dorsal/arxiv
View SchemaOptimal simulation of nonlocal Hamiltonians using local operations and classical communication
| Authors | G. Vidal, J. I. Cirac |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0108076 |
| URL | https://arxiv.org/abs/quant-ph/0108076 |
| DOI | 10.1103/PhysRevA.66.022315 |
| Journal | Phys. Rev. A 66, 022315 (2002) |
Abstract
Consider a set of $N$ systems and an arbitrary interaction Hamiltonian $H$ that couples them. We investigate the use of local operations and classical communication (LOCC), together with the Hamiltonian $H$, to simulate a unitary evolution of the $N$ systems according to some other Hamiltonian $H'$. First, we show that the most general simulation using $H$ and LOCC can be also achieved, with the same time efficiency, by just interspersing the evolution of $H$ with local unitary manipulations of each system and a corresponding local ancilla (in a so-called LU+anc protocol). Thus, the ability to make local measurements and to communicate classical information does not help in non--local Hamiltonian simulation. Second, we show that both for the case of two $d$-level systems ($d>2$), or for that of a setting with more than two systems ($N>2$), LU+anc protocols are more powerful than LU protocols. Therefore local ancillas are a useful resource for non--local Hamiltonian simulation. Third, we use results of majorization theory to explicitly solve the problem of optimal simulation of two-qubit Hamiltonians using LU (equivalently, LU+anc, LO or LOCC).
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"abstract": "Consider a set of $N$ systems and an arbitrary interaction Hamiltonian $H$\nthat couples them. We investigate the use of local operations and classical\ncommunication (LOCC), together with the Hamiltonian $H$, to simulate a unitary\nevolution of the $N$ systems according to some other Hamiltonian $H\u0027$. First,\nwe show that the most general simulation using $H$ and LOCC can be also\nachieved, with the same time efficiency, by just interspersing the evolution of\n$H$ with local unitary manipulations of each system and a corresponding local\nancilla (in a so-called LU+anc protocol). Thus, the ability to make local\nmeasurements and to communicate classical information does not help in\nnon--local Hamiltonian simulation. Second, we show that both for the case of\ntwo $d$-level systems ($d\u003e2$), or for that of a setting with more than two\nsystems ($N\u003e2$), LU+anc protocols are more powerful than LU protocols.\nTherefore local ancillas are a useful resource for non--local Hamiltonian\nsimulation. Third, we use results of majorization theory to explicitly solve\nthe problem of optimal simulation of two-qubit Hamiltonians using LU\n(equivalently, LU+anc, LO or LOCC).",
"arxiv_id": "quant-ph/0108076",
"authors": [
"G. Vidal",
"J. I. Cirac"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.022315",
"journal_ref": "Phys. Rev. A 66, 022315 (2002)",
"title": "Optimal simulation of nonlocal Hamiltonians using local operations and classical communication",
"url": "https://arxiv.org/abs/quant-ph/0108076"
},
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