dorsal/arxiv
View SchemaQuantum Walks with Entangled Coins
| Authors | S. E. Venegas-Andraca, J. L. Ball, K. Burnett, S. Bose |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411151 |
| URL | https://arxiv.org/abs/quant-ph/0411151 |
| DOI | 10.1088/1367-2630/7/1/221 |
| Journal | New Journal of Physics 7 (2005) 221 |
Abstract
We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different coin operators, two different shift operators, and one walker. We compare and contrast the performance of these quantum walks with that of a classical random walk consisting of one walker and two maximally correlated coins as well as quantum walks with coins sharing different degrees of entanglement. We illustrate that the behaviour of our walk with entangled coins can be very different in comparison to the usual quantum walk with a single coin. We also demonstrate that simply by changing the shift operator, we can generate widely different distributions. We also compare the behaviour of quantum walks with maximally entangled coins with that of quantum walks with non-entangled coins. Finally, we show that the use of different shift operators on 2 and 3 qubit coins leads to different position probability distributions in 1 and 2 dimensional graphs.
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"abstract": "We present a mathematical formalism for the description of unrestricted\nquantum walks with entangled coins and one walker. The numerical behaviour of\nsuch walks is examined when using a Bell state as the initial coin state, two\ndifferent coin operators, two different shift operators, and one walker. We\ncompare and contrast the performance of these quantum walks with that of a\nclassical random walk consisting of one walker and two maximally correlated\ncoins as well as quantum walks with coins sharing different degrees of\nentanglement.\n We illustrate that the behaviour of our walk with entangled coins can be very\ndifferent in comparison to the usual quantum walk with a single coin. We also\ndemonstrate that simply by changing the shift operator, we can generate widely\ndifferent distributions. We also compare the behaviour of quantum walks with\nmaximally entangled coins with that of quantum walks with non-entangled coins.\nFinally, we show that the use of different shift operators on 2 and 3 qubit\ncoins leads to different position probability distributions in 1 and 2\ndimensional graphs.",
"arxiv_id": "quant-ph/0411151",
"authors": [
"S. E. Venegas-Andraca",
"J. L. Ball",
"K. Burnett",
"S. Bose"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1367-2630/7/1/221",
"journal_ref": "New Journal of Physics 7 (2005) 221",
"title": "Quantum Walks with Entangled Coins",
"url": "https://arxiv.org/abs/quant-ph/0411151"
},
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