Post-quantum steering is a stronger-than-quantum resource for information processing

Abstract

We present the first instance where post-quantum steering is a stronger-than-quantum resource for information processing – remote state preparation. In addition, we show that the phenomenon of post-quantum steering is not just a mere mathematical curiosity allowed by the no-signalling principle, but it may arise within compositional theories beyond quantum theory, hence making its study fundamentally relevant. We show these results by formulating a new compositional general probabilistic theory – which we call Witworld – with strong post-quantum features, which proves to be a intuitive and useful tool for exploring steering and its applications beyond the quantum realm.

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

“…However, since the emergence of quantum information theory, the focus shifted to (finite-dimensional) composite systems, which brought renewed interest in the subject. It now is employed, for example, in the study of thermodynamics [5][6][7][8], interference [9][10][11][12][13][14], decoherence [15][16][17][18], computation [19][20][21][22][23][24][25], cryptography [26][27][28][29][30][31], information processing [2,[32][33][34][35][36][37][38], correlations [39][40][41][42][43][44][45], and more [46][47][48][49][50][51][52]…”

Assemblages and steering in general probabilistic theories

“…Nonclassical phenomena are often studied in a broader framework of general probabilistic theories (GPTs) [6], which has been used for better understanding the operational features of Bell nonlocality, incompatibility of measurements, steering and their relations [4,5,9,17,28,29]. GPTs include classical and quantum theory, as well as PR boxes exhibiting maximal violations of Bell inequalities [31], quantum channels [18] or post quantum steering [12]. Another motivation comes from quantum foundations, where the aim is to characterize quantum theory among physical theories, e.g.…”