727 research outputs found
Uncertainty reconciles complementarity with joint measurability
The fundamental principles of complementarity and uncertainty are shown to be
related to the possibility of joint unsharp measurements of pairs of
noncommuting quantum observables. A new joint measurement scheme for
complementary observables is proposed. The measured observables are represented
as positive operator valued measures (POVMs), whose intrinsic fuzziness
parameters are found to satisfy an intriguing pay-off relation reflecting the
complementarity. At the same time, this relation represents an instance of a
Heisenberg uncertainty relation for measurement imprecisions. A
model-independent consideration show that this uncertainty relation is
logically connected with the joint measurability of the POVMs in question.Comment: 4 pages, RevTeX. Title of previous version: "Complementarity and
uncertainty - entangled in joint path-interference measurements". This new
version focuses on the "measurement uncertainty relation" and its role,
disentangling this issue from the special context of path interference
duality. See also http://www.vjquantuminfo.org (October 2003
Quantifying unsharpness of observables in an outcome-independent way
Recently, a very beautiful measure of the unsharpness (fuzziness) of the
observables is discussed in the paper [Phys. Rev. A 104, 052227 (2021)]. The
measure which is defined in this paper is constructed via uncertainty and does
not depend on the values of the outcomes. There exist several properties of a
set of observables (e.g., incompatibility, non-disturbance) that do not depend
on the values of the outcomes. Therefore, the approach in the above-said paper
is consistent with the above-mentioned fact and is able to measure the
intrinsic unsharpness of the observables. In this work, we also quantify the
unsharpness of observables in an outcome-independent way. But our approach is
different than the approach of the above-said paper. In this work, at first, we
construct two Luder's instrument-based unsharpness measures and provide the
tight upper bounds of those measures. Then we prove the monotonicity of the
above-said measures under a class of fuzzifying processes (processes that make
the observables more fuzzy). This is consistent with the resource-theoretic
framework. Then we relate our approach to the approach of the above-said paper.
Next, we try to construct two instrument-independent unsharpness measures. In
particular, we define two instrument-independent unsharpness measures and
provide the tight upper bounds of those measures and then we derive the
condition for the monotonicity of those measures under a class of fuzzifying
processes and prove the monotonicity for dichotomic qubit observables. Then we
show that for an unknown measurement, the values of all of these measures can
be determined experimentally. Finally, we present the idea of the resource
theory of the sharpness of the observables.Comment: 14 pages, 3 figure
Quantum Mechanics as a Framework for Dealing with Uncertainty
Quantum uncertainty is described here in two guises: indeterminacy with its
concomitant indeterminism of measurement outcomes, and fuzziness, or
unsharpness. Both features were long seen as obstructions of experimental
possibilities that were available in the realm of classical physics. The birth
of quantum information science was due to the realization that such
obstructions can be turned into powerful resources. Here we review how the
utilization of quantum fuzziness makes room for a notion of approximate joint
measurement of noncommuting observables. We also show how from a classical
perspective quantum uncertainty is due to a limitation of measurability
reflected in a fuzzy event structure -- all quantum events are fundamentally
unsharp.Comment: Plenary Lecture, Central European Workshop on Quantum Optics, Turku
2009
Imprint of quantum gravity in the dimension and fabric of spacetime
We here conjecture that two much-studied aspects of quantum gravity,
dimensional flow and spacetime fuzziness, might be deeply connected. We
illustrate the mechanism, providing first evidence in support of our
conjecture, by working within the framework of multifractional theories, whose
key assumption is an anomalous scaling of the spacetime dimension in the
ultraviolet and a slow change of the dimension in the infrared. This sole
ingredient is enough to produce a scale-dependent deformation of the
integration measure with also a fuzzy spacetime structure. We also compare the
multifractional correction to lengths with the types of Planckian uncertainty
for distance and time measurements that was reported in studies combining
quantum mechanics and general relativity heuristically. This allows us to fix
two free parameters of the theory and leads, in one of the scenarios we
contemplate, to a value of the ultraviolet dimension which had already found
support in other quantum-gravity analyses. We also formalize a picture such
that fuzziness originates from a fundamental discrete scale invariance at short
scales and corresponds to a stochastic spacetime geometry.Comment: 6 pages; v2: phenomenology section adde
Unsharp Quantum Reality
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way
Dimensional flow and fuzziness in quantum gravity: emergence of stochastic spacetime
We show that the uncertainty in distance and time measurements found by the
heuristic combination of quantum mechanics and general relativity is reproduced
in a purely classical and flat multi-fractal spacetime whose geometry changes
with the probed scale (dimensional flow) and has non-zero imaginary dimension,
corresponding to a discrete scale invariance at short distances. Thus,
dimensional flow can manifest itself as an intrinsic measurement uncertainty
and, conversely, measurement-uncertainty estimates are generally valid because
they rely on this universal property of quantum geometries. These general
results affect multi-fractional theories, a recent proposal related to quantum
gravity, in two ways: they can fix two parameters previously left free (in
particular, the value of the spacetime dimension at short scales) and point
towards a reinterpretation of the ultraviolet structure of geometry as a
stochastic foam or fuzziness. This is also confirmed by a correspondence we
establish between Nottale scale relativity and the stochastic geometry of
multi-fractional models.Comment: 25 pages. v2: minor typos corrected, references adde
This elusive objective existence
Zurek's existential interpretation of quantum mechanics suffers from three
classical prejudices, including the belief that space and time are
intrinsically and infinitely differentiated. They compel him to relativize the
concept of objective existence in two ways. The elimination of these prejudices
makes it possible to recognize the quantum formalism's ontological implications
- the relative and contingent reality of spatiotemporal distinctions and the
extrinsic and finite spatiotemporal differentiation of the physical world -
which in turn makes it possible to arrive at an unqualified objective
existence. Contrary to a widespread misconception, viewing the quantum
formalism as being fundamentally a probability algorithm does not imply that
quantum mechanics is concerned with states of knowledge rather than states of
Nature. On the contrary, it makes possible a complete and strongly objective
description of the physical world that requires no reference to observers. What
objectively exists, in a sense that requires no qualification, is the
trajectories of macroscopic objects, whose fuzziness is empirically irrelevant,
the properties and values of whose possession these trajectories provide
indelible records, and the fuzzy and temporally undifferentiated states of
affairs that obtain between measurements and are described by counterfactual
probability assignments.Comment: To appear in IJQI; 21 pages, LaTe
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