bibkey: sekatskiguryanovakothakondaskotiniotis2025cloning
authors: Pavel Sekatski; Yelena Guryanova; Naga Bhavya Teja Kothakonda; Michalis Skotiniotis
year: 2025
title: "Cloning Quantum Channels"
doi: 10.48550/arXiv.2509.08059
url: https://arxiv.org/abs/2509.08059v1
claim: "The paper treats deterministic cloning of quantum channels with quantum processes, gives necessary conditions for super-replication, shows that amplitude-damping channels have at most linear cloning rate, compares coherent and measure-and-prepare processes, observes that a coherent process attains Choi fidelity one for amplitude-damping channels at N=M, and conjectures that no measure-and-prepare process does."
strata_touched:
  - D5/S3/Quantum/QuantumChannels/AmplitudeDampingMeasurePrepareCloning
license: citation-only
triage: anchor

Cloning Quantum Channels

P. Sekatski, Y. Guryanova, N. B. T. Kothakonda and M. Skotiniotis, arXiv:2509.08059v1 (2025). Quotations are from the v1 TeX source.

Measure-and-prepare processes:

\textit{Measure-and-prepare} processes consist of two steps: (i) a measurement process $\{\text{proc}{E}_{\ell }\}$ that consumes $N$ copies of the input channel to produce a classical outcome $\ell$ with probability $\text{proc}{E}_{\ell }[{\text{cE}}^{\times N}]$, and (ii) a global channel preparation ${\widehat{\text{cE}}}_{\ell }^{(M)}\in \text{cL}({\text{cH}}^{\otimes M}\text{tightto}{\text{cH}}^{\otimes M})$ conditioned on the value $\ell$. These processes have the general form $\text{proc}{P}_{M\&P}[{\text{cE}}^{\times N}]={\sum }_{\ell }\text{proc}{E}_{\ell }[{\text{cE}}^{\times N}]{\widehat{\text{cE}}}_{\ell }^{(M)}$

The amplitude-damping family:

$\text{ADset}:=\{{\text{cE}}_{\text{adp}}|\text{adp}\in [0,1]\}$ of qubit amplitude-damping (AD) channels ${\text{cE}}_{\text{adp}}[\cdot ]:=K_0(\text{adp})\cdot K_0^{†}(\text{adp})+K_1(\text{adp})\cdot K_1^{†}(\text{adp}),\text{with}{K}_0(\text{adp})=\left(\begin{array}{cc}1& 0\\ 0& \sqrt{1-\gamma }\end{array}\right)$, $K_1(\text{adp})=\left(\begin{array}{cc}0& \sqrt{\gamma }\\ 0& 0\end{array}\right)$ in the computational basis.

The conjecture:

In particular, it achieves ${\mathrm{F}}_{\mathrm{CJ}}^{\text{ADset}|\mathrm{coh}}=1$ at $N=M$, which, for amplitude-damping channels, we conjecture to be impossible for any measure-and-prepare process.

Verified locator

Source: https://arxiv.org/abs/2509.08059v1

• URL: https://arxiv.org/abs/2509.08059v1 (source arxiv_v1.tex, md5 abcdd29ea99d1c5adf0206c6b9a9d211):
  • measure-and-prepare processes, l. 1094–1100;
  • the amplitude-damping family, l. 1538–1553;
  • the conjecture, l. 1684–1685.
• DOI: 10.48550/arXiv.2509.08059 (https://doi.org/10.48550/arXiv.2509.08059; arXiv v1 is the only version).