Quantum Advantage in Shared Randomness Processing
Tamal Guha, Mir Alimuddin, Sumit Rout, Amit Mukherjee, Some Sankar Bhattacharya, Manik Banik · arXiv (Cornell University) · 2020
Randomness appears both in classical stochastic physics and in quantum mechanics. A number of communication models and other information protocols entail sharing randomness among distant parties. Here we report a computational scenario of shared randomness processing where quantum sources manifest clear-cut precedence over the corresponding classical counterparts. The advantage is established in a resource theoretic set-up which we formalize in this work. The classical mutual information turns out to be a faithful resource quantifier of shared randomness although it does not sufficiently characterize all possible transitions among the resources. Quantum theory exhibits advantage in shared randomness processing in the sense that the set of resourceful states obtained under free operation from a bipartite quantum system is strictly larger than the set obtained from an analogous classical system. Interestingly, the quantum advantage can be manifested in the optimal payoff of a two players co-operative game -- the `non-monopolize social subsidy' game. We also show that the quantum states resulting to the desired advantage necessitates nonclassicality in the form of quantum discord. We then address the task of distributing shared randomness between two parties. Quite interestingly, it turns out that noisy quantum channel can exhibit advantage even when it has zero quantum capacity and classical capacity much less than the corresponding classical channel. The imperfect channel examples facilitates and welcomes experiment to achieve the reported quantum advantage with presently available quantum devices.