Year: 2026
Type: preprint
Abstract: In this work, we study asymmetric $(1\to2)$ quantum cloning for pure states belonging to orbits generated by the orthogonal group. For every dimension $(d\geq3)$, we determine the full region of achievable pairs of average single-copy fidelities. Using orthogonal covariance and the Brauer algebra, we reduce the optimization over all CPTP maps to a finite-dimensional spectral problem and construct explicit optimal cloning channels. We then apply the general results to four-mode fermionic states in the even-parity sector. Using triality, we identify the fixed-concurrence fermionic families with the orthogonal orbits considered in the first part of the paper. In particular, for pure Gaussian states we show that the symmetric locally optimal cloner is unique. We also compare local and global cloning and find that the channel optimal for the joint two-copy fidelity is different from the one optimal for the single-copy fidelities. Finally, we show that the locally optimal cloner cannot be implemented using only operations which preserve fermionic Gaussian states.
Source: arXiv (Cornell University)
Authors: Ćwikliński, Piotr, Studziński, Michał
Institution: University of Gdańsk
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213939552