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arxiv: 2604.13643 · v1 · submitted 2026-04-15 · 🪐 quant-ph

Quantum secret sharing in tripartite superconducting network

W. K. Yam , C. Wilkinson , S. Gandorfer , F. Fesquet , M. Handschuh , A. Marx , R. Gross , N. Korolkova
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K. G. Fedorov
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Pith reviewed 2026-05-10 12:52 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum secret sharingsuperconducting circuitsmicrowave entanglementtwo-mode squeezed statesquantum networksno-cloning thresholdmultipartite protocols
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The pith

Superconducting microwave network implements quantum secret sharing where any two of three players reconstruct the secret with fidelity above the no-cloning limit.

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

This paper reports an experimental demonstration of a quantum secret sharing protocol using a tripartite network of superconducting circuits. Entanglement is supplied by microwave two-mode squeezed states, allowing a secret quantum state to be distributed such that at least two collaborating players can recover it faithfully. Reconstructed fidelities exceed the asymptotic no-cloning threshold of 2/3, and a parameter window is identified that supports unconditionally secure operation even when one player is dishonest. The work also maps direct operational links between secret sharing and tasks such as quantum dense coding and correction of erasure errors.

Core claim

Using microwave two-mode squeezed states as an entanglement resource, we experimentally implement a QSS protocol with n = 3, where a subset of at least k = 2 players must collaborate to faithfully reconstruct the original secret state. We demonstrate reconstructed-state fidelities that surpass the asymptotic no-cloning threshold of F_nc = 2/3 and identify a parameter regime that allows for unconditionally secure communication in the presence of an omnipotent dishonest player.

What carries the argument

Microwave two-mode squeezed states used as the entanglement resource to encode and distribute the secret across the three-party superconducting network for the (3,2) threshold scheme.

If this is right

  • A parameter regime exists in which the protocol remains secure against an omnipotent dishonest player.
  • QSS shares operational structure with quantum dense coding, allowing direct translation of resources between the two tasks.
  • The same entanglement distribution supports elementary error correction against channel erasures.
  • The protocol architecture extends naturally toward blind quantum computing applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Integration with existing superconducting processors could support distributed quantum algorithms that require secure multi-party state sharing.
  • The demonstrated noise tolerance suggests the platform can be scaled to larger player sets while preserving the threshold advantage.
  • Combining this microwave QSS with optical links may enable hybrid quantum internet nodes that mix circuit and photonic modalities.

Load-bearing premise

The experimental hardware supplies sufficient entanglement and low enough noise to reach the reported fidelities, and the model of the dishonest player accurately represents possible attacks.

What would settle it

A reconstructed-state fidelity measurement at or below 2/3 under the same entanglement and noise conditions, or an explicit successful attack by a modeled dishonest player that prevents faithful reconstruction by the honest subset.

Figures

Figures reproduced from arXiv: 2604.13643 by A. Marx, C. Wilkinson, F. Fesquet, K. G. Fedorov, M. Handschuh, N. Korolkova, R. Gross, S. Gandorfer, W. K. Yam.

Figure 1
Figure 1. Figure 1: Schematic overview of the ((𝑘, 𝑛)) threshold QSS protocol implemented in this work. (a) Illustration of secret sharing among 𝑛 players, where a subset of 𝑘 players collaborate to securely reconstruct a secret input state |𝛼⟩. (b) Experimental scheme of the Dealer part of the QSS protocol, where the Dealer superimposes an unknown secret coherent state with one mode of a TMS entanglement resource and distrib… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Negativity 𝑁 and purity 𝜇 of the resource TMS state as a function of squeezing level 𝑆. Reconstructed state fidelities for the collaborating players and the adversary as a function of TMS resource squeezing level 𝑆, using (a) the {1, 2} scheme and (b) the {2, 3} scheme with reconstruction JPA gain 𝐺 = 7 dB. Input coherent states have average displacement photon number |𝛼|2 = 1.3. Mutual information val… view at source ↗
Figure 3
Figure 3. Figure 3: Security of the QSS implementation against an attack on all modes. (a) Reconstructed state fidelities for the {2, 3} scheme at various input coherent state displacements |𝛼|2 and reconstruction JPA gains 𝐺. Solid lines represent theory model fits to the experimental QSS data. Error bars denote the standard error of the experimental data and are smaller than the symbol size when not shown. (b) Fidelity dist… view at source ↗
Figure 4
Figure 4. Figure 4: Dense coding as a reinterpretation of the {2, 3} reconstruction scheme in the QSS protocol. (a) Experimental scheme. The sender uses a hybrid ring to encode classical information from the input signal by locally displacing one part of the entangled TMS state. The encoded state is transmitted to the receiver, who uses the other part of the entangled TMS state to perform the decoding operation. By applying a… view at source ↗
Figure 5
Figure 5. Figure 5: QSS for quantum error correction of erasure errors. (a) Fidelity advantage 𝐹adv of using the QSS protocol for error correction as a function of input state displacement |𝛼|2 and erasure probability 𝜆. Solid orange line denotes the parameter regime where 𝐹adv = 0 %. The maximum advantage of 𝐹adv = 2.83 % is achieved at |𝛼|2 = 2.540 and 𝜆 = 0.466, as indicated by the red star. Fidelities as a function of (b)… view at source ↗
read the original abstract

Superconducting microwave quantum networks is a rapidly developing field, enabling distributed quantum computing and holding a promise for hybrid architectures in quantum internet. Quantum secret sharing (QSS) is one of the key protocols for multipartite quantum networks and can provide an unconditionally secure way to share quantum states among $n$ players. Using microwave two-mode squeezed states as an entanglement resource, we experimentally implement a QSS protocol with $n = 3$, where a subset of at least $k = 2$ players must collaborate to faithfully reconstruct the original secret state. We demonstrate reconstructed-state fidelities that surpass the asymptotic no-cloning threshold of $F_\textrm{nc} = 2/3$ and identify a parameter regime that allows for unconditionally secure communication in the presence of an omnipotent dishonest player. Furthermore, we experimentally explore inherent connections between QSS and other important quantum information processing tasks, such as quantum dense coding and elementary quantum error correction of channel erasures. Finally, we discuss extensions of QSS and its relation to the concept of blind quantum computing.

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

0 major / 3 minor

Summary. The paper experimentally realizes a (2,3) quantum secret sharing protocol in a tripartite superconducting microwave network. Microwave two-mode squeezed states serve as the entanglement resource; any two of the three players can reconstruct the secret state with fidelities exceeding the asymptotic no-cloning bound F_nc = 2/3. A parameter regime is identified that permits unconditional security against an omnipotent dishonest player, and connections are drawn to quantum dense coding and elementary quantum error correction of erasures.

Significance. If the reported fidelities and security bounds hold, the work constitutes a concrete experimental milestone for multipartite quantum communication in superconducting hardware. The explicit mapping between QSS, dense coding, and erasure correction, together with the identification of a secure operating regime, supplies practical guidance for scaling microwave quantum networks.

minor comments (3)
  1. [§3.2] §3.2 and Fig. 3: the caption and text should explicitly state the number of tomographic measurements per reconstructed state and the precise maximum-likelihood estimator used, as these details directly affect the quoted fidelity uncertainties.
  2. [§4.1] §4.1, Eq. (8): the bound on the dishonest player’s information is derived under a specific noise model; a short paragraph clarifying how the measured squeezing level and channel loss map onto the parameters of that model would strengthen the security claim.
  3. [Fig. 5] Fig. 5: the color scale for the reconstructed density matrices should be labeled with the numerical range and the basis ordering should be stated in the caption to allow direct comparison with the ideal target states.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of our manuscript and for recommending minor revision. We are pleased that the experimental demonstration of the (2,3) quantum secret sharing protocol, the achieved fidelities above the no-cloning bound, and the identified secure parameter regime against dishonest players were viewed as a concrete milestone for multipartite quantum communication in superconducting hardware.

Circularity Check

0 steps flagged

No significant circularity: experimental demonstration

full rationale

The manuscript reports an experimental implementation of a (2,3) quantum secret sharing protocol using microwave two-mode squeezed states in a tripartite superconducting network. Central results are measured state fidelities exceeding the no-cloning bound F_nc=2/3, supported by tomography, reconstruction procedures, and noise characterization. Security bounds are derived from measured entanglement and noise levels rather than from any self-referential fit or ansatz. No derivation chain exists that reduces predictions or uniqueness claims to the paper's own inputs by construction; the work is self-contained against external benchmarks such as the asymptotic no-cloning threshold.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work builds on standard quantum information theory and experimental techniques in circuit QED without introducing new entities or many free parameters in the abstract description.

axioms (1)
  • standard math Quantum no-cloning theorem implies a fidelity threshold of 2/3 for secure secret sharing
    Directly referenced as F_nc = 2/3 for the asymptotic case.

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