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arXiv:2409.13223 · Physical Review A

Scalable and noise-robust communication advantage of multipartite quantum entanglement

Ananya Chakraborty, Ram Krishna Patra, Kunika Agarwal, Samrat Sen, Pratik Ghosal, Sahil Gopalkrishna Naik, Manik Banik

Published Mar 20, 2025• 7 citations
arXivHTMLPDF

Abstract

Distributed computing, involving multiple servers collaborating on designated computations, faces a critical challenge in optimizing interserver communication---an issue central to the study of communication complexity. Quantum resources offer advantages over classical methods in addressing this challenge. In this work, we investigate a distributed computing scenario with multiple senders and a single receiver, establishing a scalable advantage of multipartite quantum entanglement in mitigating communication complexity. Specifically, we demonstrate that when the receiver and the senders share a multiqubit Greenberger-Horne-Zeilinger (GHZ) state---a quintessential form of genuine multipartite entanglement---certain global functions of the distributed inputs can be computed with only one bit of classical communication from each sender. In contrast, without entanglement, two bits of communication are required from all but one sender. Consequently, quantum entanglement reduces communication overhead by $n\ensuremath{-}1$ bits for $n$ senders, allowing for arbitrary scaling with an increasing number of senders. We also show that the entanglement-based protocol exhibits significant robustness under white noise, thereby establishing the potential for experimental realization of this quantum advantage.

DOI
10.1103/physreva.111.032617

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Distributed computing, involving multiple servers collaborating on designated computations, faces a critical challenge in optimizing interserver communication---an issue central to the study of communication complexity. Quantum resources offer advantages over classical methods in addressing this challenge. In this work, we investigate a distributed computing scenario with multiple senders and a single receiver, establishing a scalable advantage of multipartite quantum entanglement in mitigating communication complexity. Specifically, we demonstrate that when the receiver and the senders share a multiqubit Greenberger-Horne-Zeilinger (GHZ) state---a quintessential form of genuine multipartite entanglement---certain global functions of the distributed inputs can be computed with only one bit of classical communication from each sender. In contrast, without entanglement, two bits of communication are required from all but one sender. Consequently, quantum entanglement reduces communication overhead by n\ensuremath−1n\ensuremath{-}1n\ensuremath−1 bits for nnn senders, allowing for arbitrary scaling with an increasing number of senders. We also show that the entanglement-based protocol exhibits significant robustness under white noise, thereby establishing the potential for experimental realization of this quantum advantage.
We establish an exponential communication advantage enabled by multipartite quantum entanglement. Building on the bipartite Hidden Matching problem, we introduce a communication task involving multiple spatially separated senders and a single receiver. We show that a shared Greenberger-Horne-Zeilinger state enables completion of this task using only logarithmically many bits of classical communication from each sender. In contrast, without preshared entanglement, any protocol achieving high success probability requires polynomial communication from at least one sender, even when \emph{quantum} communication is allowed. Thus, classical communication assisted by multipartite entanglement can be exponentially more powerful than quantum communication without preshared entanglement. As a cryptographic application, we construct a seeded two-source randomness extractor and establish an exponential separation between entangled and unentangled quantum side-information. Specifically, compromising the extractor with two unentangled quantum states storing information about the two sources, respectively, requires polynomial-size memory, whereas exponentially smaller quantum memory suffices in the presence of a small amount of shared entanglement.
A central problem in quantum information theory is understanding how quantum resources can be used to communicate information more efficiently than classical resources. We introduce quantum dense network coding -- a protocol that transmits the output of a non-Boolean function to a receiver using provably half as many qubits as bits for each sender by not transmitting the entirety of the function inputs. We show this advantage requires both shared entanglement and quantum communication, is robust to noise, and the gap in success probability between quantum and classical communication can be amplified exponentially in the number of senders. Finally, we show that dense network coding gives rise to a novel, information-theoretically secure, quantum cryptographic protocol, which we call measurement-device-independent quantum key growing.
We investigate the effect of noisy channels in a classical information transfer through a multipartite state which acts as a substrate for the distributed quantum dense coding protocol between several senders and two receivers. The situation is qualitatively different from the case with one or more senders and a single receiver. We obtain an upper bound on the multipartite capacity which is tightened in the case of the covariant noisy channel. We also establish a relation between the genuine multipartite entanglement of the shared state and the capacity of distributed dense coding using that state, both in the noiseless and the noisy scenarios. Specifically, we find that, in the case of multiple senders and two receivers, the corresponding generalized Greenberger-Horne-Zeilinger states possess higher dense coding capacities as compared to a significant fraction of pure states having the same multipartite entanglement.
Abstract Efficient distributed computing offers a scalable strategy for solving resource-demanding tasks, such as parallel computation and circuit optimisation. Crucially, the communication overhead introduced by the allotment process should be minimised—a key motivation behind the communication complexity problem (CCP). Quantum resources are well-suited to this task, offering clear strategies that can outperform classical counterparts. Furthermore, the connection between quantum CCPs and non-locality provides an information-theoretic insight into fundamental quantum mechanics. Here we connect quantum CCPs with a generalised non-locality framework—beyond Bell’s paradigmatic theorem—by incorporating the underlying causal structure, which governs the distributed task, into a so-called non-local hidden-variable model. We prove that a new class of communication complexity tasks can be associated with Bell-like inequalities, whose violation is both necessary and sufficient for a quantum gain. We experimentally implement a multipartite CCP akin to the guess-your-neighbour-input scenario, and demonstrate a quantum advantage when multipartite Greenberger-Horne-Zeilinger (GHZ) states are shared among three users.
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.
Private simultaneous quantum messages (PSQM) provide a minimal model of noninteractive secure multiparty quantum computation, yet their communication complexity for concrete functions remains poorly understood. We show that familiar total functions already exhibit both genuine quantum advantages and strong structural limitations. For three-party equality on nnn-bit inputs, which determines whether the players' nnn-bit strings are identical, we construct an entanglement-assisted protocol with asymptotic communication (1.633…)n(1.633\ldots)n(1.633…)n qubits, whereas every perfectly correct protocol without prior entanglement requires at least 3n3n3n qubits. For three-bit majority, one shared GHZ state and one transmitted qubit per player suffice for perfect correctness and perfect privacy, reducing the communication from the optimal classical cost of six bits to three qubits. Three-bit AND behaves differently. No perfectly correct and perfectly private protocol exists when the players share an arbitrary three-qubit state, apply arbitrary local unitary encodings, and transmit one qubit each. However, increasing the local dimension overcomes this obstruction: one shared three-qutrit GHZ state and one transmitted qutrit per player yield a one-shot protocol with total communication 3log⁡233\log_2 33log2​3. Together with the six-bit classical lower bound, this gives a strict quantum communication advantage. More generally, for every k≥3k\geq 3k≥3, we construct a perfectly correct and perfectly private one-shot protocol for kkk-bit AND using one qudit of dimension at most kkk per player, and hence at most klog⁡2kk\log_2 kklog2​k qubits in total.