Economical quantum cloning in any dimension

Journal Article · Tue Nov 15 04:00:00 EST 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.72.0· OSTI ID:20786474

Durt, Thomas ^[1]; Fiurasek, Jaromir ^[2]; Cerf, Nicolas J ^[2]

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1. TONA-TENA, Free University of Brussels, Pleinlaan 2, 1050 Brussels (Belgium)
2. QUIC, Ecole Polytechnique, CP 165, Universite Libre de Bruxelles, 1050 Brussels (Belgium)

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{yields}2 cloning machine in any dimension. We also show, using an ansatz on the generic form of cloning machines, that the d-dimensional 1{yields}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{yields}2 Fourier-covariant cloner, which optimally clones the computational basis and its Fourier transform, is also possible only in dimension d=2.

• OSTI ID: 20786474
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
FOURIER TRANSFORMATION
INFORMATION THEORY
QUANTUM COMPUTERS
QUANTUM CRYPTOGRAPHY
QUANTUM TELEPORTATION
QUBITS