Quantum Information Theory of Entanglement

We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on matrices, rather than probability distributions, for the description of quantum ensembles. We find that conditional quantum entropies can be negative for quantum entangled systems, which leads to a violation of well-known bounds in classical information theory. Such a treatment clarifies the link between classical correlation and quantum entanglement: the latter can be understood as “super-correlation” which can induce classical correlation, while the reverse is impossible. Furthermore, negative entropy and the associated clarification of entanglement paves the way to a natural, unitary, and causal model of the measurement process, while implying all the well-known results of conventional probabilistic quantum mechanics.