87 research outputs found
The measurement postulates of quantum mechanics are operationally redundant
Understanding the core content of quantum mechanics requires us to
disentangle the hidden logical relationships between the postulates of this
theory. Here we show that the mathematical structure of quantum measurements,
the formula for assigning outcome probabilities (Born's rule) and the
post-measurement state-update rule, can be deduced from the other quantum
postulates, often referred to as "unitary quantum mechanics", and the
assumption that ensembles on finite-dimensional Hilbert spaces are
characterised by finitely many parameters. This is achieved by taking an
operational approach to physical theories, and using the fact that the manner
in which a physical system is partitioned into subsystems is a subjective
choice of the observer, and hence should not affect the predictions of the
theory. In contrast to other approaches, our result does not assume that
measurements are related to operators or bases, it does not rely on the
universality of quantum mechanics, and it is independent of the interpretation
of probability.Comment: This is a post-peer-review, pre-copyedit version of an article
published in Nature Communications. The final authenticated version is
available online at: http://dx.doi.org/10.1038/s41467-019-09348-
Any modification of the Born rule leads to a violation of the purification and local tomography principles
Using the existing classification of all alternatives to the measurement
postulates of quantum theory we study the properties of bi-partite systems in
these alternative theories. We prove that in all these theories the
purification principle is violated, meaning that some mixed states are not the
reduction of a pure state in a larger system. This allows us to derive the
measurement postulates of quantum theory from the structure of pure states and
reversible dynamics, and the requirement that the purification principle holds.
The violation of the purification principle implies that there is some
irreducible classicality in these theories, which appears like an important
clue for the problem of deriving the Born rule within the many-worlds
interpretation. We also prove that in all such modifications the task of state
tomography with local measurements is impossible, and present a simple toy
theory displaying all these exotic non-quantum phenomena. This toy model shows
that, contrarily to previous claims, it is possible to modify the Born rule
without violating the no-signalling principle. Finally, we argue that the
quantum measurement postulates are the most non-classical amongst all
alternatives.Comment: 31 pages, 12 Figure
Response to "The measurement postulates of quantum mechanics are not redundant"
Adrian Kent has recently presented a critique [arXiv:2307.06191] of our paper
[Nat. Comms. 10, 1361 (2019)] in which he claims to refute our main result: the
measurement postulates of quantum mechanics can be derived from the rest of
postulates, once we assume that the set of mixed states of a finite-dimensional
Hilbert space is finite-dimensional. To construct his argument, Kent considers
theories resulting from supplementing quantum mechanics with hypothetical
"post-quantum" measurement devices. We prove that each of these theories
contains pure states (i.e. states of maximal knowledge) which are not rays of
the Hilbert space, in contradiction with the "pure state postulate" of quantum
mechanics. We also prove that these alternatives violate the
finite-dimensionality of mixed states. Each of these two facts separately
invalidates the refutation. In this note we also clarify the assumptions used
in the above-cited paper and discuss the notions of pure state, physical
system, and the sensitivity of the structure of the state space under
modifications of the measurements or the dynamics.Comment: 7 page
A no-go theorem on the nature of the gravitational field beyond quantum theory
Recently, table-top experiments involving massive quantum systems have been
proposed to test the interface of quantum theory and gravity. In particular,
the crucial point of the debate is whether it is possible to conclude anything
on the quantum nature of the gravitational field, provided that two quantum
systems become entangled due to solely the gravitational interaction.
Typically, this question has been addressed by assuming an underlying physical
theory to describe the gravitational interaction, but no systematic approach to
characterise the set of possible gravitational theories which are compatible
with the observation of entanglement has been proposed. Here, we introduce the
framework of Generalised Probabilistic Theories (GPTs) to the study of the
nature of the gravitational field. This framework has the advantage that it
only relies on the set of operationally accessible states, transformations, and
measurements, without presupposing an underlying theory. Hence, it provides a
framework to systematically study all theories compatible with the detection of
entanglement generated via the gravitational interaction between two
non-classical systems. Assuming that such entanglement is observed we prove a
no-go theorem stating that the following statements are incompatible: i) the
two non-classical systems are independent subsystems, ii) the gravitational
field is a physical degree of freedom which mediates the interaction and iii)
the gravitational field is classical. Moreover we argue that conditions i) and
ii) should be met, and hence that the gravitational field is non-classical.
Non-classicality does not imply that the gravitational field is quantum, and to
illustrate this we provide examples of non-classical and non-quantum theories
which are logically consistent with the other conditions.Comment: 12 pages main text; 23 pages Appendices; many diagrams. Improved
presentation compared to the first versio
Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible
When gravity is sourced by a quantum system, there is tension between its
role as the mediator of a fundamental interaction, which is expected to acquire
nonclassical features, and its role in determining the properties of spacetime,
which is inherently classical. Fundamentally, this tension should result in
breaking one of the fundamental principles of quantum theory or general
relativity, but it is usually hard to assess which one without resorting to a
specific model. Here, we answer this question in a theory-independent way using
General Probabilistic Theories (GPTs). We consider the interactions of the
gravitational field with a single matter system, and derive a no-go theorem
showing that when gravity is classical at least one of the following
assumptions needs to be violated: (i) Matter degrees of freedom are described
by fully non-classical degrees of freedom; (ii) Interactions between matter
degrees of freedom and the gravitational field are reversible; (iii) Matter
degrees of freedom back-react on the gravitational field. We argue that this
implies that theories of classical gravity and quantum matter must be
fundamentally irreversible, as is the case in the recent model of Oppenheim et
al. Conversely if we require that the interaction between quantum matter and
the gravitational field are reversible, then the gravitational field must be
non-classical.Comment: 5 pages main text; 8 pages Appendices (many diagrams
Witworld: A generalised probabilistic theory featuring post-quantum steering
We introduce Witworld: a generalised probabilistic theory with strong
post-quantum features, which subsumes Boxworld. Witworld is the first theory
that features post-quantum steering, and also the first that outperforms
quantum theory at the task of remote state preparation. We further show
post-quantum steering to be the source of this advantage, and hence present the
first instance where post-quantum steering is a stronger-than-quantum resource
for information processing.Comment: 9 pages, loads of diagrams. Comments welcom
Quantum Relativity of Subsystems
One of the most basic notions in physics is the partitioning of a system into
subsystems, and the study of correlations among its parts. In this work, we
explore these notions in the context of quantum reference frame (QRF)
covariance, in which this partitioning is subject to a symmetry constraint. We
demonstrate that different reference frame perspectives induce different sets
of subsystem observable algebras, which leads to a gauge-invariant,
frame-dependent notion of subsystems and entanglement. We further demonstrate
that subalgebras which commute before imposing the symmetry constraint can
translate into non-commuting algebras in a given QRF perspective after symmetry
imposition. Such a QRF perspective does not inherit the distinction between
subsystems in terms of the corresponding tensor factorizability of the
kinematical Hilbert space and observable algebra. Since the condition for this
to occur is contingent on the choice of QRF, the notion of subsystem locality
is frame-dependent
Quantum Relativity of Subsystems
One of the most basic notions in physics is the partitioning of a system into
subsystems, and the study of correlations among its parts. In this work, we
explore these notions in the context of quantum reference frame (QRF)
covariance, in which this partitioning is subject to a symmetry constraint. We
demonstrate that different reference frame perspectives induce different sets
of subsystem observable algebras, which leads to a gauge-invariant,
frame-dependent notion of subsystems and entanglement. We further demonstrate
that subalgebras which commute before imposing the symmetry constraint can
translate into non-commuting algebras in a given QRF perspective after symmetry
imposition. Such a QRF perspective does not inherit the distinction between
subsystems in terms of the corresponding tensor factorizability of the
kinematical Hilbert space and observable algebra. Since the condition for this
to occur is contingent on the choice of QRF, the notion of subsystem locality
is frame-dependent.Comment: 8+9 pages, 1 figur
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Cause of Death and Predictors of All-Cause Mortality in Anticoagulated Patients With Nonvalvular Atrial Fibrillation : Data From ROCKET AF
M. Kaste on työryhmän ROCKET AF Steering Comm jäsen.Background-Atrial fibrillation is associated with higher mortality. Identification of causes of death and contemporary risk factors for all-cause mortality may guide interventions. Methods and Results-In the Rivaroxaban Once Daily Oral Direct Factor Xa Inhibition Compared with Vitamin K Antagonism for Prevention of Stroke and Embolism Trial in Atrial Fibrillation (ROCKET AF) study, patients with nonvalvular atrial fibrillation were randomized to rivaroxaban or dose-adjusted warfarin. Cox proportional hazards regression with backward elimination identified factors at randomization that were independently associated with all-cause mortality in the 14 171 participants in the intention-to-treat population. The median age was 73 years, and the mean CHADS(2) score was 3.5. Over 1.9 years of median follow-up, 1214 (8.6%) patients died. Kaplan-Meier mortality rates were 4.2% at 1 year and 8.9% at 2 years. The majority of classified deaths (1081) were cardiovascular (72%), whereas only 6% were nonhemorrhagic stroke or systemic embolism. No significant difference in all-cause mortality was observed between the rivaroxaban and warfarin arms (P=0.15). Heart failure (hazard ratio 1.51, 95% CI 1.33-1.70, P= 75 years (hazard ratio 1.69, 95% CI 1.51-1.90, P Conclusions-In a large population of patients anticoagulated for nonvalvular atrial fibrillation, approximate to 7 in 10 deaths were cardiovascular, whereasPeer reviewe
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