# Weekly Papers on Quantum Foundations (26)

R\’enyi entropy of magic. (arXiv:2106.12587v1 [quant-ph])

We introduce a novel measure for the quantum property commonly known as $magic$ by considering the R\’enyi entropy of the probability distribution associated to a pure quantum state given by the square of the expectation value of Pauli strings in that state. We show that this is a good measure of magic from the point of view of resource theory and show bounds with other known measures of magic. The R\’enyi entropy of magic has the advantage of being easily computable because it does not need a minimization procedure. We define the magic power of a unitary operator as the average entropy of magic attainable by the action of this operator on the magic-free states, that is, stabilizer states, and show the basic properties of this quantity. As an application, we show that the magic power is intimately connected to out-of-time-order correlation functions and that maximal levels of magic are necessary for quantum chaos.

Path Integrals: From Quantum Mechanics to Photonics. (arXiv:2105.00948v2 [quant-ph] UPDATED)

The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its dynamical evolution, is perhaps the most elegant and universal framework developed in theoretical physics, second only to the Standard Model of particle physics. In this tutorial, we retrace the steps that led to the creation of such a remarkable framework, discuss its foundations, and present some of the classical examples of problems that can be solved using the path integral formalism, as a way to introduce the readers to the topic, and help them get familiar with the formalism. Then, we focus our attention on the use of path integrals in optics and photonics, and discuss in detail how they have been used in the past to approach several problems, ranging from the propagation of light in inhomogeneous media, to parametric amplification, and quantum nonlinear optics in arbitrary media. To complement this, we also briefly present the Path Integral Monte Carlo (PIMC) method, as a valuable computational resource for condensed matter physics, and discuss its potential applications and advantages if used in photonics.

Quantum Computing for Location Determination. (arXiv:2106.11751v2 [quant-ph] UPDATED)

Quantum computing provides a new way for approaching problem solving, enabling efficient solutions for problems that are hard on classical computers. It is based on leveraging how quantum particles behave. With researchers around the world showing quantum supremacy and the availability of cloud-based quantum computers with free accounts for researchers, quantum computing is becoming a reality. In this paper, we explore both the opportunities and challenges that quantum computing has for location determination research. Specifically, we introduce an example for the expected gain of using quantum algorithms by providing an efficient quantum implementation of the well-known RF fingerprinting algorithm and run it on an instance of the IBM Quantum Experience computer. The proposed quantum algorithm has a complexity that is exponentially better than its classical algorithm version, both in space and running time. We further discuss both software and hardware research challenges and opportunities that researchers can build on to explore this exciting new domain.

Boltzmann’s Concept of Reality. (arXiv:physics/0701308v2 [physics.hist-ph] UPDATED)

Authors: Marcelo B. Ribeiro (1), Antonio A. P. Videira (2) ((1) Physics Institute, Universidade Federal do Rio de Janeiro – UFRJ, Brazil, (2) Department of Philosophy, Universidade do Estado do Rio de Janeiro – UERJ, Brazil)

In this article we describe and analyze the concept of reality developed by the Austrian theoretical physicist Ludwig Boltzmann. It is our thesis that Boltzmann was fully aware that reality could, and actually was, described by different points of view. In spite of this, Boltzmann did not renounce the idea that reality is real. We also discuss his main motivations to be strongly involved with philosophy of science, as well as further developments made by Boltzmann himself of his main philosophical ideas, namely scientific theories as images of Nature and its consequences. We end the paper with a discussion about the modernity of Boltzmann’s philosophy of science.

Electron Charge Density: A Clue from Quantum Chemistry for Quantum Foundations. (arXiv:2105.11988v2 [quant-ph] UPDATED)

Authors: Charles T. Sebens

Within quantum chemistry, the electron clouds that surround nuclei in atoms and molecules are sometimes treated as clouds of probability and sometimes as clouds of charge. These two roles, tracing back to Schr\”odinger and Born, are in tension with one another but are not incompatible. Schr\”odinger’s idea that the nucleus of an atom is surrounded by a spread-out electron charge density is supported by a variety of evidence from quantum chemistry, including two methods that are used to determine atomic and molecular structure: the Hartree-Fock method and density functional theory. Taking this evidence as a clue to the foundations of quantum physics, Schr\”odinger’s electron charge density can be incorporated into many different interpretations of quantum mechanics (and extensions of such interpretations to quantum field theory).

Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity. (arXiv:2106.12585v1 [hep-th])

From pre- to post-big bang: an (almost) self-dual cosmological history. (arXiv:2106.12865v1 [hep-th])

Authors: M. Gasperini

We present a short introduction to a non-standard cosmological scenario motivated by the duality symmetries of string theory, in which the big bang singularity is replaced with a “big bounce” at high but finite curvature. The bouncing epoch is prepared by a long (possibly infinitely extended) phase of cosmic evolution, starting from an initial state asymptotically approaching the string perturbative vacuum.

Quantization of Gravity in the Black Hole Background. (arXiv:2106.01966v2 [hep-th] UPDATED)

Authors: Renata KalloshAdel A. Rahman

We perform a covariant (Lagrangian) quantization of perturbative gravity in the background of a Schwarzschild black hole. The key tool is a decomposition of the field into spherical harmonics. We fix Regge-Wheeler gauge for modes with angular momentum quantum number $l \geq 2$, while for low multipole modes with $l$ $=$ $0$ or $1$ — for which Regge-Wheeler gauge is inapplicable — we propose a set of gauge fixing conditions which are 2D background covariant and perturbatively well-defined. We find that the corresponding Faddeev-Popov ghosts are non-propagating for the $l\geq2$ modes, but are in general nontrivial for the low multipole modes with $l = 0,1$. However, in Schwarzschild coordinates, all time derivatives acting on the ghosts drop from the action and the low multipole ghosts have instantaneous propagators. Up to possible subtleties related to quantizing gravity in a space with a horizon, Faddeev’s theorem suggests the possibility of an underlying canonical (Hamiltonian) quantization with a manifestly ghost-free Hilbert space.

Effects of Lorentz Symmetry Violation on a Relativistic Scalar Particle in Quantum Systems. (arXiv:2106.02458v2 [gr-qc] UPDATED)

Authors: Faizuddin Ahmed

In this paper, the relativistic quantum dynamics of a scalar particle under the effect of Lorentz symmetry violation determined by a tensor $(K_{F})_{\mu\,\nu\,\alpha\,\beta}$ out of the Standard Model Extension is investigated. We see that the bound-state solution of the modified Klein-Gordon equation can be obtained, and the spectrum of energy and the wave function depends on the Lorentz symmetry breaking parameters

String theory, Einstein, and the identity of physics: Theory assessment in absence of the empirical

van Dongen, Jeroen (2021) String theory, Einstein, and the identity of physics: Theory assessment in absence of the empirical. [Preprint]

Local Causation

Brunet, Tyler D. P. (2021) Local Causation. [Preprint]

Quantum pointillism with relational identity

Abstract

The feasibility of establishing a proper notion of a distinguishable object in the context of the de Broglie–Bohm approach to quantum mechanics seems, at first sight, uncontroversial by virtue of the fact that this theory can supposedly be interpreted in terms of a system of objective particles distinguished by individuating properties. However, after conducting a critical revision and evaluation of this trivial interpretation, and having assessed different alternatives that have been proposed in recent literature, I argue that within this theory an appropriate notion of a distinguishable object can only be articulated by means of the following theoretical and metaphysical strategies: firstly, by appealing to a pre-existing, symmetrized Bohmian framework that is empirically indistinguishable but physically distinguishable from the standard Bohmian formulation; and secondly, by suggesting a different interpretation of this symmetrized formulation based upon a relational notion of the distinguishable object that can only be appropriately conceived from a structuralist point of view.

Scattering and Perturbation Theory for Discrete-Time Dynamics

Author(s): Alessandro Bisio, Nicola Mosco, and Paolo Perinotti

We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasienergy which is defined only modulo 2π. Then we develop two perturbative techn…

[Phys. Rev. Lett. 126, 250503] Published Wed Jun 23, 2021

Quantum Simulation of Three-Body Interactions in Weakly Driven Quantum Systems

Author(s): Francesco Petiziol, Mahdi Sameti, Stefano Carretta, Sandro Wimberger, and Florian Mintert

The realization of effective Hamiltonians featuring many-body interactions beyond pairwise coupling would enable the quantum simulation of central models underpinning topological physics and quantum computation. We overcome crucial limitations of perturbative Floquet engineering and discuss the high…

[Phys. Rev. Lett. 126, 250504] Published Wed Jun 23, 2021

Gravity and GRACE

Belot, Gordon (2021) Gravity and GRACE. [Preprint]

How do electrons move in atoms? From the Bohr model to quantum mechanics

Gao, Shan (2021) How do electrons move in atoms? From the Bohr model to quantum mechanics. One hundred years of the Bohr atom: Proceedings from a conference (Edited by F. Aaserud and H. Kragh). Scientia Danica. Series M: Mathematica et physica, vol. 1., 2015. pp. 450-464. ISSN 1904-5514

On the Connection Between Quantum Probability and Geometry

Holik, Federico (2021) On the Connection Between Quantum Probability and Geometry. Quanta.

Beauty, Truth and Understanding

Milena, Ivanova (2020) Beauty, Truth and Understanding. [Preprint]

Scientific Perspectivism and the Methodology of Modern Mathematical Physics

Stemeroff, Noah (2021) Scientific Perspectivism and the Methodology of Modern Mathematical Physics. [Preprint]

Do molecules have structure in isolation? How models can provide the answer

Seifert, Vanessa A. (2021) Do molecules have structure in isolation? How models can provide the answer. [Preprint]

Induced osmotic vorticity in the quantum hydrodynamical picture (arXiv:2106.13225 [quant-ph])

Authors: C Dedes

A nonlinear wave mechanical equation is proposed by inserting an imaginary quantum potential into the Schrödinger equation. An explicit expression for its solution is given under certain assumptions and it is shown that it entails attenuation related effects as non-unitary evolution, non-exponential quantum decay and entropy production. In the quantum hydrodynamical formulation the existence of circulation effects for the osmotic velocity field is established. Finally, a time-invariant equation for the probability density is derived, analogous to the tensor Lighthill equation in aeroacoustics, which admits both retarded and advanced solutions.