Quantum Information Theory

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It is was recently proved that there are situations in which the quantum phenomenon called entanglement can increase the capacity of a quantum channel used to transmit classical information. Such channels are called non-additive; however, no explicit examples are known. Even more recently, it was observed that the anti-symmetry associated with the Pauli exclusion principle can be used to give an example of a channel which is non-additive for a related quantity, called the minimal output Renyi entropy, when p 2. This grant is intended to construct more examples of non-additive channels and clarify our understanding of this phenomenon. In connection with this, the PI will closely examine the role of permutational symmetry in quantum information theory. The PI will also study entropy inequalities and cones of entropy vectors for composite systems. This highly interdisciplinary work will clarify the role of the Pauli exclusion principle, which is often suppressed in quantum information theory. It will also be of interest to quantum chemists and condensed matter physicists, particularly those who used reduced density matrices. The work should help identify situations in which quantum systems have advantages over classical ones for communication, as well as computation.