dorsal/arxiv
View SchemaSome bounds for quantum copying
| Authors | A. E. Rastegin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108014 |
| URL | https://arxiv.org/abs/quant-ph/0108014 |
Abstract
We propose new optimality criterion for the estimation of state-dependent cloning. We call this measure the relative error because the one compares the errors in the copies with contiguous size taking into account the similarity of states to be copied. A copying transformation and dimension of state space are not specified. Only the unitarity of quantum mechanical transformations is used. The presented approach is based on the notion of the angle between two states. Firstly, several useful statements simply expressed in terms of angles are proved. Among them there are the spherical triangle inequality and the inequality establishing the upper bound on the modulus of difference between probability distributions generated by two any states for an arbitrary measurement. The tightest lower bound on the relative error is then obtained. Hillery and Buzek originally examined an approximate state-dependent copying and obtained the lower bound on the absolute error. We consider relationship between the size of error and the corresponding probability distributions and obtain the tightest lower bound on the absolute error. Thus, the proposed approach supplements and reinforces the results obtained by Hillery and Buzek. Finally, the basic findings of investigation for the relative error are discussed.
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"abstract": "We propose new optimality criterion for the estimation of state-dependent\ncloning. We call this measure the relative error because the one compares the\nerrors in the copies with contiguous size taking into account the similarity of\nstates to be copied. A copying transformation and dimension of state space are\nnot specified. Only the unitarity of quantum mechanical transformations is\nused. The presented approach is based on the notion of the angle between two\nstates. Firstly, several useful statements simply expressed in terms of angles\nare proved. Among them there are the spherical triangle inequality and the\ninequality establishing the upper bound on the modulus of difference between\nprobability distributions generated by two any states for an arbitrary\nmeasurement. The tightest lower bound on the relative error is then obtained.\nHillery and Buzek originally examined an approximate state-dependent copying\nand obtained the lower bound on the absolute error. We consider relationship\nbetween the size of error and the corresponding probability distributions and\nobtain the tightest lower bound on the absolute error. Thus, the proposed\napproach supplements and reinforces the results obtained by Hillery and Buzek.\nFinally, the basic findings of investigation for the relative error are\ndiscussed.",
"arxiv_id": "quant-ph/0108014",
"authors": [
"A. E. Rastegin"
],
"categories": [
"quant-ph"
],
"title": "Some bounds for quantum copying",
"url": "https://arxiv.org/abs/quant-ph/0108014"
},
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