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arxiv: 2605.04271 · v1 · submitted 2026-05-05 · 🪐 quant-ph · cs.IT· math.IT

Quantum Compression for Distributed Entanglement

Jan {\O}stergaard , Shashi Raj Pandey , Christophe Biscio , Torben Bach Pedersen , Petar Popovski This is my paper

Pith reviewed 2026-05-08 17:03 UTC · model grok-4.3

classification 🪐 quant-ph cs.ITmath.IT
keywords quantum entanglementsource codingweighted Dicke statesmultipartite entanglementcompressionnon-asymptotic boundsdistributed entanglementunknown partitions
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The pith

Joint design of resource states and compression maps increases average entanglement across unknown partitions under a fixed transmission budget.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to show that when the partitioning of a multipartite quantum state is unknown ahead of time, preparing a symmetric entangled state and pairing it with a family of compression schemes designed jointly can deliver more average entanglement to the receivers than preparing a state optimized for a guessed partition. This matters because quantum networks often face uncertainty about which parties will receive which parts of the entanglement, and transmission resources like channel uses are limited. By casting the task as a source coding problem with entanglement as the figure of merit, the authors obtain non-asymptotic upper and lower bounds on the achievable entanglement for a given average coding rate. They further exploit the symmetry of weighted Dicke states to make the joint optimization of states and maps computationally feasible. Practical constructions are given that nearly meet the bounds in the bipartite case.

Core claim

The central claim is 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. This is formulated as a source coding problem, yielding non-asymptotic upper and lower bounds on the achievable average entanglement subject to an average coding rate. Efficient optimization is enabled by the symmetry of weighted Dicke states, and practical constructions for bipartite and multipartite cases are provided that approach the bounds.

What carries the argument

weighted Dicke states, whose symmetry properties enable tractable joint optimization of the prepared state and the lossless compression maps for different possible partitions

Load-bearing premise

The partition of the quantum state is unknown at the time of preparation, and the symmetry properties of weighted Dicke states suffice for tractable joint optimization of states and compression maps without significant performance loss.

What would settle it

A calculation for a small number of qubits showing that the average entanglement achieved by the joint design falls below the value obtained by separate optimization for each possible partition, or that the achieved value violates the derived upper bound.

Figures

Figures reproduced from arXiv: 2605.04271 by Christophe Biscio, Jan {\O}stergaard, Petar Popovski, Shashi Raj Pandey, Torben Bach Pedersen.

Figure 1
Figure 1. Figure 1: An n = 7 qubit symmetric state |ϕ⟩ is prepared. Three randomly chosen qubits are selected for Alice and the remaining four for Bob. The subsystems are compressed such that the entanglement is confined to a lower-dimensional support, allowing it to be represented losslessly using fewer qubits. This reduces communication costs and increases the amount of entanglement per transmitted qubit. The random selecti… view at source ↗
Figure 2
Figure 2. Figure 2: Entanglement-rate curves for m = 2 and n = 2, . . . , 15. The upper and lower bounds are given by Theorems 1 and 2, respectively. The weighted Dicke states are the solutions to (39) and the Comb states are given by (20). Also shown is the performance of AME states (55). The numbers on the curves indicate n. upper bound. Note that it is in fact unclear whether the upper bound is even achievable in these sit… view at source ↗
Figure 3
Figure 3. Figure 3: Entanglement-rate curves for m = 3 and n = 3, . . . , 15. The upper and lower bounds are given by Theorems 3 and 4, respectively. The weighted Dicke states are the solutions to (39) and the Comb states are given by (20). The numbers on the curves indicate n. For n > 6, the lower bound is greater than EAME(n), which demonstrates the efficiency of compression. B. Three parties: m = 3 In this simulation, we f… view at source ↗
Figure 4
Figure 4. Figure 4: Uncompressed transmission of two three qubit systems with channel noise. Compressed transmission of the systems with and without view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that when the partition of a multipartite quantum state is unknown at preparation, a joint design of the resource state (restricted to weighted Dicke states) and a family of lossless compression maps can increase the average entanglement delivered across partitions under a fixed average coding rate. It formulates the task as a quantum source-coding problem, derives non-asymptotic upper and lower bounds on achievable average entanglement, and gives an efficient symmetry-exploiting optimization procedure together with explicit bipartite constructions that approach the upper bound and general multipartite constructions.

Significance. If the bounds are tight and the symmetry-restricted constructions are near-optimal, the work would be significant for quantum network protocols that must distribute entanglement without prior knowledge of the receiver partition. The non-asymptotic character of the bounds and the explicit use of symmetry to obtain tractable joint optimization are genuine strengths that distinguish the contribution from purely asymptotic analyses.

major comments (2)
  1. [§4] §4 (joint optimization via weighted Dicke symmetry): the manuscript asserts that the symmetry of weighted Dicke states suffices to make the joint optimization over states and compression maps tractable without significant performance loss, yet provides no quantitative bound or comparison showing the sub-optimality gap relative to the unrestricted optimum. This assumption is load-bearing for the claim that the reported constructions closely approach the derived upper bound, especially in the multipartite regime where only general constructions are given.
  2. [§3] §3 (non-asymptotic bounds): the upper and lower bounds are stated to follow from coding-theoretic arguments, but the manuscript does not include an explicit error analysis or verification that the inequalities remain valid once the compression maps are restricted to the symmetric family; without this, it is unclear whether the gap between the constructions and the upper bound is an artifact of the symmetry restriction rather than an intrinsic limit.
minor comments (2)
  1. The abstract and introduction would benefit from a brief statement of the precise figure of merit (average entanglement per transmitted qubit) and the precise definition of the average coding rate to avoid ambiguity for readers outside quantum information.
  2. Notation for the weighted Dicke states and the associated compression maps should be introduced with a short table or diagram in §2 so that the symmetry arguments in later sections are immediately readable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the thorough review and the encouraging assessment of the significance of our work. We respond to the major comments point by point below.

read point-by-point responses

  1. Referee: [§4] §4 (joint optimization via weighted Dicke symmetry): the manuscript asserts that the symmetry of weighted Dicke states suffices to make the joint optimization over states and compression maps tractable without significant performance loss, yet provides no quantitative bound or comparison showing the sub-optimality gap relative to the unrestricted optimum. This assumption is load-bearing for the claim that the reported constructions closely approach the derived upper bound, especially in the multipartite regime where only general constructions are given.

    Authors: We agree that the manuscript does not provide a general quantitative bound on the sub-optimality gap introduced by restricting to weighted Dicke states. In the bipartite case, our explicit constructions are shown numerically to approach the upper bound closely, indicating that the symmetry restriction incurs only small loss in that regime. For multipartite systems, the restriction is adopted to ensure computational tractability, as the unrestricted joint optimization is intractable. We will revise the manuscript to explicitly note that the upper bound holds for general maps while the constructions are symmetry-restricted, and to highlight the bipartite numerical evidence as support for the approach's near-optimality. revision: partial

  2. Referee: [§3] §3 (non-asymptotic bounds): the upper and lower bounds are stated to follow from coding-theoretic arguments, but the manuscript does not include an explicit error analysis or verification that the inequalities remain valid once the compression maps are restricted to the symmetric family; without this, it is unclear whether the gap between the constructions and the upper bound is an artifact of the symmetry restriction rather than an intrinsic limit.

    Authors: The upper and lower bounds in §3 are derived from general coding-theoretic arguments that apply to arbitrary compression maps and do not rely on symmetry. The upper bound therefore remains a valid general limit, while the symmetric constructions achieve a (possibly lower) rate within the restricted family. The observed gap may thus include the effect of the restriction. We will revise the manuscript to state this distinction explicitly and clarify that the bounds are general while the constructions provide achievable performance under symmetry. revision: yes

Circularity Check

0 steps flagged

No circularity in the derivation chain

full rationale

The paper formulates the entanglement compression task as a standard source-coding problem and derives non-asymptotic upper and lower bounds directly from coding-theoretic arguments. The joint optimization over states and maps is made tractable by an explicit modeling restriction to the symmetric family of weighted Dicke states; this is presented as a design choice rather than a result that is forced by redefinition or by a self-citation chain. No step reduces a claimed prediction or bound to a fitted parameter or to an input that is defined in terms of the output, and the constructions are offered as practical approximations whose performance is compared against independently derived bounds.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract; no explicit free parameters, invented entities, or non-standard axioms are described. The work relies on standard quantum mechanics and information-theoretic coding principles.

axioms (1)
  • standard math Standard axioms of quantum mechanics and quantum information theory, including definitions of entanglement and coding rate constraints
    Invoked to define the problem, entanglement measures, and derive the stated bounds.

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Reference graph

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