Chapter 4 - Introduction to Quantum Information Processing

Abstract

The chapter introduces key quantum mechanical ideas that play an important role in quantum information processing (QIP) tasks. We begin by presenting the fundamental and important notion of quantum superposition. Quantum superposition makes quantum parallelism possible, which we discuss next. A couple of other consequences of quantum parallelism are the no cloning theorem and our inability to reliably distinguishing non-orthogonal states. Both these ideas are discussed in depth. We then introduce quantum entanglement of pure state in composite systems. We present its mathematical formulation and its practical consequence. Decoherence, a consequence of entanglement of the quantum systems with the environment, is an important source of error in QIP tasks. We explain its meaning and discuss its effect on quantum systems. Finally, we derive the operator-sum representation to efficiently represent decoherence. This representation plays an important role in protocols and algorithms in quantum computing and quantum communication over noisy channels.