Optimal manipulations with qubits: universal quantum cloning and universal logical NOT operation

Vladimir Buzek; Mark Hillery

doi:10.1117/12.353044

14 July 1999 Optimal manipulations with qubits: universal quantum cloning and universal logical NOT operation

Vladimir Buzek, Mark Hillery

Proceedings Volume 3820, 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics; (1999) https://doi.org/10.1117/12.353044
Event: Eleventh Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 1998, Stara Lesna, Slovakia

Abstract

We analyze how information encoded in quantum systems can be optimally processed. In particular, we investigate copying (cloning) of quantum information (represented as states of 2-level quantum systems--qubits). We present unitary transformations which describe the optimal universal cloning of a qubit. Universality of the transformation guarantees that the fidelity of the cloning does not depend on the input state of the qubit, i.e. all states are cloned equally well. We present network for the optimal universal quantum cloning `machine' (transformation) which produces N + 1 copies from the original qubit. Here again the quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copes, N. We also present the `machine' which universally and optimally clones states of quantum objects in arbitrary- dimensional Hilbert spaces. In particular, we discuss universal cloning of quantum registers. In addition to cloning of qubits we analyzed another universal operation-- the Universal NOT. We present the optimal transformation and the corresponding logical network which optimally complements an arbitrary input state of a qubit. We show that the fidelity of the performance of the Universal NOT operation increases as a function of the number of input qubits prepared in the same state.

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Vladimir Buzek and Mark Hillery "Optimal manipulations with qubits: universal quantum cloning and universal logical NOT operation", Proc. SPIE 3820, 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, (14 July 1999); https://doi.org/10.1117/12.353044

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KEYWORDS

Quantum communications

Quantum information

Quantum networks

Quantum physics

Adaptive optics

Poincaré sphere

Physics

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