85 research outputs found
The Structure of Qubit Unextendible Product Bases
Unextendible product bases have been shown to have many important uses in
quantum information theory, particularly in the qubit case. However, very
little is known about their mathematical structure beyond three qubits. We
present several new results about qubit unextendible product bases, including a
complete characterization of all four-qubit unextendible product bases, which
we show there are exactly 1446 of. We also show that there exist p-qubit UPBs
of almost all sizes less than .Comment: 20 pages, 3 tables, 7 figure
Multipartite Nonlocality without Entanglement in Many Dimensions
We present a generic method to construct a product basis exhibiting
Nonlocality Without Entanglement with parties each holding a system of
dimension at least . 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
with , makes it possible to
construct (i) a basis exhibiting Nonlocality Without Entanglement, (ii) an
Unextendible Product Basis, and (iii) a Bound Entangled state.Comment: 8 pages, 4 figure
Unextendible Product Basis for Fermionic Systems
We discuss the concept of unextendible product basis (UPB) and generalized
UPB for fermionic systems, using Slater determinants as an analogue of product
states, in the antisymmetric subspace \wedge^ N \bC^M. We construct an
explicit example of generalized fermionic unextendible product basis (FUPB) of
minimum cardinality for any . We also show that any
bipartite antisymmetric space \wedge^ 2 \bC^M of codimension two is spanned
by Slater determinants, and the spaces of higher codimension may not be spanned
by Slater determinants. Furthermore, we construct an example of complex FUPB of
with minimum cardinality . In contrast, we show that a real FUPB
does not exist for . Finally we provide a systematic construction for
FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions.Comment: 17 pages, no figure. Comments are welcom
Exploring the Local Orthogonality Principle
Nonlocality is arguably one of the most fundamental and counterintuitive
aspects of quantum theory. Nonlocal correlations could, however, be even more
nonlocal than quantum theory allows, while still complying with basic physical
principles such as no-signaling. So why is quantum mechanics not as nonlocal as
it could be? Are there other physical or information-theoretic principles which
prohibit this? So far, the proposed answers to this question have been only
partially successful, partly because they are lacking genuinely multipartite
formulations. In Nat. Comm. 4, 2263 (2013) we introduced the principle of Local
Orthogonality (LO), an intrinsically multipartite principle which is satisfied
by quantum mechanics but is violated by non-physical correlations.
Here we further explore the LO principle, presenting new results and
explaining some of its subtleties. In particular, we show that the set of
no-signaling boxes satisfying LO is closed under wirings, present a
classification of all LO inequalities in certain scenarios, show that all
extremal tripartite boxes with two binary measurements per party violate LO,
and explain the connection between LO inequalities and unextendible product
bases.Comment: Typos corrected; data files uploade
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