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Optimal Copying of One Quantum Bit

Chi-Sheng Niu·Robert B. Griffiths
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Abstract

A quantum copying machine producing two (in general non-identical) copies of an arbitrary input state of a two-dimensional Hilbert space (qubit) is studied using a quality measure based on distinguishability of states, rather than fidelity. The problem of producing optimal copies is investigated with the help of a Bloch sphere representation, and shown to have a well-defined solution, including cases in which the two copies have unequal quality, or the quality depends upon the input state (is ``anisotropic'' in Bloch sphere language), or both. A simple quantum circuit yields the optimal copying machine. With a suitable choice of parameters it becomes an optimal eavesdropping machine for some versions of quantum cryptography, or reproduces the Buzek and Hillery result for isotropic copies.

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Chi-Sheng Niu, Robert B. Griffiths. 1998-05-22. Optimal Copying of One Quantum Bit. https://doi.org/10.1103/physreva.58.4377

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