum security which has not been treated in
existing book is explained. This book treats quantum cryptography from a
more practical viewpoint.
