"3"^^ . "Economical quantum cloning in any dimension" . "RIV/61989592:15310/05:00002106!RIV06-MSM-15310___" . . "Ekonomick\u00E9 kvantov\u00E9 kop\u00EDrov\u00E1n\u00ED v libovoln\u00E9 dimenzi"@cs . "72" . "Ekonomick\u00E9 kvantov\u00E9 kop\u00EDrov\u00E1n\u00ED v libovoln\u00E9 dimenzi"@cs . "Byla studov\u00E1na mo\u017Enost klonov\u00E1n\u00ED d-dimenzion\u00E1ln\u00EDho kvantov\u00E9ho syst\u00E9mu bezvyu\u017Eit\u00ED pomocn\u00FDch kvantov\u00FDch syst\u00E9m\u016F. Byla dok\u00E1z\u00E1na \u0159ada teor\u00E9m\u016F\u0159\u00EDkaj\u00EDc\u00EDch, \u017Ee optim\u00E1ln\u00ED kvantov\u00E9 kop\u00EDrov\u00E1n\u00ED nelze realizovat t\u00EDmtoekonomick\u00FDm zp\u016Fsobem bez vyu\u017Eit\u00ED pomocn\u00FDch syst\u00E9m\u016F."@cs . "[EC1F4817DD19]" . "15310" . "Economical quantum cloning in any dimension" . . "Fiur\u00E1\u0161ek, Jarom\u00EDr" . "Z(MSM6198959213)" . . "Economical quantum cloning in any dimension"@en . . . "Cerf, Nicolas J." . "Economical quantum cloning in any dimension"@en . . "ekonomick\u00E9 kvantov\u00E9 kop\u00EDrov\u00E1n\u00ED"@en . . "Physical Review A" . "052322-1-8" . "Durt, Thomas" . "1050-2947" . "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 -> 2 cloning machine in any dimension. We also show, using an ansatz on the generic form of cloning machines, that the d-dimensional 1 -> 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 -> 2 Fourier-covariant cloner, which optimally clones the computational basis and its Fourier" . "5" . "519097" . . . . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . "6"^^ . "RIV/61989592:15310/05:00002106" . "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 -> 2 cloning machine in any dimension. We also show, using an ansatz on the generic form of cloning machines, that the d-dimensional 1 -> 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 -> 2 Fourier-covariant cloner, which optimally clones the computational basis and its Fourier"@en . . "1"^^ .