bibkey: kotowski2026smallancilla
authors: Marcin Kotowski; Michał Kotowski
year: 2026
title: "Randomized simulation of quantum channels using small ancilla"
doi: null
url: https://arxiv.org/abs/2606.08784v1
claim: "The paper defines simulation of a channel with classical randomization and postselection, and asks (Question 6.1) whether every channel can be simulated with success probability Omega(1) using one additional qubit and O(1) rounds of projective measurements and adaptive unitaries."
strata_touched:
  - D5/S3/Quantum/QuantumChannels/OneQubitAdaptiveSimulationRefutation
license: citation-only
triage: anchor

Randomized simulation of quantum channels using small ancilla

Marcin Kotowski and Michał Kotowski, arXiv:2606.08784v1 (quant-ph), 2026-06-07. Quotations are from the v1 TeX source.

Simulation with postselection (Section 2.2, Definition 2.3):

We say that a channel $\Phi \in \text{channels}({\text{C}}^d)$ can be {\normalfont simulated with classical randomization and postselection} with ancilla dimension $k$ and success probability $q\in [0,1]$ if there exists a channel ${\Phi }^{\prime }\in \text{channels}({\text{C}}^d,{\text{C}}^d\otimes {\text{C}}^2)$ such that for any input state $\rho$ \begin{equation}\label{eq:postselection} \Phi’(\rho) = q \cdot \Phi(\rho) \otimes \ketbra{0}{0} + (1-q)\Phi^{\junk}(\rho)\otimes \ketbra{1} {1},

The open question (Section 6):

Consider the model of simulation with postselection that allows: 1) unitary operations with ancilla; 2) classical randomization; 3) projective measurements; 4) adaptive unitary operations based on measurement results. Can \textit{every} channel $\Phi$ be simulated in this way with success probability $\Omega (1)$ using one additional qubit and $O(1)$ rounds?

Verified locator

• URL: https://arxiv.org/abs/2606.08784v1 (v1, 2026-06-07, the only version; source draft.tex, md5 1312d35350116ee04e888e1605e23f61): Definition 2.3 (l. 221–226) and Question 6.1 (l. 1026–1028).