dorsal/arxiv
View SchemaA note on quantum one-way permutations
| Authors | Elham Kashefi, Harumichi Nishimura, Vlatko Vedral |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109157 |
| URL | https://arxiv.org/abs/quant-ph/0109157 |
Abstract
We discuss the question of the existence of quantum one-way permutations. First, we prove the equivalence between inverting a permutation and that of constructing a polynomial size network for reflecting about a given quantum state. Next, we consider the question: if a state is difficult to prepare, is the operator reflecting about that state difficult to construct? By revisiting Grover's algorithm, we present the relationship between this question and the existence of one-way permutations. Moreover, we compare our method to Grover's algorithm and discuss possible applications of our results.
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"abstract": "We discuss the question of the existence of quantum one-way permutations.\nFirst, we prove the equivalence between inverting a permutation and that of\nconstructing a polynomial size network for reflecting about a given quantum\nstate. Next, we consider the question: if a state is difficult to prepare, is\nthe operator reflecting about that state difficult to construct? By revisiting\nGrover\u0027s algorithm, we present the relationship between this question and the\nexistence of one-way permutations. Moreover, we compare our method to Grover\u0027s\nalgorithm and discuss possible applications of our results.",
"arxiv_id": "quant-ph/0109157",
"authors": [
"Elham Kashefi",
"Harumichi Nishimura",
"Vlatko Vedral"
],
"categories": [
"quant-ph"
],
"title": "A note on quantum one-way permutations",
"url": "https://arxiv.org/abs/quant-ph/0109157"
},
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