dorsal/arxiv
View SchemaTwo qubit copying machine for economical quantum eavesdropping
| Authors | Chi-Sheng Niu, Robert B. Griffiths |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9810008 |
| URL | https://arxiv.org/abs/quant-ph/9810008 |
| DOI | 10.1103/PhysRevA.60.2764 |
| Journal | Phys.Rev. A60 (1999) 2764-2776 |
Abstract
We study the mapping which occurs when a single qubit in an arbitrary state interacts with another qubit in a given, fixed state resulting in some unitary transformation on the two qubit system which, in effect, makes two copies of the first qubit. The general problem of the quality of the resulting copies is discussed using a special representation, a generalization of the usual Schmidt decomposition, of an arbitrary two-dimensional subspace of a tensor product of two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can reproduce the results of any two qubit copying machine of this type. A simple stochastic generalization (using a ``classical'' random signal) of the copying machine is also considered. These copying machines provide simple embodiments of previously proposed optimal eavesdropping schemes for the BB84 and B92 quantum cryptography protocols.
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"abstract": "We study the mapping which occurs when a single qubit in an arbitrary state\ninteracts with another qubit in a given, fixed state resulting in some unitary\ntransformation on the two qubit system which, in effect, makes two copies of\nthe first qubit. The general problem of the quality of the resulting copies is\ndiscussed using a special representation, a generalization of the usual Schmidt\ndecomposition, of an arbitrary two-dimensional subspace of a tensor product of\ntwo 2-dimensional Hilbert spaces. We exhibit quantum circuits which can\nreproduce the results of any two qubit copying machine of this type. A simple\nstochastic generalization (using a ``classical\u0027\u0027 random signal) of the copying\nmachine is also considered. These copying machines provide simple embodiments\nof previously proposed optimal eavesdropping schemes for the BB84 and B92\nquantum cryptography protocols.",
"arxiv_id": "quant-ph/9810008",
"authors": [
"Chi-Sheng Niu",
"Robert B. Griffiths"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.60.2764",
"journal_ref": "Phys.Rev. A60 (1999) 2764-2776",
"title": "Two qubit copying machine for economical quantum eavesdropping",
"url": "https://arxiv.org/abs/quant-ph/9810008"
},
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