2004/12/26 by Thomas Durt, Jaromı́r Fiurášek, Jaromir Fiurasek +1
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.72.052322
published as Phys. Rev. A 72, 052322 (2005). · 8 pages RevTex
arxiv created 2004/12/26 · openalex publication_date 2005/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The possibility of cloning a d-dimensional quantum system without an ancilla is explored, extending on the economical phase-covariant cloning machine for qubits found in Phys. Rev. A 60, 2764 (1999). We prove the impossibility of constructing an economical version of the optimal universal 1\ensuremath→2 cloning machine in any dimension. We also show, using an ansatz on the generic form of cloning machines, that the d-dimensional 1\ensuremath→2 phase-covariant cloner, which optimally clones all balanced superpositions with arbitrary phases, can be realized economically only in dimension d=2. The used ansatz is supported by numerical evidence up to d=7. An economical phase-covariant cloner can nevertheless be constructed for d>2, albeit with a slightly lower fidelity than that of the optimal cloner requiring an ancilla. Finally, using again an ansatz on cloning machines, we show that an economical version of the 1\ensuremath→2 Fourier-covariant cloner, which optimally clones the computational basis and its Fourier transform, is also possible only in dimension d=2.