After going through
the chapter on entanglement you will have reached the end of our book.
As the subtitle suggests, its aim was literally to present an
introduction to the subject of quantum entanglement.
We have left untouched several important aspects of quantum
entanglement, including multipartite systems, infinite dimensional
systems, and continuous variables. Moreover, we believe that some
key ideas presented in the book might be extended much further
then we have managed to do. For instance the maps--states duality,
illustrated in chapter 11, might be used to find relations between
capacities of quantum channels and measures of entanglement of the
corresponding states of an extended system.
In the book we have consistently used a geometric approach to
highlight similarities and differences between the classical and
quantum spaces of states. What is the knowledge gained by studying the
book good for? We hope it will contribute to a better understanding of
quantum mechanics. We hope also that it will provide a solid foundation
for a new, emerging field of science -- the theory of quantum
information processing. Quantum entanglement plays a decisive role in
all branches of the field including quantum cryptography, quantum
error correction, and quantum computing.
In trying to describe the intricate geometry of the space of
quantum states, we have deliberately restricted ourselves to discussing
the statics of quantum theory. We have presented the arena, in which
quantum information can be processed. We have not attempted to inject
any concrete dynamics into our arena, but hope that readers equipped
with some knowledge of its properties may introduce into it spectacular
action.
In a sense we have characterised all the peculiarities of football
fields of various sizes, without even specifying the rules of the game.
Having at your disposal a huge flat grassy field, you can play soccer,
cricket, American football, rugby, or Australian football, according to
your mood and wishes.
In a similar way you can play different games in the
multi--dimensional arena of quantum states. It stays there right
in the center of the beautiful Platonic world of quantum theory,
accessible to all of us.
Its rich structure provides a real challenge especially for young
researchers.
We wish you a good game in fine company!
Good luck !