dorsal/arxiv
View SchemaMultipartite Nonlocality without Entanglement in Many Dimensions
| Authors | J. Niset, N. J. Cerf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606227 |
| URL | https://arxiv.org/abs/quant-ph/0606227 |
| DOI | 10.1103/PhysRevA.74.052103 |
| Journal | Physical Review A, 74, 052103 (2006) |
Abstract
We present a generic method to construct a product basis exhibiting Nonlocality Without Entanglement with $n$ parties each holding a system of dimension at least $n-1$. This basis is generated via a quantum circuit made of control-Discrete Fourier Transform gates acting on the computational basis. The simplicity of our quantum circuit allows for an intuitive understanding of this new type of nonlocality. We also show how this circuit can be used to construct Unextendible Product Bases and their associated Bound Entangled States. To our knowledge, this is the first method which, given a general Hilbert space $\bigotimes_{i=1}^n {\cal H}_{d_i}$ with $d_i\le n-1$, makes it possible to construct (i) a basis exhibiting Nonlocality Without Entanglement, (ii) an Unextendible Product Basis, and (iii) a Bound Entangled state.
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"abstract": "We present a generic method to construct a product basis exhibiting\nNonlocality Without Entanglement with $n$ parties each holding a system of\ndimension at least $n-1$. This basis is generated via a quantum circuit made of\ncontrol-Discrete Fourier Transform gates acting on the computational basis. The\nsimplicity of our quantum circuit allows for an intuitive understanding of this\nnew type of nonlocality. We also show how this circuit can be used to construct\nUnextendible Product Bases and their associated Bound Entangled States. To our\nknowledge, this is the first method which, given a general Hilbert space\n$\\bigotimes_{i=1}^n {\\cal H}_{d_i}$ with $d_i\\le n-1$, makes it possible to\nconstruct (i) a basis exhibiting Nonlocality Without Entanglement, (ii) an\nUnextendible Product Basis, and (iii) a Bound Entangled state.",
"arxiv_id": "quant-ph/0606227",
"authors": [
"J. Niset",
"N. J. Cerf"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.052103",
"journal_ref": "Physical Review A, 74, 052103 (2006)",
"title": "Multipartite Nonlocality without Entanglement in Many Dimensions",
"url": "https://arxiv.org/abs/quant-ph/0606227"
},
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