par Massar, Serge ;Patra, Manas Kumar
Référence Physical Review A. General Physics, 89, 052124
Publication Publié, 2014-05-20
Article révisé par les pairs
Résumé : Generalized probabilistic theories (GPTs) provide a framework in which one can formulate physical theories that includes classical and quantum theories, but also many other alternative theories. In order to compare different GPTs, we advocate an approach in which one views a state in a GPT as a resource and quantifies the cost of interconverting between different such resources. We illustrate this approach on polygon theories [New J. Phys. 13, 063024 (2011).NJOPFM1367-263010.1088/1367-2630/13/6/063024] that interpolate (as the number n of edges of the polygon increases) between a classical trit (when n=3) and a real quantum bit (when n=). Our main results are that simulating the transmission of a single n-gon state requires more than one qubit, or more than log(log(n)) bits, and that n-gon states with n odd cannot be simulated by n′-gon states with n′ even (for all n,n′). These results are obtained by showing that the classical capacity of a single n-gon state with n even is 1 bit, whereas it is larger than 1 bit when n is odd; by showing that transmitting a single n-gon state with n even violates information causality; and by studying the communication complexity cost of the nondeterministic not-equal function using n-gon states. © 2014 American Physical Society.