The principles of quantum information theory, Dirac's equation, and locality beyond relativity

pp. 247-263

in: Arkady Plotnitsky, The principles of quantum theory, from Planck's quanta to the Higgs boson, Berlin, Springer, 2016

Abstract

This chapter considers the principles of quantum information theory in conjunction with the principles of QM and QFT, as discussed in earlier chapters. Several recent approaches to quantum information theory will be addressed, such as those by B. Coecke and, more extensively, L. Hardy. Particular attention will, however, be given to the recent work by G. M. D"Ariano and co-workers, G. Chiribella and P. Perinotti. The approach to quantum information theory that they developed allowed D"Ariano and Perinotti to derive Dirac's equation from the principles of quantum information alone, rather than, as Dirac did, by combining the principles of quantum theory and special relativity. The locality principle, however, plays a key role in this derivation, which, I suggest, may have important implications for fundamental physics. I will proceed as follows. After brief introductory remarks given in Sects. 7.1, 7.2 considers D"Ariano, Chiribella, and Perinotti's program of finite-dimensional quantum theory (QFDT), based on these principles, and related work, especially that of Hardy, in terms of the operational language of circuits. Sect. 7.3 discusses D"Ariano and Perinotti's derivation of Dirac's equation.