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.
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.
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.
We investigate the quantum advantage that can arise in typical two-party communication scenarios, where the sender and the receiver are allowed to share prior correlations. Focusing on communication tasks constrained by the distinguishability of the sender's inputs, we demonstrate that entanglement-assisted communication with both classical and quantum message can outperform classical communication supplemented with shared randomness. We begin by developing a general framework for communication tasks with pre-shared correlations. Within this framework, we establish an equivalence among entanglement-assisted classical communication, entanglement-assisted quantum communication, and quantum communication, showing that no hierarchy exists between these three paradigms. We then investigate the scenario where the receiver has no input and prove that no advantage can arise in this case. However, an advantage in the entanglement-assisted setting emerges once additional constraints are imposed on the dimension of the communicated message. This further highlights the superiority of entanglement-assisted classical communication over standard quantum communication. Then we demonstrate several tasks where the entanglement-assisted protocol using one-bit communication proves to be advantageous over classical communication. Finally, by constructing an explicit class of communication tasks, we show that a non-maximally entangled states outperform the maximally entangled state as a pre-shared resource between the communicating parties.
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.
Quantum mechanics enables information-processing advantages even at the level of a single qubit. A paradigmatic example is the 2$\to$1 random access code (RAC), where a qubit outperforms a classical bit in retrieving encoded information. In the standard form, however, this quantum advantage is restricted to a single receiver, since decoding measurements inevitably destroy the encoded information. Contrary to this, we address how long the information encoded in a single qubit remains accessible even after multiple decoding, each with a quantum advantage. Introducing preparation distinguishability as an operational resource associated with the sender, we show that its interplay with measurement incompatibility on the receiver's side can mitigate measurement-induced disturbance, thereby enabling an arbitrarily long sequence of receivers to each retain a quantum advantage. Our results show that, even under repeated measurements, the information encoded in a qubit need not be entirely exhausted, revealing a stronger communication feature than previously recognised.
Quantum resources may provide an advantage over their classical counterparts in communication tasks. We refer to this as quantum advantage. Here, we consider a single communication task to study different approaches of observing quantum advantage. We call this setting a unified scenario. Our task is described as the following. There are three parties---the Manager, Alice, and Bob. The Manager sends a value of a random variable to Alice, and at the same time Bob receives some partial information regarding that value. Initially, neither Alice nor Bob knows the input of the other, which is received from the Manager. The goal of the task is achieved if and only if the value of the random variable, sent to Alice by the Manager, is identified by Bob with a success probability greater than half all the time. Here, nonzero error probability is allowed. However, to help Bob, Alice sends a limited amount of classical or quantum information to him (cbit or qubit). We show that the goal of the task can be achieved when Alice sends a qubit. On the other hand, a cbit communication is not sufficient for achieving the goal. Thus, it establishes quantum advantage. We further show that the optimal success probability in the overall process for a qubit communication can be higher than the optimal success probability for a cbit communication. In fact, this success probability is higher for qubit communication even if along with cbit communication Alice and Bob share randomness which allows mixing of classical strategies. Clearly, it not only establishes quantum advantage, it also demonstrates a more prominent nonclassical feature. Actually, we obtain higher success probability compared to other tasks. This also suggests the experiment-friendly nature of our task. For applications, we connect our task with semi-device-independence and show how our task can be useful to detect quantumness of a communication in a secure way. Moreover, within the same setting, we provide a way to detect universal coherence present in an ensemble. For a high-dimensional random variable, to achieve the goal, it may require a high-dimensional classical communication, while it can be achieved with only a qubit communication. This establishes a large separation between the quantum and the classical communication.
We implement an experiment on a photonic quantum processor establishing efficacy of the elementary quantum system in classical information storage. The advantage is established by considering a class of simple bipartite games played with the communication resource qubit and classical bit (c bit), respectively. Conventional wisdom, supported by the no-go theorems of Holevo and Frenkel-Weiner, suggests that such a quantum advantage is unattainable when the sender and receiver share randomness or classical correlations. However, our results reveal a quantum advantage in a scenario devoid of any shared randomness. Our experiment involves the development of a variational triangular polarimeter, enabling the realization of positive operator value measurements crucial for establishing the targeted quantum advantage. Beyond showcasing a robust communication advantage with a single qubit, our work paves the way for immediate applications in near-term quantum technologies. It provides a semi-device-independent certification scheme for quantum encoding-decoding systems and offers an efficient method for information loading and transmission in quantum networks.