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International Conference on Quantum Communications, Networking, and Computing (QCNC)

Compression-Aware Entanglement Efficiency Rate via Multiple Hamming Weighted States

Jan Østergaard

Published Apr 6, 2026• 1 citation
Publisher

Abstract

We propose a notion of compression-aware entanglement efficiency that accounts for the communication cost associated with distributing entangled qubits. Our analysis focuses on a class of pure bipartite quantum states constructed as amplitude-weighted superpositions of Dicke states. By optimizing the amplitude distribution and the choice of Hamming weights, we demonstrate that it is possible to maximize the ratio of entanglement entropy to the number of qubits that must be transmitted. This approach offers a principled way to quantify and enhance the efficiency of entanglement distribution in quantum communication protocols. The proposed symmetric states are highly compressible, and for$n=2,3,4$, and 6 qubits, they achieve the optimal entanglement efficiency rates.

DOI
10.1109/qcnc69040.2026.00143

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We study compression strategies for multipartite entanglement distribution under uncertainty in the partitioning of the quantum state. When the partition is not known at the time of state preparation, we show that a joint design of the resource state and a family of compression schemes can increase the entanglement across partitions under a fixed transmission budget. We formulate this as a source coding problem and derive non-asymptotic upper and lower bounds on the achievable average entanglement subject to an average coding rate. We furthermore design an efficient method for jointly optimizing states and lossless compression maps by exploiting the inherent symmetry of weighted Dicke states. In the bipartite case, we propose practical constructions that closely approach the derived upper bound, and more generally we provide practical constructions for multipartite settings.
We study compression strategies for multipartite entanglement distribution under uncertainty in the partitioning of the quantum state. When the partition is not known at the time of state preparation, we show that a joint design of the resource state and a family of compression schemes can increase the entanglement across partitions under a fixed transmission budget. We formulate this as a source coding problem and derive non-asymptotic upper and lower bounds on the achievable average entanglement subject to an average coding rate. We furthermore design an efficient method for jointly optimizing states and lossless compression maps by exploiting the inherent symmetry of weighted Dicke states. In the bipartite case, we propose practical constructions that closely approach the derived upper bound, and more generally we provide practical constructions for multipartite settings.
We consider implementations of a bipartite unitary on many pairs of unknown input states by local operation and classical communication assisted by shared entanglement. We investigate to what extent the entanglement cost and the classical communication cost can be compressed by allowing nonzero but vanishing error in the asymptotic limit of infinite pairs. We show that a lower bound on the minimal entanglement cost, the forward classical communication cost, and the backward classical communication cost per pair is given by the Schmidt strength of the unitary. We also prove that an upper bound on these three kinds of the cost is given by the amount of randomness that is required to partially decouple a tripartite quantum state associated with the unitary. In the proof, we construct a protocol in which quantum state merging is used. For generalized Clifford operators, we show that the lower bound and the upper bound coincide. We then apply our result to the problem of distributed compression of tripartite quantum states, and derive a lower and an upper bound on the optimal quantum communication rate required therein.
We investigate entanglement-based quantum key distribution protocols, with particular emphasis on their efficiency under realistic conditions of satellite quantum communications, where performance is limited by the low power of a received signal and background radiation. We focus on scenarios where each photon pair is used to encode multiple qubits in order to optimally utilize the weak signal. By optimizing over the source intensity and the number of encoded qubits we study the theoretical information limit for the QKD efficiency. We show that the optimal efficiency is attained for finite entangled photons pair production probability which is in contrast to conventional communication efficiency maximized in the limit of vanishing signal strength. The multiqubit encoding can enhance the secret key rate by up to an order of magnitude compared to single-qubit schemes.
This paper proposes a novel approach to entropy compression leveraging the unique properties of quantum entanglement. We demonstrate that, through the careful design of entangled states, it is possible to achieve compression rates exceeding those predicted by the classical Shannon limit. The core mechanism relies on encoding information within the quantum state distribution of an entangled state and exploiting the non-classical correlations inherent in entanglement for efficient probability distribution compression. Unlike traditional entropy compression methods which rely on statistical properties of classical information, our approach directly utilizes the correlations provided by entanglement, offering a fundamentally different strategy. We formulate the theoretical framework, outlining the key mathematical concepts and presenting a detailed analysis of the compression process. The central argument is that entanglement allows for a more effective representation of information than is possible with purely classical distributions, leading to a demonstrable advantage in compression. This work challenges the conventional understanding of entropy and compression, suggesting a new paradigm where quantum phenomena can be harnessed to surpass classical limitations. The presented model incorporates the concepts of entropy, entanglement entropy, and quantum state tomography to provide a comprehensive framework for this novel compression technique. The theoretical foundation is built upon the principles of quantum information theory, with a particular focus on the role of entanglement in information processing and storage. ---
We revisit the task of visible compression of an ensemble of quantum states with entanglement assistance in the one-shot setting. The protocols achieving the best compression use many more qubits of shared entanglement than the number of qubits in the states in the ensemble. Other compression protocols, with potentially larger communication cost, have entanglement cost bounded by the number of qubits in the given states. This motivates the question as to whether entanglement is truly necessary for compression, and if so, how much of it is needed. Motivated by questions in communication complexity, we lift certain restrictions that are placed on compression protocols in tasks such as state-splitting and channel simulation. We show that an ensemble of the form designed by Jain, Radhakrishnan, and Sen (ICALP'03) saturates the known bounds on the sum of communication and entanglement costs, even with the relaxed compression protocols we study. The ensemble and the associated one-way communication protocol have several remarkable properties. The ensemble is incompressible by more than a constant number of qubits without shared entanglement, even when constant error is allowed. Moreover, in the presence of shared entanglement, the communication cost of compression can be arbitrarily smaller than the entanglement cost. The quantum information cost of the protocol can thus be arbitrarily smaller than the cost of compression without shared entanglement. The ensemble can also be used to show the impossibility of reducing, via compression, the shared entanglement used in two-party protocols for computing Boolean functions.