dorsal/arxiv
View SchemaOptimal Copying of One Quantum Bit
| Authors | Chi-Sheng Niu, Robert B. Griffiths |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9805073 |
| URL | https://arxiv.org/abs/quant-ph/9805073 |
| DOI | 10.1103/PhysRevA.58.4377 |
| Journal | Phys.Rev. A58 (1998) 4377-4393 |
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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"abstract": "A quantum copying machine producing two (in general non-identical) copies of\nan arbitrary input state of a two-dimensional Hilbert space (qubit) is studied\nusing a quality measure based on distinguishability of states, rather than\nfidelity. The problem of producing optimal copies is investigated with the help\nof a Bloch sphere representation, and shown to have a well-defined solution,\nincluding cases in which the two copies have unequal quality, or the quality\ndepends upon the input state (is ``anisotropic\u0027\u0027 in Bloch sphere language), or\nboth. A simple quantum circuit yields the optimal copying machine. With a\nsuitable choice of parameters it becomes an optimal eavesdropping machine for\nsome versions of quantum cryptography, or reproduces the Buzek and Hillery\nresult for isotropic copies.",
"arxiv_id": "quant-ph/9805073",
"authors": [
"Chi-Sheng Niu",
"Robert B. Griffiths"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevA.58.4377",
"journal_ref": "Phys.Rev. A58 (1998) 4377-4393",
"title": "Optimal Copying of One Quantum Bit",
"url": "https://arxiv.org/abs/quant-ph/9805073"
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