# Weekly Papers on Quantum Foundations (49)

Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics. (arXiv:2112.04694v1 [quant-ph])

In the framework of quantum thermodynamics preparing a quantum system in a general state requires the consumption of two distinct resources, namely, work and coherence. It has been shown that the work cost of preparing a quantum state is determined by its free energy. Considering a similar setting, here we determine the coherence cost of preparing a general state when there are no restrictions on work consumption. More precisely, the coherence cost is defined as the minimum rate of consumption of systems in a pure coherent state, that is needed to prepare copies of the desired system. We show that the coherence cost of any system is determined by its quantum Fisher information about the time parameter, hence introducing a new operational interpretation of this central quantity of quantum metrology. Our resource-theoretic approach also reveals a previously unnoticed connection between two fundamental properties of quantum Fisher information.

Bekenstein bound and uncertainty relations. (arXiv:2009.12530v2 [hep-th] UPDATED)

The non zero value of Planck constant $h$ underlies the emergence of several inequalities that must be satisfied in the quantum realm, the most prominent one being Heisenberg Uncertainty Principle. Among these inequalities, Bekenstein bound provides a universal limit on the entropy that can be contained in a localized quantum system of given size and total energy. In this Letter, we explore how Bekenstein bound is affected when Heisenberg uncertainty relation is deformed so as to accommodate gravitational effects close to Planck scale (Generalized Uncertainty Principle). By resorting to general thermodynamic arguments, and in regimes where the equipartition theorem still holds, we derive in this way a “generalized Bekenstein bound”. Physical implications of this result are discussed for both cases of positive and negative values of the deformation parameter.

Generalized uncertainty principle or curved momentum space?. (arXiv:2110.11067v3 [gr-qc] UPDATED)

The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar applications such as doubly special relativity. We introduce a duality between theories yielding generalized uncertainty principles and quantum mechanics on nontrivial momentum space. In particular, we find canonically conjugate variables which map the former into the latter. In that vein, we explicitly derive the vielbein corresponding to a generic generalized uncertainty principle in $d$ dimensions. Assuming the predominantly used quadratic form of the modification, the curvature tensor in momentum space is proportional to the noncommutativity of the coordinates in the modified Heisenberg algebra. Yet, the metric is non-Euclidean even in the flat case corresponding to commutative space, because the resulting momentum basis is noncanonical. These insides are used to constrain the curvature and the deviation from the canonical basis.

Leggett-Garg inequalities in the quantum field theory of neutrino oscillations. (arXiv:2111.09979v2 [quant-ph] UPDATED)

We investigate Leggett-Garg temporal inequalities in flavor-mixing processes. We derive an exact flavor-mass uncertainty product and we establish that it is an upper bound to the violation of the inequalities. This finding relates temporal nonclassicality to quantum uncertainty and provides a time analog of the Tsirelson upper bound to the violation of the spatial Bell inequalities. By studying the problem both in the exact field-theoretical setting and in the limiting quantum mechanical approximation, we show that Leggett-Garg inequalities are violated more strongly in quantum field theory than in quantum mechanics.

The origin of irreversibility and thermalization in thermodynamic processes

Publication date: 19 January 2022

Source: Physics Reports, Volume 944

Author(s): Emil Roduner, Tjaart P.J. Krüger

Wave function of the Universe as a sum over eventually inflating universes. (arXiv:2112.04522v1 [gr-qc])

Authors: Karthik Rajeev

We consider a proposal to define the wave function of the Universe as a sum over spacetimes that eventually inflate. In the minisuperspace model, we explicitly show that a simple family of initial conditions, parametrized by a positive real number $a_0$, can be imposed to realise this prescription. The resulting wave function is found to be proportional to the Hartle-Hawking wave function and its dependence on $a_0$ is only through an overall phase factor. Motivated by this observation, we ask whether it is possible to analytically extend $a_0$ to an extended region $\bar{\mathcal{D}}$ in complex $a_0-$plane, while retaining the Hartle-Hawking form of the wave function. We use the condition for convergence of path integral and a recent theorem due to Kontsevich and Segal, further extended by Witten, to explicitly find $\bar{\mathcal{D}}$. Interestingly, a special point on the boundary of $\bar{\mathcal{D}}$ recovers the exact no-boundary wave function. Following that, we show that our prescription leads to a family of quantum states for the perturbations, which give rise to scale-invariant power spectra. If we demand, as an extra ingredient to our prescription, a matching condition at the “no-boundary point” in $\bar{\mathcal{D}}$, we converge on a unique quantum state for the perturbations.

Minimal Length Phenomenology and the Black Body Radiation. (arXiv:2112.04609v1 [gr-qc])

Authors: Pasquale BossoJuan Manuel López Vega

The generalized uncertainty principle (GUP) modifies the uncertainty relation between momentum and position giving room for a minimal length, as predicted by candidates theories of quantum gravity. Inspired by GUP, Planck’s distribution is derived by considering a new quantization of the electromagnetic field. We elaborate on the thermodynamics of the black body radiation obtaining Wien’s law and the Stefan-Boltzmann law. We show that such thermodynamics laws are modified at Planck-scale.

Holographic Complexity of Quantum Black Holes. (arXiv:2112.04860v1 [hep-th])

We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the quantum BTZ black hole, which encompasses in an exact manner the effects of conformal fields with large central charge in the presence of the black hole, including the backreaction corrections to the BTZ metric. Our results show that Volume Complexity admits a consistent quantum expansion and correctly reproduces known limits. On the other hand, the generalized Action Complexity fails to account for the additional contributions from bulk quantum fields and does not lead to the correct classical limit. Furthermore, we show that the doubly-holographic setup allows computing the complexity coming purely from quantum fields – a notion that has proven evasive in usual holographic setups. We find that in holographic induced-gravity scenarios the complexity of quantum fields in a black hole background vanishes to leading order in the gravitational strength of CFT effects.

A cautionary case of casual causality. (arXiv:2112.05031v1 [hep-th])

We distinguish between the notions of asymptotic causality and infrared causality for gravitational effective field theories, and show that the latter gives constraints consistent with gravitational positivity bounds. We re-explore the scattering of gravitational waves in a spherically symmetric background in the EFT of gravity in $D\ge 5$, for which the leading-order correction to Einstein gravity is determined by the Gauss-Bonnet operator. We reproduce the known result that the truncated effective theory exhibits apparent time advances relative to the background geometry for specific polarisations, which naively signal a violation of causality. We show that by properly identifying the regime of validity of the effective theory, the apparent time advance can be shown to be unresolvable. To illustrate this, we identify specific higher-dimension operators in the EFT expansion which become large for potentially resolvable time advances, rendering the EFT expansion invalid. Our results demonstrate how staying within the confines of the EFT, neither infrared nor asymptotic causality are ever violated for Einstein-Gauss-Bonnet gravity, no matter how low the scale, and furthermore its causality can be understood without appealing to a precise UV completion such as string theory.

A null test of the equivalence principle using relativistic effects in galaxy surveys. (arXiv:2004.06457v2 [astro-ph.CO] UPDATED)

The weak equivalence principle is one of the cornerstone of general relativity. Its validity has been tested with impressive precision in the Solar System, with experiments involving baryonic matter and light. However, on cosmological scales and when dark matter is concerned, the validity of this principle is still unknown. In this paper we construct a null test that probes the validity of the equivalence principle for dark matter. Our test has the strong advantage that it can be applied on data without relying on any modelling of the theory of gravity. It involves a combination of redshift-space distortions and relativistic effects in the galaxy number-count fluctuation, that vanishes if and only if the equivalence principle holds. We show that the null test is very insensitive to typical uncertainties in other cosmological parameters, including the magnification bias parameter, and to non-linear effects, making this a robust null test for modified gravity.

The epistemic schism of statistical mechanics

Anta, Javier (2021) The epistemic schism of statistical mechanics. THEORIA. An International Journal for Theory, History and Foundations of Science, 36 (3). pp. 399-419. ISSN 2171-679X

Farr, Matt (2021) Conventionalism about time direction. [Preprint]

Philosophy, physics, and the problems of spacetime emergence

Jaksland, Rasmus and Salimkhani, Kian (2021) Philosophy, physics, and the problems of spacetime emergence. [Preprint]

Transforms for the early Kerr metric

Abbott, Stephen (2021) Transforms for the early Kerr metric. UNSPECIFIED.

Arguments from scientific practice in the debate about the physical equivalence of symmetry-related models

Luc, Joanna (2021) Arguments from scientific practice in the debate about the physical equivalence of symmetry-related models. [Preprint]

The Metaphysics of Emergent Spacetime Theories

Martens, Niels C.M. (2019) The Metaphysics of Emergent Spacetime Theories. Philosophy Compass, 14 (7).

Introduction to Logical Entropy and Its Relationship to Shannon Entropy

Ellerman, David (2022) Introduction to Logical Entropy and Its Relationship to Shannon Entropy. [Preprint]

Irreversibility, Loschmidt Echo, and Thermodynamic Uncertainty Relation

Author(s): Yoshihiko Hasegawa

Entropy production characterizes irreversibility. This viewpoint allows us to consider the thermodynamic uncertainty relation, which states that a higher precision can be achieved at the cost of higher entropy production, as a relation between precision and irreversibility. Considering the original …

[Phys. Rev. Lett. 127, 240602] Published Tue Dec 07, 2021

How to engineer a quantum wavefunction

Evans, Peter W. and Hangleiter, Dominik and Thebault, Karim P Y (2021) How to engineer a quantum wavefunction. [Preprint]