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arxiv: 2604.12823 · v1 · submitted 2026-04-14 · 🪐 quant-ph

The use of the output states generated by the broadcasting of entanglement in quantum teleportation

Iulia Ghiu , Catalina Cirneci , George Alexandru Nemnes This is my paper

Pith reviewed 2026-05-10 16:09 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum teleportationentanglement broadcastingX-statesconcurrencefidelityasymmetric broadcastingquantum channels
0
0 comments X p. Extension

The pith

Output states from local and nonlocal asymmetric broadcasting of entanglement serve as useful quantum channels for teleportation, with the nonlocal case delivering higher maximal fidelity.

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

The paper derives a theorem that directly links the maximal fidelity achievable in quantum teleportation to the concurrence of an inseparable X-state used as the quantum channel. It then calculates the concurrence for the output states produced by both local and nonlocal asymmetric entanglement broadcasting protocols and shows that these states remain inseparable X-states. Because the states are inseparable, the theorem establishes that they can all function as teleportation channels, and the higher concurrence in the nonlocal case produces a strictly better teleportation fidelity than the local case.

Core claim

A theorem relates the maximal teleportation fidelity to the concurrence of an inseparable X-state channel. The output states of local and nonlocal asymmetric broadcasting of entanglement are inseparable X-states with positive concurrence, so all of them can be used as quantum channels. The nonlocal broadcasting protocol generates states of higher concurrence and therefore higher maximal teleportation fidelity than the local protocol.

What carries the argument

The theorem connecting maximal teleportation fidelity to the concurrence of an X-state quantum channel, applied to the output states of local and nonlocal asymmetric entanglement broadcasting.

If this is right

  • Every inseparable output state generated by either broadcasting protocol can be employed as a quantum channel that exceeds the classical teleportation limit.
  • The nonlocal asymmetric broadcasting protocol systematically produces channels with larger concurrence and therefore higher teleportation fidelity than the local protocol.
  • Any future comparison of broadcasting schemes for quantum communication can be ranked by the concurrence of their output X-states.

Where Pith is reading between the lines

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

  • The same broadcasting outputs could be tested as resources for other protocols such as quantum key distribution or entanglement swapping.
  • If experimental implementations of the broadcasting operations deviate from ideal X-state form, the theorem would need an extension to general two-qubit states.
  • Optimizing the asymmetry parameters in the nonlocal protocol might further increase concurrence and fidelity beyond the values reported.

Load-bearing premise

The specific output states produced by the defined broadcasting operations are X-states to which the new theorem applies directly.

What would settle it

Perform quantum teleportation using an output state from the nonlocal asymmetric broadcasting protocol as the channel and measure whether the achieved fidelity is higher than the fidelity obtained with the corresponding local-broadcasting state, as predicted by the concurrence values.

Figures

Figures reproduced from arXiv: 2604.12823 by Catalina Cirneci, George Alexandru Nemnes, Iulia Ghiu.

Figure 1
Figure 1. Figure 1: Concurrence of ρ a1b1 (left) and ρ a2b2 (right) using local asymmetric cloning machines. Let us find the condition for the maximum of the concurrence of these two states. Therefore, we evaluate the partial derivative of the concurrence with respect to |α|: ∂C(ρ a1b1 ) ∂|α| = 2 [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A comparison between the concurrence of ρ a1b1 and the concurrence of ρ a2b2 when local asymmetric cloning machines are employed. ∂C(ρ a2b2 ) ∂|α| = 2 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The range of |α| given by Eq. (37) for which the state ρ a1b1 is inseparable is situated between the black curves. The range of |α| given by Eq. (41) for which the state ρ a2b2 is inseparable is situated between the red curves. The region obtained by the intersection represents the range of both |α| and p such that the two states are simultaneously inseparable. We obtain the conditions for both states ρ a1… view at source ↗
Figure 4
Figure 4. Figure 4: Concurrence of ρ a1b1 (left) and ρ a2b2 (right) using a nonlocal asymmetric cloning machine. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: A comparison between the concurrence of ρ a1b1 and the concurrence of ρ a2b2 when a nonlocal asymmetric cloning machine is employed. We analyze now in which conditions the two output states are simultaneously inseparable: see [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The range of |α| given by Eq. (53) for which the state ρ a1b1 is inseparable is situated between the black curves. The range of |α| given by Eq. (56) for which the state ρ a2b2 is inseparable is situated between the red curves. The region obtained by the intersection represents the range of both |α| and p such that the two states are simultaneously inseparable. We obtain the conditions for both states ρ a1… view at source ↗
Figure 7
Figure 7. Figure 7: Fidelity of teleportation, when the states [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Fidelity of teleportation, when the states [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
read the original abstract

In this article, we find a theorem that gives a relation between the maximal fidelity of teleportation and the concurrence of the inseparable $X$ state used as a quantum channel in this process. Furthermore, we evaluate the concurrence of the output states generated by the local and nonlocal asymmetric broadcasting of entanglement and prove that the concurrence is greater in the case of nonlocal broadcasting. We analyze the possibility of using the output states obtained by the broadcasting of entanglement as quantum channels in quantum teleportation. We prove, with the help of the above-mentioned theorem, that all the inseparable states given by the local and nonlocal asymmetric broadcasting of entanglement are useful for quantum teleportation. Finally, we show that the maximal fidelity of teleportation is greater in the case when the second scenario is used, i.e., when the quantum channel is generated by the nonlocal asymmetric broadcasting of entanglement.

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 paper derives a theorem relating the maximal teleportation fidelity to the concurrence of an inseparable X-state quantum channel. It evaluates concurrences of output states from local and nonlocal asymmetric entanglement broadcasting, proves nonlocal broadcasting yields higher concurrence, shows via the theorem that all inseparable broadcast outputs are useful for teleportation (fidelity > 2/3), and concludes that the nonlocal scenario produces strictly higher maximal fidelity.

Significance. If the theorem holds exactly for the parametrized X-states produced by the broadcasting maps and the outputs are confirmed to be X-states, the work supplies a concrete, quantitative link between entanglement broadcasting protocols and teleportation performance, with a clear preference for the nonlocal asymmetric case. This could inform channel optimization in quantum communication, building on standard entanglement measures to yield falsifiable comparisons.

major comments (2)
  1. [the theorem] The main theorem: the derivation of the relation between maximal teleportation fidelity and concurrence for X-states must be given explicitly (including the functional form F_max(C) and any conditions on matrix elements or parameter ranges) to confirm it applies directly to the specific density matrices generated by the local and nonlocal asymmetric broadcasting protocols without additional restrictions.
  2. [analysis of broadcasting protocols] Broadcasting output states: the manuscript assumes the outputs of the defined local and nonlocal asymmetric broadcasting operations are X-states to which the theorem applies. Explicit parametrization of these density matrices (including verification that off-diagonal elements and zero positions match the X-form used in the theorem) is required, as any mismatch would undermine the proofs that all inseparable states are useful for teleportation and that nonlocal broadcasting gives higher F_max.
minor comments (2)
  1. [abstract] The abstract refers to 'the above-mentioned theorem' without stating its content; a one-sentence summary of the theorem's relation would aid readability.
  2. [introduction] Notation for the local versus nonlocal broadcasting maps and the resulting state parameters should be introduced consistently in the first section where they appear.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and will incorporate the requested explicit details in a revised version to improve clarity and rigor.

read point-by-point responses

  1. Referee: The main theorem: the derivation of the relation between maximal teleportation fidelity and concurrence for X-states must be given explicitly (including the functional form F_max(C) and any conditions on matrix elements or parameter ranges) to confirm it applies directly to the specific density matrices generated by the local and nonlocal asymmetric broadcasting protocols without additional restrictions.

    Authors: We agree that the derivation of the theorem requires explicit presentation to confirm its applicability. In the revised manuscript, we will provide the complete step-by-step derivation of the relation between maximal teleportation fidelity and concurrence for X-states, including the functional form F_max(C) and the conditions on matrix elements and parameter ranges. This will demonstrate that the theorem applies directly to the density matrices produced by both broadcasting protocols. revision: yes

  2. Referee: Broadcasting output states: the manuscript assumes the outputs of the defined local and nonlocal asymmetric broadcasting operations are X-states to which the theorem applies. Explicit parametrization of these density matrices (including verification that off-diagonal elements and zero positions match the X-form used in the theorem) is required, as any mismatch would undermine the proofs that all inseparable states are useful for teleportation and that nonlocal broadcasting gives higher F_max.

    Authors: We acknowledge the need for explicit parametrization to verify the X-state structure. In the revised manuscript, we will include the full explicit forms of the output density matrices for the local and nonlocal asymmetric broadcasting protocols. We will detail all matrix elements, confirm the positions of zeros and off-diagonal terms match the X-form assumed in the theorem, and thereby support the proofs that all inseparable outputs are useful for teleportation with the nonlocal case yielding higher maximal fidelity. revision: yes

Circularity Check

0 steps flagged

No circularity: theorem derived from definitions; comparisons use explicit concurrence calculations

full rationale

The paper presents a new theorem relating maximal teleportation fidelity to concurrence for X-states, derived directly from the standard definitions of fidelity and concurrence without any reduction to fitted parameters or prior self-citations. Concurrence for the output states of the local and nonlocal asymmetric broadcasting protocols is computed explicitly from the protocol maps and density-matrix parametrizations. Usefulness for teleportation is then shown by applying the theorem to states with positive concurrence, and the nonlocal advantage follows from direct comparison of those computed concurrences. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear; the chain remains self-contained against the external definitions of concurrence and teleportation fidelity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claims rest on standard quantum mechanics, the definition of concurrence for two-qubit states, the definition of teleportation fidelity, and the assumption that the broadcast outputs remain X-states. No free parameters or new entities are introduced in the abstract.

axioms (1)
  • standard math Standard axioms of quantum mechanics together with the definitions of concurrence and teleportation fidelity for two-qubit states.
    All calculations presuppose the usual Hilbert-space formalism and established entanglement measures.

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Reference graph

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