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arxiv: 2604.07849 · v1 · submitted 2026-04-09 · 🪐 quant-ph

Analysis of State Teleportation using Noisy Quantum Gates

Imama Tul Birrah Khan , Muhammad Faryad This is my paper

Pith reviewed 2026-05-10 17:25 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum teleportationnoise analysisfidelityquantum channelsdepolarizationbit flipphase fliperror mitigation
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The pith

Quantum state teleportation fidelity decreases polynomially with noise strength across common error types, but only linearly when noise remains weak.

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

The paper studies the effect of realistic noise on the standard quantum teleportation protocol by modeling depolarization, bit-flip, and phase-flip errors as quantum channels applied after each gate. It derives exact expressions for the fidelity between the ideal output state and the noisy teleported state. The central result is that fidelity falls as a polynomial in the noise parameter for all three error models, yet reduces to a linear dependence in the small-noise limit. This distinction matters because it shows how teleportation behaves under increasing error rates and points to where simple error models remain useful.

Core claim

When each noise channel acts independently on the qubits after the corresponding unitary gates in the teleportation circuit, the fidelity of the output state decreases polynomially with rising noise strength for depolarization, bit-flip, and phase-flip noise; the same fidelity decreases only linearly in the low-noise regime.

What carries the argument

Quantum channels for depolarization, bit-flip, and phase-flip noise applied individually after each unitary operation, followed by explicit calculation of the fidelity between the resulting density operator and the ideal teleported state.

If this is right

  • Error characterization for teleportation can use closed-form fidelity expressions derived from the channel models.
  • Noise mitigation strategies should account for the change from linear to polynomial degradation as noise strength increases.
  • The protocol remains relatively robust provided operation stays inside the low-noise regime where fidelity loss is linear.
  • Different noise mechanisms produce qualitatively similar fidelity scaling, so mitigation need not be tailored to one error type alone.

Where Pith is reading between the lines

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

  • The linear low-noise result suggests that first-order perturbation approximations may suffice for estimating performance in near-term devices.
  • Similar channel-by-channel analysis could be applied to other quantum communication primitives such as entanglement swapping.
  • Experimental tests on superconducting or ion-trap platforms could directly verify the predicted polynomial coefficients.
  • Extending the model to include correlated or time-dependent noise would test how far the independent-channel assumption can be stretched.

Load-bearing premise

Each type of noise can be represented as an independent quantum channel that acts separately on every qubit right after the ideal unitary gates.

What would settle it

Laboratory measurement of output fidelity versus controlled noise amplitude in a teleportation experiment on a few-qubit device, checking whether the observed curve is polynomial overall and linear at small noise values.

Figures

Figures reproduced from arXiv: 2604.07849 by Imama Tul Birrah Khan, Muhammad Faryad.

Figure 1
Figure 1. Figure 1: Circuit diagram for the ideal three-qubit [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Noisy three qubit teleportation circuit used [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fidelity of the teleported state as a func [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Fidelity of the teleported state as a func [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Fidelity of the teleported state as a function [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.

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 / 0 minor

Summary. The manuscript analytically studies the impact of depolarization, bit-flip, and phase-flip noise on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel applied individually to all qubits after the corresponding unitary operations. The fidelity between the ideal and noisy teleported states is evaluated, with the central claim that this fidelity decreases polynomially with noise strength in general but only linearly in the low-noise regime.

Significance. The provision of closed-form analytical expressions for the teleported-state fidelity under standard Kraus-operator noise channels constitutes a concrete, verifiable calculation. The polynomial character follows directly from the finite number of noise insertions in the teleportation circuit and the affine dependence of the channels on the noise parameter p; the linear low-noise correction is the expected first-order perturbative result. Such explicit formulas can serve as a reference for error scaling in quantum communication protocols and support noise-mitigation design, although the underlying modeling employs conventional quantum-channel tools without introducing new methodological elements.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. We appreciate the recognition that the closed-form fidelity expressions constitute a concrete, verifiable contribution that can serve as a reference for error scaling in quantum communication protocols.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper analytically computes the fidelity of teleported states under standard Pauli and depolarizing channels applied after each unitary in the teleportation circuit. The claimed polynomial dependence on noise strength p and linear leading correction for small p follow directly from the finite composition of trace-preserving CP maps that are affine in p; this is first-order perturbation on the channel and requires no internal fitting or self-referential definitions. Kraus operators are the standard external forms for bit-flip, phase-flip, and depolarizing channels. No self-citations, uniqueness theorems, or ansatzes are load-bearing. The result is externally verifiable by direct matrix multiplication on the circuit and is independent of any fitted parameters or prior results by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no explicit free parameters, axioms, or invented entities can be extracted; the work relies on the standard definition of quantum channels and fidelity, which are external.

pith-pipeline@v0.9.0 · 5443 in / 1033 out tokens · 32649 ms · 2026-05-10T17:25:52.804286+00:00 · methodology

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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

  1. [1]

    M. A. Nielsen and I. L. Chuang,Quantum Com- putation and Quantum Information(Cambridge University Press, 2000). 8

    work page 2000

  2. [2]

    Brassard, Teleportation as a quantum com- putation, arXiv:quant-ph/9600043

    G. Brassard, Teleportation as a quantum com- putation, arXiv:quant-ph/9600043

    work page arXiv

  3. [3]

    Pirandola, J

    S. Pirandola, J. Eisert, C. Weedbrook, A. Furu- sawa and S. L. Braunstein, Advances in quantum teleportation,Nat. Photonics9(2015) 641–652

    work page 2015

  4. [4]

    Uotila, Gate teleportation in noisy quantum networks with the SquidASM simulator, inProc

    V. Uotila, Gate teleportation in noisy quantum networks with the SquidASM simulator, inProc. IEEE Int. Conf. Quantum Comput. Eng.(2024), pp. 161–166

    work page 2024

  5. [5]

    Resch and U

    S. Resch and U. R. Karpuzcu, Benchmarking quantum computers and the impact of quantum noise,ACM Comput. Surv.54(2021) 142

    work page 2021

  6. [6]

    S. N. Filippov, T. Ryb´ ar and M. Ziman, Lo- cal two-qubit entanglement-annihilating chan- nels,Phys. Rev. A85(2012) 012303

    work page 2012

  7. [7]

    Georgopoulos, C

    K. Georgopoulos, C. Emary and P. Zuliani, Modeling and simulating the noisy behavior of near-term quantum computers,Phys. Rev. A 104(2021) 062432

    work page 2021

  8. [8]

    L. T. Knoll, C. T. Schmiegelow and M. A. Laro- tonda, Noisy quantum teleportation: An exper- imental study on the influence of local environ- ments,Phys. Rev. A90(2014) 042332

    work page 2014

  9. [9]

    Fonseca, High-dimensional quantum telepor- tation under noisy environments,Phys

    A. Fonseca, High-dimensional quantum telepor- tation under noisy environments,Phys. Rev. A 100(2019) 062311

    work page 2019

  10. [10]

    D.-G. Im, J. Kim and H. Nha, Quantum telepor- tation in noisy environments,npj Quantum Inf. 7(2021) 86

    work page 2021

  11. [11]

    Kumar and P

    D. Kumar and P. N. Pandey, Effect of noise on quantum teleportation,Phys. Rev. A68(2003) 012317

    work page 2003

  12. [12]

    S. Oh, S. Lee and H.-W. Lee, Fidelity of quan- tum teleportation through noisy channels,Phys. Rev. A66(2002) 022316

    work page 2002

  13. [13]

    M. M. Wilde,Quantum Information Theory (Cambridge University Press, 2013)

    work page 2013

  14. [14]

    Dutta, A

    S. Dutta, A. S. Majumdar and A. K. Pati, Noise effects in quantum teleportation protocols, Physica Scripta98(2023) 115113

    work page 2023

  15. [15]

    C. H. Bennett, G. Brassard, C. Cr´ epeau, R. Jozsa, A. Peres and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,Phys. Rev. Lett.70(1993) 1895

    work page 1993

  16. [16]

    Knill and R

    E. Knill and R. Laflamme, A theory of quan- tum error-correcting codes,Phys. Rev. Lett.84 (2000) 2525. 9

    work page 2000