9,197 research outputs found
The structure of classical extensions of quantum probability theory
On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed
Approximating incompatible von Neumann measurements simultaneously
We study the problem of performing orthogonal qubit measurements
simultaneously. Since these measurements are incompatible, one has to accept
additional imprecision. An optimal joint measurement is the one with the least
possible imprecision. All earlier considerations of this problem have concerned
only joint measurability of observables, while in this work we also take into
account conditional state transformations (i.e., instruments). We characterize
the optimal joint instrument for two orthogonal von Neumann instruments as
being the Luders instrument of the optimal joint observable.Comment: 9 pages, 4 figures; v2 has a more extensive introduction + other
minor correction
Relativistic Quantum Mechanics and Relativistic Entanglement in the Rest-Frame Instant Form of Dynamics
A new formulation of relativistic quantum mechanics is proposed in the
framework of the rest-frame instant form of dynamics with its instantaneous
Wigner 3-spaces and with its description of the particle world-lines by means
of derived non-canonical predictive coordinates. In it we quantize the frozen
Jacobi data of the non-local 4-center of mass and the Wigner-covariant relative
variables in an abstract (frame-independent) internal space whose existence is
implied by Wigner-covariance. The formalism takes care of the properties of
both relativistic bound states and scattering ones. There is a natural solution
to the \textit{relativistic localization problem}. The non-relativistic limit
leads to standard quantum mechanics but with a frozen Hamilton-Jacobi
description of the center of mass. Due to the \textit{non-locality} of the
Poincar\'e generators the resulting theory of relativistic entanglement is both
\textit{kinematically non-local and spatially non-separable}: these properties,
absent in the non-relativistic limit, throw a different light on the
interpretation of the non-relativistic quantum non-locality and of its impact
on foundational problems.Comment: 73 pages, includes revision
Uncertainty Relations for Positive Operator Valued Measures
How much unavoidable randomness is generated by a Positive Operator Valued
Measure (POVM)? We address this question using two complementary approaches.
First we study the variance of a real variable associated to the POVM outcomes.
In this context we introduce an uncertainty operator which measures how much
additional noise is introduced by carrying out a POVM rather than a von Neumann
measurement. We illustrate this first approach by studying the variances of
joint estimates of \sigma_x and \sigma_z for spin 1/2 particles. We show that
for unbiased measurements the sum of these variances is lower bounded by 1. In
our second approach we study the entropy of the POVM outcomes. In particular we
try to establish lower bounds on the entropy of the POVM outcomes. We
illustrate this second approach by examples.Comment: 5 pages, minor modifications and clarification
Sharp crossover from composite fermionization to phase separation in mesoscopic mixtures of ultracold bosons
We show that a two-component mixture of a few repulsively interacting
ultracold atoms in a one-dimensional trap possesses very different quantum
regimes and that the crossover between them can be induced by tuning the
interactions in one of the species. In the composite fermionization regime,
where the interactions between both components are large, none of the species
show large occupation of any natural orbital. Our results show that by
increasing the interaction in one of the species, one can reach the
phase-separated regime. In this regime, the weakly interacting component stays
at the center of the trap and becomes almost fully phase coherent, while the
strongly interacting component is displaced to the edges of the trap. The
crossover is sharp, as observed in the in the energy and the in the largest
occupation of a natural orbital of the weakly interacting species. Such a
transition is a purely mesoscopic effect which disappears for large atom
numbers.Comment: 5 pages, 3 figure
The conditions for quantum violation of macroscopic realism
Why do we not experience a violation of macroscopic realism in every-day
life? Normally, no violation can be seen either because of decoherence or the
restriction of coarse-grained measurements, transforming the time evolution of
any quantum state into a classical time evolution of a statistical mixture. We
find the sufficient condition for these classical evolutions for spin systems
under coarse-grained measurements. Then we demonstrate that there exist
"non-classical" Hamiltonians whose time evolution cannot be understood
classically, although at every instant of time the quantum spin state appears
as a classical mixture. We suggest that such Hamiltonians are unlikely to be
realized in nature because of their high computational complexity.Comment: 4 pages, 2 figures, revised version, journal reference adde
Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures
We present the complete phase diagram for one-dimensional binary mixtures of
bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with
direct numerical diagonalization for small number of atoms, which permits us to
quantify quantum many-body correlations. The quantum Monte Carlo method is used
to calculate energies and density profiles for larger system sizes. We study
the system properties for a wide range of interaction parameters. For the
extreme values of these parameters, different correlation limits can be
identified, where the correlations are either weak or strong. We investigate in
detail how the correlation evolve between the limits. For balanced mixtures in
the number of atoms in each species, the transition between the different
limits involves sophisticated changes in the one- and two-body correlations.
Particularly, we quantify the entanglement between the two components by means
of the von Neumann entropy. We show that the limits equally exist when the
number of atoms is increased, for balanced mixtures. Also, the changes in the
correlations along the transitions among these limits are qualitatively
similar. We also show that, for imbalanced mixtures, the same limits with
similar transitions exist. Finally, for strongly imbalanced systems, only two
limits survive, i.e., a miscible limit and a phase-separated one, resembling
those expected with a mean-field approach.Comment: 18 pages, 8 figure
On localization and position operators in Moebius-covariant theories
Some years ago it was shown that, in some cases, a notion of locality can
arise from the group of symmetry enjoyed by the theory, thus in an intrinsic
way. In particular, when Moebius covariance is present, it is possible to
associate some particular transformations to the Tomita Takesaki modular
operator and conjugation of a specific interval of an abstract circle. In this
context we propose a way to define an operator representing the coordinate
conjugated with the modular transformations. Remarkably this coordinate turns
out to be compatible with the abstract notion of locality. Finally a concrete
example concerning a quantum particle on a line is also given.Comment: 19 pages, UTM 705, version to appear in RM
The canonical phase measurement is pure
We show that the canonical phase measurement is pure in the sense that the
corresponding positive operator valued measure (POVM) is extremal in the convex
set of all POVMs. This means that the canonical phase measurement cannot be
interpreted as a noisy measurement, even if it is not a projection valued
measure.Comment: 4 page
Dark-Bright Solitons in Inhomogeneous Bose-Einstein Condensates
We investigate dark-bright vector solitary wave solutions to the coupled
non-linear Schr\"odinger equations which describe an inhomogeneous two-species
Bose-Einstein condensate. While these structures are well known in non-linear
fiber optics, we show that spatial inhomogeneity strongly affects their motion,
stability, and interaction, and that current technology suffices for their
creation and control in ultracold trapped gases. The effects of controllably
different interparticle scattering lengths, and stability against
three-dimensional deformations, are also examined.Comment: 5 pages, 5 figure
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