3,019 research outputs found
Super-KMS functionals for graded-local conformal nets
Motivated by a few preceding papers and a question of R. Longo, we introduce
super-KMS functionals for graded translation-covariant nets over R with
superderivations, roughly speaking as a certain supersymmetric modification of
classical KMS states on translation-covariant nets over R, fundamental objects
in chiral algebraic quantum field theory. Although we are able to make a few
statements concerning their general structure, most properties will be studied
in the setting of specific graded-local (super-) conformal models. In
particular, we provide a constructive existence and partial uniqueness proof of
super-KMS functionals for the supersymmetric free field, for certain subnets,
and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a
separate result, we classify bounded super-KMS functionals for graded-local
conformal nets over S^1 with respect to rotations.Comment: 30 pages, revised version (to appear in Ann. H. Poincare
On the mixing property for a class of states of relativistic quantum fields
Let be a factor state on the quasi-local algebra of
observables generated by a relativistic quantum field, which in addition
satisfies certain regularity conditions (satisfied by ground states and the
recently constructed thermal states of the theory). We prove that
there exist space and time translation invariant states, some of which are
arbitrarily close to in the weak* topology, for which the time
evolution is weakly asymptotically abelian
Relative entropy and the Bekenstein bound
Elaborating on a previous work by Marolf et al, we relate some exact results
in quantum field theory and statistical mechanics to the Bekenstein universal
bound on entropy. Specifically, we consider the relative entropy between the
vacuum and another state, both reduced to a local region. We propose that, with
the adequate interpretation, the positivity of the relative entropy in this
case constitutes a well defined statement of the bound in flat space. We show
that this version arises naturally from the original derivation of the bound
from the generalized second law when quantum effects are taken into account. In
this formulation the bound holds automatically, and in particular it does not
suffer from the proliferation of the species problem. The results suggest that
while the bound is relevant at the classical level, it does not introduce new
physical constraints semiclassically.Comment: 12 pages, 1 figure, minor changes and references adde
Spin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer
What is the simplest Hamiltonian which can implement quantum computation
without requiring any control operations during the computation process? In a
previous paper we have constructed a 10-local finite-range interaction among
qubits on a 2D lattice having this property. Here we show that
pair-interactions among qutrits on a 2D lattice are sufficient, too, and can
also implement an ergodic computer where the result can be read out from the
time average state after some post-selection with high success probability.
Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle
located at a specific lattice site, the third state is its absence. Usual
hopping terms together with an attractive force among adjacent particles induce
a coupled quantum walk where the particle spins are subjected to spatially
inhomogeneous interactions implementing holonomic quantum computing. The
holonomic method ensures that the implemented circuit does not depend on the
time needed for the walk.
Even though the implementation of the required type of spin-spin interactions
is currently unclear, the model shows that quite simple Hamiltonians are
powerful enough to allow for universal quantum computing in a closed physical
system.Comment: More detailed explanations including description of a programmable
version. 44 pages, 12 figures, latex. To appear in PR
The - divergence and Mixing times of quantum Markov processes
We introduce quantum versions of the -divergence, provide a detailed
analysis of their properties, and apply them in the investigation of mixing
times of quantum Markov processes. An approach similar to the one presented in
[1-3] for classical Markov chains is taken to bound the trace-distance from the
steady state of a quantum processes. A strict spectral bound to the convergence
rate can be given for time-discrete as well as for time-continuous quantum
Markov processes. Furthermore the contractive behavior of the
-divergence under the action of a completely positive map is
investigated and contrasted to the contraction of the trace norm. In this
context we analyse different versions of quantum detailed balance and, finally,
give a geometric conductance bound to the convergence rate for unital quantum
Markov processes
Local Nature of Coset Models
The local algebras of the maximal Coset model C_max associated with a chiral
conformal subtheory A\subset B are shown to coincide with the local relative
commutants of A in B, provided A contains a stress energy tensor.
Making the same assumption, the adjoint action of the unique
inner-implementing representation U^A associated with A\subset B on the local
observables in B is found to define net-endomorphisms of B. This property is
exploited for constructing from B a conformally covariant holographic image in
1+1 dimensions which proves useful as a geometric picture for the joint
inclusion A\vee C_max \subset B.
Immediate applications to the analysis of current subalgebras are given and
the relation to normal canonical tensor product subfactors is clarified. A
natural converse of Borchers' theorem on half-sided translations is made
accessible.Comment: 33 pages, no figures; typos, minor improvement
Semicausal operations are semilocalizable
We prove a conjecture by DiVincenzo, which in the terminology of Preskill et
al. [quant-ph/0102043] states that ``semicausal operations are
semilocalizable''. That is, we show that any operation on the combined system
of Alice and Bob, which does not allow Bob to send messages to Alice, can be
represented as an operation by Alice, transmitting a quantum particle to Bob,
and a local operation by Bob. The proof is based on the uniqueness of the
Stinespring representation for a completely positive map. We sketch some of the
problems in transferring these concepts to the context of relativistic quantum
field theory.Comment: 4 pages, 1 figure, revte
Quantum control without access to the controlling interaction
In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum
system and its controller. We show under which conditions measurements, state
preparations, and unitary implementations on the system can be performed by
quantum operations on the controller only.
It turns out that a measurement of the observable A and an implementation of
the one-parameter group exp(iAr) can be performed by almost the same sequence
of control operations. Furthermore measurement procedures for A+B, for (AB+BA),
and for i[A,B] can be constructed from measurements of A and B. This shows that
the algebraic structure of the set of observables can be explained by the Lie
group structure of the unitary evolutions on the joint Hilbert space of the
measuring device and the measured system.
A spin chain model with nearest neighborhood coupling shows that the border
line between controller and system can be shifted consistently.Comment: 10 pages, Revte
Imaging the Earth's Interior: the Angular Distribution of Terrestrial Neutrinos
Decays of radionuclides throughout the Earth's interior produce geothermal
heat, but also are a source of antineutrinos. The (angle-integrated)
geoneutrino flux places an integral constraint on the terrestrial radionuclide
distribution. In this paper, we calculate the angular distribution of
geoneutrinos, which opens a window on the differential radionuclide
distribution. We develop the general formalism for the neutrino angular
distribution, and we present the inverse transformation which recovers the
terrestrial radioisotope distribution given a measurement of the neutrino
angular distribution. Thus, geoneutrinos not only allow a means to image the
Earth's interior, but offering a direct measure of the radioactive Earth, both
(1) revealing the Earth's inner structure as probed by radionuclides, and (2)
allowing for a complete determination of the radioactive heat generation as a
function of radius. We present the geoneutrino angular distribution for the
favored Earth model which has been used to calculate geoneutrino flux. In this
model the neutrino generation is dominated by decays in the Earth's mantle and
crust; this leads to a very ``peripheral'' angular distribution, in which 2/3
of the neutrinos come from angles > 60 degrees away from the downward vertical.
We note the possibility of that the Earth's core contains potassium; different
geophysical predictions lead to strongly varying, and hence distinguishable,
central intensities (< 30 degrees from the downward vertical). Other
uncertainties in the models, and prospects for observation of the geoneutrino
angular distribution, are briefly discussed. We conclude by urging the
development and construction of antineutrino experiments with angular
sensitivity. (Abstract abridged.)Comment: 25 pages, RevTeX, 7 figures. Comments welcom
Quantum simulations under translational symmetry
We investigate the power of quantum systems for the simulation of Hamiltonian
time evolutions on a cubic lattice under the constraint of translational
invariance. Given a set of translationally invariant local Hamiltonians and
short range interactions we determine time evolutions which can and those that
can not be simulated. Whereas for general spin systems no finite universal set
of generating interactions is shown to exist, universality turns out to be
generic for quadratic bosonic and fermionic nearest-neighbor interactions when
supplemented by all translationally invariant on-site Hamiltonians.Comment: 9 pages, 2 figures, references added, minor change
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