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arXiv:2605.04271

Quantum Compression for Distributed Entanglement

Jan Østergaard, Shashi Raj Pandey, Christophe Biscio, Torben Bach Pedersen, Petar Popovski

quant-phcs.ITSubmitted May 5, 2026• Announced May 7, 2026• 0 citations
v1 · May 5, 2026v2 · Jun 19, 2026
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Abstract

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.

Comments
Submitted to JSAIT. Proofs available in the supplemental part

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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.
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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 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 forn=2,3,4n=2,3,4n=2,3,4, and 6 qubits, they achieve the optimal entanglement efficiency rates.
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We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length of a quantum string is the maximal length in the superposition). This complements work by Schumacher and Westmoreland who calculated the corresponding rate for minimizing the output's average length. Our compressed code words are prefix-free indeterminate-length quantum bit strings which can be concatenated in the case of multiple sources. Therefore, we generalize the known theory of prefix-free quantum codes to the case where strings have indeterminate length. Moreover, we describe a communication model which allows the lossless transmission of the compressed code words. The benefit of compression is then the reduction of transmission errors in the presence of noise.