Related papers: Optimal complex conjugation of unknown isometry channels

Optimal complex conjugation of unknown isometry channels

URL: http://arxiv.org/abs/2607.29054v1
Date: Fri, 31 Jul 2026 06:13:40 GMT
Title: Optimal complex conjugation of unknown isometry channels
Abstract summary: We prove that a parallel protocol is optimal even among general quantum superchannels, including adaptive and indefinitecausal-order strategies.<n>We also present a circuit construction based on the quantum Schur transform and the dual Clebsch--Gordan transform, with circuit complexity $O(mathrmpoly(D,1/))$.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Access to the complex conjugate of an unknown quantum channel is a useful resource in quantum oracle problems, motivating the question of how such access can be simulated using only a limited number of calls to the original channel. We determine the optimal deterministic protocol for approximately implementing the complex conjugate isometry $\overline{V}$ from $n$ uses of an unknown isometry channel $V: \mathbb{C}^d\to\mathbb{C}^D$. We derive a closed-form expression for the optimal fidelity and prove that a parallel protocol is optimal even among general quantum superchannels, including adaptive and indefinite-causal-order strategies. The formula implies a query complexity $n=Θ(d[(D-d)/ε+1])$ for achieving infidelity $ε$. We also present a circuit construction based on the quantum Schur transform and the dual Clebsch--Gordan transform, with circuit complexity $O(\mathrm{poly}(D,1/ε))$. This task is extended to the multi-copy case $V^{\otimes n}\mapsto \overline{V}^{\otimes k}$. For fixed $d<D$ and $k$, we show that the optimal fidelity for the multi-copy case is $1-kd(D-d)/n+o(n^{-1})$, and that this value is asymptotically attained by a parallel estimation-based protocol. Finally, combining the isometry protocol with random Stinespring dilations yields a protocol for complex conjugation of unknown rank-$r$ quantum channels whose query complexity is optimal up to a constant factor if the Kraus rank $r$ is constant.

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