Quantum resources, such as entanglement or quantum communication, offer significant communication advantages in information processing. We develop an operational framework for realizing these communication advantages in resource-constrained quantum networks. The framework computes linear bounds on the input/output probabilities of classical networks with limited communication and globally shared randomness. Since the violation of these classical bounds witnesses nonclassicality, a measurable communication advantage, the framework maximizes the violation of the classical bound using variational quantum optimization methods tailored to the communication network and quantum resources. This operational framework for nonclassicality can be scaled on quantum computers or deployed in the field to optimize noisy quantum networks for communication advantages. Applying this framework, we investigate the nonclassicality of communication networks that are assisted by quantum resources. We find that entanglement between communication-constrained parties is sufficient for nonclassicality to be found, whereas in networks with multiple senders, quantum communication with no entanglement-assistance is sufficient for nonclassicality to be found. As a result, entanglement is necessary for nonclassicality when a single sender broadcasts to multiple receivers.
Quantum resources, such as entanglement or quantum communication, offer significant communication advantages in information processing. We develop an operational framework for realizing these communication advantages in resource-constrained quantum networks. The framework computes linear bounds on the input/output probabilities of classical networks with limited communication and globally shared randomness. Since the violation of these classical bounds witnesses nonclassicality, a measurable communication advantage, the framework maximizes the violation of the classical bound using variational quantum optimization methods tailored to the communication network and quantum resources. This operational framework for nonclassicality can be scaled on quantum computers or deployed in the field to optimize noisy quantum networks for communication advantages. Applying this framework, we investigate the nonclassicality of communication networks that are assisted by quantum resources. We find that entanglement between communication-constrained parties is sufficient for nonclassicality to be found, whereas in networks with multiple senders, quantum communication with no entanglement-assistance is sufficient for nonclassicality to be found. As a result, entanglement is necessary for nonclassicality when a single sender broadcasts to multiple receivers.
Quantum information investigates the possibility of enhancing our ability to process and transmit information by directly exploiting quantum mechanical laws. When searching for improvement opportunities, one typically starts by assessing the range of outcomes classically attainable, and then investigates to what extent control over the quantum features of the system could be helpful, as well as the best performance that could be achieved. In this thesis we provide examples of these aspects, in linear optics, quantum metrology, and quantum communication. We start by providing a criterion able to certify whether the outcome of a linear optical evolution cannot be explained by the classical wave-like theory of light. We do so by identifying a tight lower bound on the amount of correlations that could be detected among output intensities, when classical electrodynamics theory is used to describe the fields. Rather than simply detecting nonclassicality, we then focus on its quantification. In particular, we consider the characterisation of the amount of squeezing encoded on selected quantum probes by an unknown external device, without prior information on the direction of application. We identify the single-mode Gaussian probes leading to the largest average precision in noiseless and noisy conditions, and discuss the advantages arising from the use of correlated two-mode probes. Finally, we improve current bounds on the ultimate performance attainable in a quantum communication scenario. Specifically, we bound the number of maximally entangled qubits, or private bits, shared by two parties after a communication protocol over a quantum network, without restrictions on their classical communication. As in previous investigations, our approach is based on the evaluation of the maximum amount of entanglement that could be generated by the channels in the network, but it includes the possibility of changing entanglement measure on a channel-by-channel basis. Examples where this is advantageous are discussed.
Quantum networks connect systems at separate locations via quantum links, enabling a wide range of quantum information tasks between distant parties. Large-scale networks have the potential to enable global secure communication, distributed quantum computation, enhanced clock synchronization, and high-precision multiparameter metrology. For the optimal development of these technologies, however, it is essential to identify the necessary resources and sub-routines that will lead to the quantum advantage, but this is demanding even for the simplest protocols in quantum information processing. Here we show that quantum networks relying on the long-distance distribution of bipartite entanglement, combined with local operations and shared randomness, cannot achieve a relevant quantum advantage. Specifically, we prove that these networks do not help in preparing resourceful quantum states such as Greenberger-Horne-Zeilinger states or cluster states, despite the free availability of long-distance entanglement. At an abstract level, our work points towards a fundamental difference between bipartite and multipartite entanglement. From a practical perspective, our results highlight the need for classical communication combined with quantum memories to fully harness the power of quantum networks.
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.
The noise and complexity inherent to quantum communication networks leads to technical challenges in designing quantum network protocols using classical methods. We address this issue with a hybrid variational quantum optimization framework (VQO) that simulates quantum networks on quantum hardware and optimizes the simulation using differential programming. We maximize nonlocality in noisy quantum networks to showcase our VQO framework. Using a classical simulator we investigate the noise robustness of quantum nonlocality. Our VQO methods reproduce known results and uncover novel phenomena. We find that maximally entangled states maximize nonlocality in the presence of unital qubit channels, while nonmaximally entangled states can maximize nonlocality in the presence of nonunital qubit channels. Thus, we show VQO to be a practical design tool for quantum networks even when run on a classical simulator. Finally, using IBM quantum computers we demonstrate that our VQO framework can maximize nonlocality on noisy quantum hardware. In the long-term, our VQO techniques show promise of scaling beyond classical approaches and can be deployed on quantum network hardware to optimize network protocols against their inherent noise.
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.
Current advancements in communication equipment demand the investigation of classical information transfer over quantum channels, by encompassing realistic scenarios in finite dimensions. To address this issue, we develop a framework for analyzing classical capacities of quantum channels where the set of states used for encoding information is restricted based on various physical properties. Specifically, we provide expressions for the classical capacities of noiseless and noisy quantum channels when the average energy of the encoded ensemble or the energy of each of the constituent states in the ensemble is bounded. In the case of qubit energy-preserving dephasing channels, we demonstrate that a nonuniform probability distribution based on the energy constraint maximizes capacity, while we derive the compact form of the capacity for equiprobable messages. We suggest an energy-constrained dense coding (DC) protocol that we prove to be optimal in the two-qubit situation and obtain a closed-form expression for the DC capacity. Additionally, we demonstrate a no-go result, which states that when the dimension of the sender and the receiver is two, no energy-preserving operation can offer any quantum advantage for energy-constrained entanglement-assisted capacity. We exhibit that, in the energy-constrained situation, classical-quantum noisy channels can show improved capabilities under entanglement assistance, a phenomenon that is unattainable in the unrestricted scenario.