dorsal/arxiv
View SchemaQuantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization
| Authors | Lawrence M. Ioannou, Benjamin C. Travaglione |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602223 |
| URL | https://arxiv.org/abs/quant-ph/0602223 |
| DOI | 10.1103/PhysRevA.73.052314 |
| Journal | Phys. Rev. A 73, 052314 (2006) |
Abstract
We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal observables. We review the concept of an entanglement witness from the geometrical point of view and use this geometry to show that the set of separable states is not a polytope and to characterize the class of entanglement witnesses (observables) that detect entangled states on opposite sides of the set of separable states. All this serves to motivate a classical algorithm which, given the expected values of a subset of an orthogonal basis of observables of an otherwise unknown quantum state, searches for an entanglement witness in the span of the subset of observables. The idea of such an algorithm, which is an efficient reduction of the quantum separability problem to a global optimization problem, was introduced in PRA 70 060303(R), where it was shown to be an improvement on the naive approach for the quantum separability problem (exhaustive search for a decomposition of the given state into a convex combination of separable states). The last section of the paper discusses in more generality such algorithms, which, in our case, assume a subroutine that computes the global maximum of a real function of several variables. Despite this, we anticipate that such algorithms will perform sufficiently well on small instances that they will render a feasible test for separability in some cases of interest (e.g. in 3-by-3 dimensional systems).
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"abstract": "We focus on determining the separability of an unknown bipartite quantum\nstate $\\rho$ by invoking a sufficiently large subset of all possible\nentanglement witnesses given the expected value of each element of a set of\nmutually orthogonal observables. We review the concept of an entanglement\nwitness from the geometrical point of view and use this geometry to show that\nthe set of separable states is not a polytope and to characterize the class of\nentanglement witnesses (observables) that detect entangled states on opposite\nsides of the set of separable states. All this serves to motivate a classical\nalgorithm which, given the expected values of a subset of an orthogonal basis\nof observables of an otherwise unknown quantum state, searches for an\nentanglement witness in the span of the subset of observables. The idea of such\nan algorithm, which is an efficient reduction of the quantum separability\nproblem to a global optimization problem, was introduced in PRA 70 060303(R),\nwhere it was shown to be an improvement on the naive approach for the quantum\nseparability problem (exhaustive search for a decomposition of the given state\ninto a convex combination of separable states). The last section of the paper\ndiscusses in more generality such algorithms, which, in our case, assume a\nsubroutine that computes the global maximum of a real function of several\nvariables. Despite this, we anticipate that such algorithms will perform\nsufficiently well on small instances that they will render a feasible test for\nseparability in some cases of interest (e.g. in 3-by-3 dimensional systems).",
"arxiv_id": "quant-ph/0602223",
"authors": [
"Lawrence M. Ioannou",
"Benjamin C. Travaglione"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.052314",
"journal_ref": "Phys. Rev. A 73, 052314 (2006)",
"title": "Quantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization",
"url": "https://arxiv.org/abs/quant-ph/0602223"
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