Multipartite Nonlocality without Entanglement in Many Dimensions

Details Multipartite Nonlocality without Entanglement in Many Dimensions Multipartite Nonlocality without Entanglement in Many Dimensions

2006-06-27

arxiv.org/abs/quant-ph/0606227v1

Physical Review A, 74, 052103 (2006)

Physics

Quantum Physics

8 pages, 4 figures

Scientific paper

10.1103/PhysRevA.74.052103

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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