Chapter 4 - Quantum Information Processing Fundamentals

Abstract

This chapter is devoted to the basic concepts of quantum information processing (QIP). After describing the elementary QIP features, the chapter introduces the superposition principle and quantum parallelism concept as well as QIP basics. It continues with formulation and proof of no-cloning theorem. We further formulate and prove an important theorem, which claims that it is impossible unambiguously to distinguish nonorthogonal quantum states. The next section is devoted to the various aspects of entanglement, including the Schmidt decomposition theorem, purification, superdense coding, and entanglement swapping. How entanglement can be used in detecting and correcting quantum errors is described as well. Various measures of entanglement are introduced, including the entanglement of formation, concurrence, and entanglement fidelity. Furthermore, we discuss the operator-sum representation of a quantum operation and apply this concept to describe the quantum errors and decoherence. The bit-flip, phase-flip, phase-damping, depolarizing, and amplitude-damping channels are described as well. Then we describe different quantum computing libraries, including Qiskit, Cirq, Forest, and Quantum Development Kit. After summarizing the chapter, a set of problems is provided for better understanding of QIP concepts.