dorsal/arxiv
View SchemaQuantum Entanglement and the Communication Complexity of the Inner Product Function
| Authors | Richard Cleve, Wim van Dam, Michael Nielsen, Alain Tapp |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9708019 |
| URL | https://arxiv.org/abs/quant-ph/9708019 |
| Journal | Lect.Notes Comput.Sci. 1509 (1998) 61-74 |
Abstract
We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability. Our proofs employ a novel kind of "quantum" reduction from a quantum information theory problem to the problem of computing the inner product. The communication required for the former problem can then be bounded by an application of Holevo's theorem. We also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit.
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"abstract": "We consider the communication complexity of the binary inner product function\nin a variation of the two-party scenario where the parties have an a priori\nsupply of particles in an entangled quantum state. We prove linear lower bounds\nfor both exact protocols, as well as for protocols that determine the answer\nwith bounded-error probability. Our proofs employ a novel kind of \"quantum\"\nreduction from a quantum information theory problem to the problem of computing\nthe inner product. The communication required for the former problem can then\nbe bounded by an application of Holevo\u0027s theorem. We also give a specific\nexample of a probabilistic scenario where entanglement reduces the\ncommunication complexity of the inner product function by one bit.",
"arxiv_id": "quant-ph/9708019",
"authors": [
"Richard Cleve",
"Wim van Dam",
"Michael Nielsen",
"Alain Tapp"
],
"categories": [
"quant-ph"
],
"journal_ref": "Lect.Notes Comput.Sci. 1509 (1998) 61-74",
"title": "Quantum Entanglement and the Communication Complexity of the Inner Product Function",
"url": "https://arxiv.org/abs/quant-ph/9708019"
},
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