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.
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.
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a resource called shared randomness, quantum systems provide an advantage over their classical counterpart. Precisely, we show that appropriate albeit fixed measurements on a shared two-qubit state can generate correlations which cannot be obtained from any possible state on two classical bits. In a resource theoretic set-up, this feature of quantum systems can be interpreted as an advantage in winning a two players co-operative game, which we call the `non-monopolize social subsidy' game. It turns out that the quantum states leading to the desired advantage must possess non-classicality in the form of quantum discord. On the other hand, while distributing such sources of shared randomness between two parties via noisy channels, quantum channels with zero capacity as well as with classical capacity strictly less than unity perform more efficiently than the perfect classical channel. Protocols presented here are noise-robust and hence should be realizable with state-of-the-art quantum devices.
We analyze utility of communication channels in absence of any short of quantum or classical correlation shared between the sender and the receiver. To this aim, we propose a class of two-party communication games, and show that the games cannot be won given a noiseless 1 -bit classical channel from the sender to the receiver. Interestingly, the goal can be perfectly achieved if the channel is assisted with classical shared randomness. This resembles an advantage similar to the quantum superdense coding phenomenon where pre-shared entanglement can enhance the communication utility of a perfect quantum communication line. Quite surprisingly, we show that a qubit communication without any assistance of classical shared randomness can achieve the goal, and hence establishes a novel quantum advantage in the simplest communication scenario. In pursuit of a deeper origin of this advantage, we show that an advantageous quantum strategy must invoke quantum interference both at the encoding step by the sender and at the decoding step by the receiver. We also study communication utility of a class of non-classical toy systems described by symmetric polygonal state spaces. We come up with communication tasks that can be achieved neither with 1 -bit of classical communication nor by communicating a polygon system, whereas 1 -qubit communication yields a perfect strategy, establishing quantum advantage over them. To this end, we show that the quantum advantages are robust against imperfect encodings-decodings, making the protocols implementable with presently available quantum technologies.
Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of the system. We show that already in the simplest possible scenarios it is possible to detect a definite, unbounded advantage of quantum systems over classical systems. We do this by constructing a family of operationally meaningful communication tasks, each of which, on the one hand, can be implemented by using just a single qubit but which, on the other hand, require an unboundedly larger classical system for classical implementation. Furthermore, we show that even though, with the additional resource of shared randomness, the proposed communication tasks can be implemented by both quantum and classical systems of the same size, the number of coordinated actions needed for the classical implementation also grows unboundedly. In particular, no finite storage can be used to store all the coordinated actions required to implement all possible quantum communication tasks with classical systems. As a consequence, shared randomness cannot be viewed as a free resource.
Quantum communication can outperform classical communication in a variety of information-processing tasks, but such advantages are typically established for a fixed communication network. Here we introduce topology-independent quantum advantage, in which a quantum protocol outperforms every classical protocol subject to the same communication constraint, irrespective of how the classical communication resource is distributed among the parties or which communication topology is employed, even when the parties may share unlimited classical randomness. We first demonstrate this phenomenon through a simple three-party equality task: two senders receive ternary classical inputs, while an input-free receiver determines whether the inputs are equal. We then formulate a general framework for topology-independent communication and completely characterize the corresponding classical correlation polytope in the minimal three-party scenario. Its facet inequalities reveal several instances of topology-independent quantum advantage. Remarkably, one of these inequalities enables the semi-device-independent certification of a nonunitary quantum channel, while another certifies a sequential quantum network topology without any prior assumption about the network configuration. Finally, we extend the framework to four-party networks, characterize the relevant classical communication structures, and identify a communication task exhibiting quantum advantages against all admissible classical topologies. Our results establish topology independence as a genuine and robust form of quantum advantage in communication networks.
In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of any type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of any type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.
We consider two-stage hybrid protocols that combine quantum resources and classical resources to generate classical correlations shared by two separated players. Our motivation is twofold. First, in the near future, the scale of quantum information processing is quite limited, and when quantum resource available is not sufficient for certain tasks, a possible way to strengthen the capability of quantum schemes is introducing extra classical resources. We analyze the mathematical structures of these hybrid protocols, and characterize the relation between the amount of quantum resources and classical resources needed. Second, a fundamental open problem in communication complexity theory is to describe the advantage of sharing prior quantum entanglement over sharing prior randomness, which is still widely open. It turns out that our quantum and classical hybrid protocols provide new insight into this important problem.