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Fortschritte der Physik

Optimal quantum machines by linear and non‐linear optics

Fabio Sciarrino, F. De Martini

Published Oct 11, 2004• 0 citations
Publisher

Abstract

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.

DOI
10.1002/prop.200410177

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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.
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.
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The impossibility of perfectly copying (or cloning) an unknown quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These ``quantum cloning machines'' are important tools for studying a wide variety of tasks, e.g., state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines both for discrete-dimensional and for continuous-variable quantum systems. In addition, it presents the role of cloning in quantum cryptography, the link between optimal cloning and light amplification via stimulated emission, and the experimental demonstrations of optimal quantum cloning.
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 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.
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.