415 research outputs found
Coexistence in interval effect algebras
Motivated by the notion of coexistence of effect-valued observables, we give
a characterization of coexistent subsets of interval effect algebras
Separability for lattice systems at high temperature
Equilibrium states of infinite extended lattice systems at high temperature
are studied with respect to their entanglement. Two notions of separability are
offered. They coincide for finite systems but differ for infinitely extended
ones. It is shown that for lattice systems with localized interaction for high
enough temperature there exists no local entanglement. Even more quasifree
states at high temperature are also not distillably entangled for all local
regions of arbitrary size. For continuous systems entanglement survives for all
temperatures. In mean field theories it is possible, that local regions are not
entangled but the entanglement is hidden in the fluctuation algebra
Bell inequality and common causal explanation in algebraic quantum field theory
Bell inequalities, understood as constraints between classical conditional
probabilities, can be derived from a set of assumptions representing a common
causal explanation of classical correlations. A similar derivation, however, is
not known for Bell inequalities in algebraic quantum field theories
establishing constraints for the expectation of specific linear combinations of
projections in a quantum state. In the paper we address the question as to
whether a 'common causal justification' of these non-classical Bell
inequalities is possible. We will show that although the classical notion of
common causal explanation can readily be generalized for the non-classical
case, the Bell inequalities used in quantum theories cannot be derived from
these non-classical common causes. Just the opposite is true: for a set of
correlations there can be given a non-classical common causal explanation even
if they violate the Bell inequalities. This shows that the range of common
causal explanations in the non-classical case is wider than that restricted by
the Bell inequalities
Bond dimension witnesses and the structure of homogeneous matrix product states
For the past twenty years, Matrix Product States (MPS) have been widely used
in solid state physics to approximate the ground state of one-dimensional spin
chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via
site-independent tensors and a boundary condition. Exploiting a connection with
the theory of matrix algebras, we derive two structural properties shared by
all hMPS, namely: a) there exist local operators which annihilate all hMPS of a
given bond dimension; and b) there exist local operators which, when applied
over any hMPS of a given bond dimension, decouple (cut) the particles where
they act from the spin chain while at the same time join (glue) the two loose
ends back again into a hMPS. Armed with these tools, we show how to
systematically derive `bond dimension witnesses', or 2-local operators whose
expectation value allows us to lower bound the bond dimension of the underlying
hMPS. We extend some of these results to the ansatz of Projected Entangled
Pairs States (PEPS). As a bonus, we use our insight on the structure of hMPS
to: a) derive some theoretical limitations on the use of hMPS and hPEPS for
ground state energy computations; b) show how to decrease the complexity and
boost the speed of convergence of the semidefinite programming hierarchies
described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of
finite-dimensional quantum correlations.Comment: Accepted for publication in Quantum. We still do not acknowledge
support from the European Research Counci
Generalizations of entanglement based on coherent states and convex sets
Unentangled pure states on a bipartite system are exactly the coherent states
with respect to the group of local transformations. What aspects of the study
of entanglement are applicable to generalized coherent states? Conversely, what
can be learned about entanglement from the well-studied theory of coherent
states? With these questions in mind, we characterize unentangled pure states
as extremal states when considered as linear functionals on the local Lie
algebra. As a result, a relativized notion of purity emerges, showing that
there is a close relationship between purity, coherence and (non-)entanglement.
To a large extent, these concepts can be defined and studied in the even more
general setting of convex cones of states. Based on the idea that entanglement
is relative, we suggest considering these notions in the context of partially
ordered families of Lie algebras or convex cones, such as those that arise
naturally for multipartite systems. The study of entanglement includes notions
of local operations and, for information-theoretic purposes, entanglement
measures and ways of scaling systems to enable asymptotic developments. We
propose ways in which these may be generalized to the Lie-algebraic setting,
and to a lesser extent to the convex-cones setting. One of our original
motivations for this program is to understand the role of entanglement-like
concepts in condensed matter. We discuss how our work provides tools for
analyzing the correlations involved in quantum phase transitions and other
aspects of condensed-matter systems.Comment: 37 page
Entanglement between smeared field operators in the Klein-Gordon vacuum
Quantum field theory is the application of quantum physics to fields. It
provides a theoretical framework widely used in particle physics and condensed
matter physics. One of the most distinct features of quantum physics with
respect to classical physics is entanglement or the existence of strong
correlations between subsystems that can even be spacelike separated. In
quantum fields, observables restricted to a region of space define a subsystem.
While there are proofs on the existence of local observables that would allow a
violation of Bell's inequalities in the vacuum states of quantum fields as well
as some explicit but technically demanding schemes requiring an extreme
fine-tuning of the interaction between the fields and detectors, an
experimentally accessible entanglement witness for quantum fields is still
missing. Here we introduce smeared field operators which allow reducing the
vacuum to a system of two effective bosonic modes. The introduction of such
collective observables is motivated by the fact that no physical probe has
access to fields in single spatial (mathematical) points but rather smeared
over finite volumes. We first give explicit collective observables whose
correlations reveal vacuum entanglement in the Klein-Gordon field. We then show
that the critical distance between the two regions of space above which two
effective bosonic modes become separable is of the order of the Compton
wavelength of the particle corresponding to the massive Klein-Gordon field.Comment: 21 pages, 11 figure
Analysing and Comparing Encodability Criteria
Encodings or the proof of their absence are the main way to compare process
calculi. To analyse the quality of encodings and to rule out trivial or
meaningless encodings, they are augmented with quality criteria. There exists a
bunch of different criteria and different variants of criteria in order to
reason in different settings. This leads to incomparable results. Moreover it
is not always clear whether the criteria used to obtain a result in a
particular setting do indeed fit to this setting. We show how to formally
reason about and compare encodability criteria by mapping them on requirements
on a relation between source and target terms that is induced by the encoding
function. In particular we analyse the common criteria full abstraction,
operational correspondence, divergence reflection, success sensitiveness, and
respect of barbs; e.g. we analyse the exact nature of the simulation relation
(coupled simulation versus bisimulation) that is induced by different variants
of operational correspondence. This way we reduce the problem of analysing or
comparing encodability criteria to the better understood problem of comparing
relations on processes.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.06347. The Isabelle/HOL
source files, and a full proof document, are available in the Archive of
Formal Proofs, at
http://afp.sourceforge.net/entries/Encodability_Process_Calculi.shtm
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