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arXiv:quant-ph/0304070 · Physical Review Letters

Teleportation Scheme Implementing the Universal Optimal Quantum Cloning Machine and the Universal NOT Gate

Marco Ricci, Fabio Sciarrino, Carlo Sias, F. De Martini

Published Jan 30, 2004• 97 citations
arXivHTMLPDF

Abstract

By a significant modification of the standard protocol of quantum state teleportation, two processes "forbidden" by quantum mechanics in their exact form, the universal NOT gate and the universal optimal quantum cloning machine, have been implemented contextually and optimally by a fully linear method. In particular, the first experimental demonstration of the tele-UNOT gate, a novel quantum information protocol, has been reported. The experimental results are found in full agreement with theory.

DOI
10.1103/physrevlett.92.047901

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By a significant modification of the standard protocol of quantum state teleportation, two processes "forbidden" by quantum mechanics in their exact form, the universal NOT gate and the universal optimal quantum cloning machine, have been implemented contextually and optimally by a fully linear method. In particular, the first experimental demonstration of the tele-UNOT gate, a novel quantum information protocol, has been reported. The experimental results are found in full agreement with theory.
A simultaneous, contextual experimental demonstration of the two processes of cloning an input qubit $|\ensuremath{\Psi}〉$ and of flipping it into the orthogonal qubit $|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉$ is reported. The adopted experimental apparatus, a quantum-injected optical parametric amplifier is transformed simultaneously into a universal optimal quantum cloning machine and into a universal-NOT quantum-information gate. The two processes, indeed forbidden in their exact form for fundamental quantum limitations, were found to be universal and optimal, i.e., the measured fidelity of both processes F<1F<1F<1 was found close to the limit values evaluated by quantum theory. A contextual theoretical and experimental investigation of these processes, which may represent the basic difference between the classical and the quantum worlds, can reveal in a unifying manner the detailed structure of quantum information. It may also enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.
A simultaneous realization of the universal optimal quantum cloning machine and of the universal-NOT gate by a quantum injected optical parametric amplification, is reported. The two processes, forbidden in their exact form for fundamental quantum limitations, are found universal and optimal, and the measured fidelity F<1 is found close to the limit values evaluated by quantum theory. This work may enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.
Abstract Since manipulations of qubits are constrained by the quantum mechanical rules, several classical information tasks can not be perfectly extended to the quantum world. The more relevant limitations in quantum information processing are the impossibility to perfectly clone any unknown qubit and to map it in its orthogonal state. Even if these two processes are unrealizable in their exact forms, they can be optimally approximated by the so‐called universal quantum machines: the optimal quantum cloning machine (UOQCM) and the universal‐NOT (U‐NOT) gate. Investigation of these optimal transformations is important since it reveals bounds on optimal manipulations of information with quantum systems. The 1−>1 U‐NOT gate and the 1−>2 UOQCM have been experimentally demonstrated by adopting the process of stimulated emission into an optical parametric amplifier and by slightly modifying the quantum state teleportation protocol.
Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable teleportation of any generic optimal antiunitary map. In addition, the contextual realization of the $N\ensuremath{\rightarrow}M$ cloning map and of the teleportation of the $N\ensuremath{\rightarrow}(M\ensuremath{-}N)$ universal-NOT (UNOT) gate is analyzed by a very general angular momentum theory. An extended set of experimental realizations by state symmetrization linear optical procedures is reported. These include the $1\ensuremath{\rightarrow}2$ cloning process, the UNOT gate and the quantum tomographic characterization of the optimal partial transpose map of polarization encoded qubits.
Abstract An arbitrary quantum state cannot be “cloned” perfectly, i.e. reproduced with “fidelity” F = 1 into M > 1 states identical to the original by any conceivable physical device. The main root of this impossibility resides in the linearity of quantum mechanics. A second “quantum impossibility” process, based on the complete positivity character of any quantum operation and conceivably subtly related to the first one, forbids the realization of a universal NOT gate i.e. one that flips exactly any input qubit into an orthogonal one. A detailed investigation of these results, representing the most fundamental difference between classical and quantum information, indeed can reveal the detailed structure of the latter one. We report an experimental demonstration of the process of cloning of N = 1 input qubit into M = 2 output qubits by a quantum‐injected optical parametric amplifier OPA. By the same apparatus the realization of a universal NOT gate is also demonstrated. The two processes will be found to be “universal” and optimal, i.e. the measured fidelity of both processes F < 1 will be found close to the theoretical values.
Abstract No-cloning theorem forbids perfect cloning of an unknown quantum state. A universal quantum cloning machine (UQCM), capable of producing two copies of any input qubit with the optimal fidelity, is of fundamental interest and has applications in quantum information processing. This is enabled by delicately tailored nonclassical correlations between the input qubit and the copying qubits, which distinguish the UQCM from a classical counterpart, but whose experimental demonstrations are still lacking. We here implement the UQCM in a superconducting circuit and investigate these correlations. The measured entanglements well agree with our theoretical prediction that they are independent of the input state and thus constitute a universal quantum behavior of the UQCM that was not previously revealed. Another feature of our experiment is the realization of deterministic and individual cloning, in contrast to previously demonstrated UQCMs, which either were probabilistic or did not constitute true cloning of individual qubits.