Colloquium on October 23th, 2006

Pawel Horodecki
Gdansk University of Technology

Quantum entanglement phenomenon and quantum communication

Quantum entanglement is one of the most fascinating phenomena in quantum mechanics. Since seminal observations by Einstein, Rosen, Podolski (EPR) and Schroedinger it has been known that the composed quantum systems have peculiar properties. In particular there are composed quantum systems which we have maximal information about but at the same time we have no information about their subsystems. This property can not take place in "classical" world. According to John Bell milestone paper this kind of property is, in a sense, objective ie. can not be simulated by any so called local realistic description. In 1991 entanglement started its rapidly developing carrer in quantum information theory becoming a fundamental resource of quantum information processing especially quantum communication. Due to the key property called entanglement monogamy it can serve for cryptographic purposes. It also allows for so called dense coding schemes and intriguing effect called quantum teleportation. Finally it is the key resource in known quantum computing schemes.
Unfortunately in labs we usually deal with noisy entanglement due to uncontrolled interaction with environment. This implies key questions: how to quantify and detect such form of quantum entanglement and how to make it still useful for quantum communication. To answer the first question we shall first review the key elements of entanglement measures theory. Then we shall present some of entanglement detection methods including the basic entanglement witness approach and collective measurements one. The second crucial problem of how to use noisy entanglement will be studied especially in context of entanglement distillation protocol with application to quantum communication. This leads to bound entanglement phenomenon and its surprising application in quantum cryptography. Finally the close relation of quantum entanglement to quantum channels theory will be illustrated.
We shall conclude with summary and some of open questions about entanglement that are addressed to us by the fascinating domain of quantum information theory.