185 research outputs found
Quantum analogues of Hardy's nonlocality paradox
Hardy's nonlocality is a "nonlocality proof without inequalities": it
exemplifies that quantum correlations can be qualitatively stronger than
classical correlations. This paper introduces variants of Hardy's nonlocality
in the CHSH scenario which are realized by the PR-box, but not by quantum
correlations. Hence this new kind of Hardy-type nonlocality is a proof without
inequalities showing that superquantum correlations can be qualitatively
stronger than quantum correlations.Comment: minor fixe
Kochen-Specker Sets and Generalized Orthoarguesian Equations
Every set (finite or infinite) of quantum vectors (states) satisfies
generalized orthoarguesian equations (OA). We consider two 3-dim
Kochen-Specker (KS) sets of vectors and show how each of them should be
represented by means of a Hasse diagram---a lattice, an algebra of subspaces of
a Hilbert space--that contains rays and planes determined by the vectors so as
to satisfy OA. That also shows why they cannot be represented by a special
kind of Hasse diagram called a Greechie diagram, as has been erroneously done
in the literature. One of the KS sets (Peres') is an example of a lattice in
which 6OA pass and 7OA fails, and that closes an open question of whether the
7oa class of lattices properly contains the 6oa class. This result is important
because it provides additional evidence that our previously given proof of noa
=< (n+1)oa can be extended to proper inclusion noa < (n+1)oa and that nOA form
an infinite sequence of successively stronger equations.Comment: 16 pages and 5 figure
Relational Hidden Variables and Non-Locality
We use a simple relational framework to develop the key notions and results
on hidden variables and non-locality. The extensive literature on these topics
in the foundations of quantum mechanics is couched in terms of probabilistic
models, and properties such as locality and no-signalling are formulated
probabilistically. We show that to a remarkable extent, the main structure of
the theory, through the major No-Go theorems and beyond, survives intact under
the replacement of probability distributions by mere relations.Comment: 42 pages in journal style. To appear in Studia Logic
Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
A diagrammatic representation is given of the 24 rays of Peres that makes it
easy to pick out all the 512 parity proofs of the Kochen-Specker theorem
contained in them. The origin of this representation in the four-dimensional
geometry of the rays is pointed out.Comment: 14 pages, 6 figures and 3 tables. Three references have been added.
Minor typos have been correcte
Axisymmetric versus Non-axisymmetric Vortices in Spinor Bose-Einstein Condensates
The structure and stability of various vortices in F=1 spinor Bose-Einstein
condensates are investigated by solving the extended Gross-Pitaevskii equation
under rotation. We perform an extensive search for stable vortices, considering
both axisymmetric and non-axisymmetric vortices and covering a wide range of
ferromagnetic and antiferromagnetic interactions. The topological defect called
Mermin-Ho (Anderson-Toulouse) vortex is shown to be stable for ferromagnetic
case. The phase diagram is established in a plane of external rotation Omega vs
total magnetization M by comparing the free energies of possible vortices. It
is shown that there are qualitative differences between axisymmetric and
non-axisymmetric vortices which are manifested in the Omega- and M-dependences.Comment: 9 pages, 9 figure
Magnetism in a lattice of spinor Bose condensates
We study the ground state magnetic properties of ferromagnetic spinor
Bose-Einstein condensates confined in a deep optical lattices. In the Mott
insulator regime, the ``mini-condensates'' at each lattice site behave as
mesoscopic spin magnets that can interact with neighboring sites through both
the static magnetic dipolar interaction and the light-induced dipolar
interaction. We show that such an array of spin magnets can undergo a
ferromagnetic or anti-ferromagnetic phase transition under the magnetic dipolar
interaction depending on the dimension of the confining optical lattice. The
ground-state spin configurations and related magnetic properties are
investigated in detail
Unbounded violation of tripartite Bell inequalities
We prove that there are tripartite quantum states (constructed from random
unitaries) that can lead to arbitrarily large violations of Bell inequalities
for dichotomic observables. As a consequence these states can withstand an
arbitrary amount of white noise before they admit a description within a local
hidden variable model. This is in sharp contrast with the bipartite case, where
all violations are bounded by Grothendieck's constant. We will discuss the
possibility of determining the Hilbert space dimension from the obtained
violation and comment on implications for communication complexity theory.
Moreover, we show that the violation obtained from generalized GHZ states is
always bounded so that, in contrast to many other contexts, GHZ states do in
this case not lead to extremal quantum correlations. The results are based on
tools from the theories of operator spaces and tensor norms which we exploit to
prove the existence of bounded but not completely bounded trilinear forms from
commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more
accessible for a non-specialized reade
Measurement-based quantum foundations
I show that quantum theory is the only probabilistic framework that permits
arbitrary processes to be emulated by sequences of local measurements. This
supports the view that, contrary to conventional wisdom, measurement should not
be regarded as a complex phenomenon in need of a dynamical explanation but
rather as a primitive -- and perhaps the only primitive -- operation of the
theory.Comment: 8 pages, version to appear in Found. Phy
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