Quantum entanglement

Abstract

All our former experience with application of quantum theory seems to say that what is predicted by quantum formalism must occur in the laboratory. But the essence of quantum formalism---entanglement, recognized by Einstein, Podolsky, Rosen, and Schr\"odinger---waited over $70\phantom{\rule{0.3em}{0ex}}\text{years}$ to enter laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, has potential for many quantum processes, including canonical ones: quantum cryptography, quantum teleportation, and dense coding. However, it appears that this new resource is complex and difficult to detect. Although it is usually fragile to the environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation, and quantification. In particular, various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, and quantum cryptography are discussed, and some interrelations are pointed out. The basic role of entanglement in quantum communication within a distant laboratory paradigm is stressed, and some peculiarities such as the irreversibility of entanglement manipulations are also discussed including its extremal form---the bound entanglement phenomenon. The basic role of entanglement witnesses in detection of entanglement is emphasized.