Despite the conceptual importance of contextuality in quantum mechanics, there is a hitherto limited number of applications requiring contextuality but not entanglement. Here, we show that for any quantum state and observables of sufficiently small dimensions producing contextuality, there exists a communication task with quantum advantage. Conversely, any quantum advantage in this task admits a proof of contextuality whenever an additional condition holds. We further show that given any set of observables allowing for quantum state-independent contextuality, there exists a class of communication tasks wherein the difference between classical and quantum communication complexities increases as the number of inputs grows. Finally, we show how to convert each of these communication tasks into a semi-device-independent protocol for quantum key distribution.
Despite the conceptual importance of contextuality in quantum mechanics, there is a hitherto limited number of applications requiring contextuality but not entanglement. Here, we show that for any quantum state and observables of sufficiently small dimensions producing contextuality, there exists a communication task with quantum advantage. Conversely, any quantum advantage in this task admits a proof of contextuality whenever an additional condition holds. We further show that given any set of observables allowing for quantum state-independent contextuality, there exists a class of communication tasks wherein the difference between classical and quantum communication complexities increases as the number of inputs grows. Finally, we show how to convert each of these communication tasks into a semi-device-independent protocol for quantum key distribution.
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.
Abstract Although ‘quantum contextuality’ is one of the most fundamental non-classical feature, its generic role in information processing and computation is an open quest. In this article, we present a family of distributed computing tasks pertaining to every logical proof of Kochen–Specker (KS) contextuality in two different one-way communication scenarios: (I) communication of bounded dimensional system, (II) communication of unbounded dimensional system while keeping certain information oblivious, namely, oblivious communication (OC). As the later remains largely unexplored, we introduce a general framework for OC tasks and provide a methodology for obtaining an upper bound on the success of OC tasks in classical communication. We show that quantum communication comprised of every KS set of vectors outperforms classical communication and perfectly accomplish the task in both the aforementioned scenarios. We explicitly discuss the communication tasks pertaining to the simplest state independent contextuality sets of dimension three and four. Our results establish an operational significance to single system contextuality and open up the possibility of semi-device independent quantum information processing based on that. Alongside, we identify any advantage in OC tasks as a witness of preparation contextuality.
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.
Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the preparation, transmission, and measurement of a single quantum system, in other words, quantum communication. Here, we show the advantages of the latter over the former in high-dimensional Hilbert space. We focus on a family of CCPs, based on facet Bell inequalities, study the advantage of high-dimensional quantum communication, and realize such quantum communication strategies using up to ten-dimensional systems. The experiment demonstrates, for growing dimension, an increasing advantage over quantum strategies based on Bell inequality violation. For sufficiently high dimensions, quantum communication also surpasses the limitations of the postquantum Bell correlations obeying only locality in the macroscopic limit. We find that the advantages are tied to the use of measurements that are not rank-one projective, and provide an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.
When considering the complexity of communication protocols, the aim is to perform a certain task with the minimum amount of communication resources, such as time and transmitted information. The use of quantum states may lead to an exponential advantage in the use of such resources. Here, we are interested in the task of calculating the Euclidean distance between two vectors representing real data sets. It has been previously shown that it is possible to obtain an advantage for this task based on quantum fingerprinting. This protocol is defined in the simultaneous message passing model of communication complexity, where the two parties do not communicate with each other but send data to a third party, and exploits practical fingerprints generated using trains of coherent state pulses instead of highly entangled qubit states that are hard to generate for large input sizes needed to demonstrate an exponential advantage. We perform a proof-of-principle experimental demonstration of the Euclidean distance protocol using amplitude modulation techniques for encoding non-binary data sets and high-performance superconducting nanowire single-photon detectors required to increase the accessible input size. We show a quantum advantage in transmitted information surpassing the best classical protocol for an input size of 108, for diverse types of data sets, including those corresponding to real grayscale images, and with reasonable precision and error bounds. Our results highlight the potential of quantum communication complexity for use in a broad set of applications.
Quantum mechanics exhibits many counter-intuitive features, which challenge our classical understanding of the world. This makes the theory simultaneously difficult to grasp, and a source of great potential for new technologies. We study various characteristics of classical and quantum mechanics and their respective roles in computation. This is interesting from a philosophical perspective, as it brings us a small step closer to understanding the nature of quantum mechanics. Furthermore, it leads us to discover scenarios where quantum resources provide a genuine advantage over classical resources, as well as more intuitive ways to model quantum protocols. Firstly, we explore the concept of quantum contextuality, which distinguishes uniquely-quantum experimental outcomes from outcomes that can be realised classically. In pursuit of a universal theory of contextuality, we unify two abstract frameworks: the sheaf-theoretic approach to contextuality by Abramsky and Brandenburger and the equivalence-based approach by Spekkens. We apply the sheaf-theoretic formalism to the field of communication complexity. We derive a bound on the success probability of a communication complexity protocol, based on the amount of contextuality present in its quantum resource. We provide a set of necessary conditions for distributed functions that allow a contextual advantage. Secondly, we consider a family of bicategorical models to describe the interaction of classical and quantum information in quantum protocols. We prove that this family is symmetric monoidal, and therefore suitable for describing compound and parallel protocols. This family serves as a mathematical foundation for the planar language for quantum protocols by Vi- cary. Important examples of this family are the bicategories 2Hilb and 2Vect. Additionally, we introduce the structure 2[CP∗[FHilb]], which contains a symmetric monoidal bicategory of mixed states and completely positive maps. This allows a unified description of quantum teleportation and classical encryption in a single 2-category, as well as a universal security proof applicable simultaneously to both scenarios. As part of the process, we develop extensive categorical machinery for constructing symmetric monoidal structures of bicategories, pseudo functors, pseudo transformations and modifications. We consider a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories. We show that this method can be generalised to a functor from the locally cubical bicategory of monoidal double categories to the locally cubical bicategory of monoidal bicategories.