Abstract: We explore entanglement in composite quantum systems
and how its peculiar properties are exploited in quantum
information and communication protocols by means of Diagrams
of States, a novel method to graphically represent and analyze how
quantum information is elaborated during computations performed
by quantum circuits.
We present quantum diagrams of states for Bell states generation,
measurements and projections, for dense coding and quantum teleportation,
for probabilistic quantum machines designed to perform
approximate quantum cloning and universal NOT and, finally, for
quantum privacy amplification based on entanglement purification.
Diagrams of states prove to be a useful approach to analyze quantum
computations, by offering an intuitive graphic representation of the
processing of quantum information. They also help in conceiving
novel quantum computations, from describing the desired information
processing to deriving the final implementation by quantum gate
arrays.
Abstract: A potentially serious problem with current payment systems is that their underlying hard problems from number theory may be solved by either a quantum computer or unanticipated future advances in algorithms and hardware. A new quantum payment system is proposed in this paper. The suggested system makes use of fundamental principles of quantum mechanics to ensure the unconditional security without prior arrangements between customers and vendors. More specifically, the new system uses Greenberger-Home-Zeilinger (GHZ) states and Quantum Key Distribution to authenticate the vendors and guarantee the transaction integrity.