3,701 research outputs found
Quantum steering: a review with focus on semidefinite programming
Quantum steering refers to the non-classical correlations that can be
observed between the outcomes of measurements applied on half of an entangled
state and the resulting post-measured states that are left with the other
party. From an operational point of view, a steering test can be seen as an
entanglement test where one of the parties performs uncharacterised
measurements. Thus, quantum steering is a form of quantum inseparability that
lies in between the well-known notions of Bell nonlocality and entanglement.
Moreover, quantum steering is also related to several asymmetric quantum
information protocols where some of the parties are considered untrusted.
Because of these facts, quantum steering has received a lot of attention both
theoretically and experimentally. The main goal of this review is to give an
overview of how to characterise quantum steering through semidefinite
programming. This characterisation provides efficient numerical methods to
address a number of problems, including steering detection, quantification, and
applications. We also give a brief overview of some important results that are
not directly related to semidefinite programming. Finally, we make available a
collection of semidefinite programming codes that can be used to study the
topics discussed in this articleComment: v2: 31 pages, 2 figures. Published version. New material added.
Matlab codes to accompany this review can be found at https://git.io/vax9
Generalised boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field
The most general admissible boundary conditions are derived for an idealised
Aharonov-Bohm flux intersecting the plane at the origin on the background of a
homogeneous magnetic field. A standard technique based on self-adjoint
extensions yields a four-parameter family of boundary conditions; other two
parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic
field. The generalised boundary conditions may be regarded as a combination of
the Aharonov-Bohm effect with a point interaction. Spectral properties of the
derived Hamiltonians are studied in detail.Comment: 32 pages, a LaTeX source file with 2 eps figures; submitted to J.
Math. Phy
Presuppositions in Context: Constructing Bridges
About the book: The First International and Interdisciplinary Conference on Modelling and Using Context, Rio de Janeiro, January 1997, gave rise to the present book, which contains a selection of the papers presented there, thoroughly refereed and revised. The treatment of contexts as bona fide objects of logical formalisation has gained wide acceptance, following the seminal impetus given by McCarthy in his Turing Award address. The field of natural language offers a particularly rich variety of examples and challenges to researchers concerned with the formal modelling of context, and several chapters in the volume deal with contextualisation in the setting of natural language. Others adopt a purely formal-logical viewpoint, seeking to develop general models of even wider applicability. The 12 chapters are organised in three groups: formalisation of contextual information in natural language understanding and generation, the application of context in mechanised reasoning domains, and novel non-classical logics for contextual application
Comment on ``Validity of Feynman's prescription of disregarding the Pauli principle in intermediate states''
In a recent paper Coutinho, Nogami and Tomio [Phys. Rev. A 59, 2624 (1999);
quant-ph/9812073] presented an example in which, they claim, Feynman's
prescription of disregarding the Pauli principle in intermediate states of
perturbation theory fails. We show that, contrary to their claim, Feynman's
prescription is consistent with the exact solution of their example.Comment: 1 pag
Vandermonde-subspace Frequency Division Multiplexing for Two-Tiered Cognitive Radio Networks
Vandermonde-subspace frequency division multiplexing (VFDM) is an overlay
spectrum sharing technique for cognitive radio. VFDM makes use of a precoder
based on a Vandermonde structure to transmit information over a secondary
system, while keeping an orthogonal frequency division multiplexing
(OFDM)-based primary system interference-free. To do so, VFDM exploits
frequency selectivity and the use of cyclic prefixes by the primary system.
Herein, a global view of VFDM is presented, including also practical aspects
such as linear receivers and the impact of channel estimation. We show that
VFDM provides a spectral efficiency increase of up to 1 bps/Hz over cognitive
radio systems based on unused band detection. We also present some key design
parameters for its future implementation and a feasible channel estimation
protocol. Finally we show that, even when some of the theoretical assumptions
are relaxed, VFDM provides non-negligible rates while protecting the primary
system.Comment: 9 pages, accepted for publication in IEEE Transactions on
Communication
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