dorsal/arxiv
View SchemaQuantum-state filtering applied to the discrimination of Boolean functions
| Authors | Janos A. Bergou, Mark Hillery |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507092 |
| URL | https://arxiv.org/abs/quant-ph/0507092 |
| DOI | 10.1103/PhysRevA.72.012302 |
| Journal | Physical Review A 72, 012302 (2005) |
Abstract
Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are divided into two subsets and the first set consists of one state only while the second consists of all of the remaining states, is termed quantum state filtering. We derived previously the optimal strategy for the case of N non-orthogonal states, {|\psi_{1} >, ..., |\psi_{N} >}, for distinguishing |\psi_1 > from the set {|\psi_2 >, ..., |\psi_N >} and the corresponding optimal success and failure probabilities. In a previous paper [PRL 90, 257901 (2003)], we sketched an appplication of the results to probabilistic quantum algorithms. Here we fill in the gaps and give the complete derivation of the probabilstic quantum algorithm that can optimally distinguish between two classes of Boolean functions, that of the balanced functions and that of the biased functions. The algorithm is probabilistic, it fails sometimes but when it does it lets us know that it did. Our approach can be considered as a generalization of the Deutsch-Jozsa algorithm that was developed for the discrimination of balanced and constant Boolean functions.
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"abstract": "Quantum state filtering is a variant of the unambiguous state discrimination\nproblem: the states are grouped in sets and we want to determine to which\nparticular set a given input state belongs.The simplest case, when the N given\nstates are divided into two subsets and the first set consists of one state\nonly while the second consists of all of the remaining states, is termed\nquantum state filtering. We derived previously the optimal strategy for the\ncase of N non-orthogonal states, {|\\psi_{1} \u003e, ..., |\\psi_{N} \u003e}, for\ndistinguishing |\\psi_1 \u003e from the set {|\\psi_2 \u003e, ..., |\\psi_N \u003e} and the\ncorresponding optimal success and failure probabilities. In a previous paper\n[PRL 90, 257901 (2003)], we sketched an appplication of the results to\nprobabilistic quantum algorithms. Here we fill in the gaps and give the\ncomplete derivation of the probabilstic quantum algorithm that can optimally\ndistinguish between two classes of Boolean functions, that of the balanced\nfunctions and that of the biased functions. The algorithm is probabilistic, it\nfails sometimes but when it does it lets us know that it did. Our approach can\nbe considered as a generalization of the Deutsch-Jozsa algorithm that was\ndeveloped for the discrimination of balanced and constant Boolean functions.",
"arxiv_id": "quant-ph/0507092",
"authors": [
"Janos A. Bergou",
"Mark Hillery"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevA.72.012302",
"journal_ref": "Physical Review A 72, 012302 (2005)",
"title": "Quantum-state filtering applied to the discrimination of Boolean functions",
"url": "https://arxiv.org/abs/quant-ph/0507092"
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