# Weekly Papers on Quantum Foundations (41)

Relational Quantum Mechanics is about Facts, not States: A reply to Pienaar and Brukner

Di Biagio, Andrea and Rovelli, Carlo (2021) Relational Quantum Mechanics is about Facts, not States: A reply to Pienaar and Brukner. [Preprint]

Trans-Planckian Philosophy of Cosmology

Schneider, Mike D. (2021) Trans-Planckian Philosophy of Cosmology. [Preprint]

Mutually Unbiased Quantum Observables. (arXiv:2110.03099v1 [quant-ph])

We begin by defining mutually unbiased (MU) observables on a finite dimensional Hilbert space. We also consider the more general concept of parts of MU observables. The relationships between MU observables, value-complementary observables and two other conditions involving sequential products of observables are discussed. We next present a special motivating case of MU observables called finite position and momentum observables. These are atomic observables related by a finite Fourier transform. Finite position and momentum observables are employed to give examples of parts of MU observables that are value-complementary and those that are not value-complementary. Various open problems involving these concepts are presented. These problems mainly involve extending this work from sharp observables to unsharp observables.

Quantum Measurement Theory for Systems with Finite Dimensional State Spaces. (arXiv:2110.03219v1 [quant-ph])

In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set of the real numbers. We develop the theory in a deductive manner from the basic postulates for quantum mechanics and a few plausible axioms for general quantum measurements. We derive an axiomatic characterization of all the physically realizable finite quantum measurements. Mathematical tools necessary to describe measurement statistics, such as POVMs and quantum instruments, are not assumed at the outset, but we introduce them as natural consequences of our axioms. Our objective is to show that those mathematical tools can be naturally derived from obvious theoretical requirements.

From Classical to quantum stochastic process. (arXiv:2110.03668v1 [cond-mat.stat-mech])

We construct quantum analogs of classical stochastic processes, by replacing random “which path” decisions with superposition of all paths. This procedure typically leads to non-unitary quantum evolution, where coherences are continuously generated and destroyed. In spite of their transient nature, these coherences can change the scaling behavior of classical observables. Using the zero temperature Glauber dynamics in a linear Ising spin chain, we find quantum analogs with different domain growth exponents. In some cases, this exponent is even smaller than for the original classical process, which means that coherence can lead to an important speed up the relaxation process.

Projection Hypothesis from the von Neumann-type Interaction with a Bose-Einstein Condensate. (arXiv:2012.01886v4 [quant-ph] UPDATED)

We derive the projection hypothesis in projective quantum measurement by restricting the set of observables. This projection hypothesis accompanies a bipartite system with the von Neumann-type interaction, which consists of a quantum mechanical system, with a meter variable to be measured, and a quantum field theoretically macroscopic extended object, that is, a spatiotemporally inhomogeneous Bose-Einstein condensate in quantum field theory with the quantum coordinate, that is, the zero-energy Goldstone mode(s) of the spontaneously broken global spatial translational symmetry. The key steps in the derivation are the return of the symmetry translation of this quantum coordinate to the inverse translation of the c-number spatial coordinate in quantum field theory and the reduction of quantum fluctuations to classical fluctuations with respect to the Goldstone mode(s) due to a superselection rule.

Quantum Undergraduate Education and Scientific Training. (arXiv:2109.13850v2 [physics.ed-ph] UPDATED)

Currently, education and workforce training in quantum information science and technology (QIST) exists primarily at the graduate and postdoctoral levels, with few undergraduate efforts beginning to grow out of these. In order to meet the anticipated quantum workforce needs and to ensure that the workforce is demographically representative and inclusive to all communities, the United States must expand these efforts at the undergraduate level beyond what is occurring at larger PhD granting institutions and incorporate quantum information science into the curriculum at the nation’s predominantly undergraduate institutions (PUIs). On June 3rd and 4th, 2021 the Quantum Undergraduate Education and Scientific Training (QUEST) workshop was held virtually with the goal of bringing together faculty from PUIs to learn the state of undergraduate QIST education, identify challenges associated with implementing QIST curriculum at PUIs, and to develop strategies and solutions to deal with these challenges. This manuscript summarizes the results of workshop discussions with the hope of assisting faculty at PUIs attempting to incorporate quantum information science into their curriculum.

Can we detect the quantum nature of weak gravitational fields?. (arXiv:2110.02542v1 [gr-qc] CROSS LISTED)

A theoretical framework for the quantization of gravity has been an elusive Holy Grail since the birth of quantum theory and general relativity. While generations of scientists have attempted solutions to this deep riddle, an alternative path built upon the idea that experimental evidence could determine whether gravity is quantized has been decades in the making. The possibility of an experimental answer to the question of the quantization of gravity is of renewed interest in the era of gravitational wave detectors. We review and investigate an important subset of phenomenological quantum gravity, detecting quantum signatures of weak gravitational fields in table-top experiments and interferometers.

The Life and Science of Thanu Padmanabhan. (arXiv:2110.03208v1 [physics.hist-ph])

Thanu Padmanabhan was a renowned Indian theoretical physicist known for his research in general relativity, cosmology, and quantum gravity. In an extraordinary career spanning forty-two years, he published more than three hundred research articles, wrote ten highly successful technical and popular books, and mentored nearly thirty graduate students and post-doctoral fellows. He is best known for his deep work investigating gravitation as an emergent thermodynamic phenomenon. He was an outstanding teacher, and an indefatigable populariser of science, who travelled very widely to motivate and inspire young students. Paddy, as he was affectionately known, was also a close friend to his students and collaborators, treating them as part of his extended academic family. On September 17, 2021 Paddy passed away very unexpectedly, at the age of sixty-four and at the height of his research career, while serving as a Distinguished Professor at the Inter-University Centre for Astronomy and Astrophysics, Pune. His untimely demise has come as a shock to his family and friends and colleagues. In this article, several of them have come together to pay their tributes and share their fond memories of Paddy.

Probability distribution for the quantum universe. (arXiv:2110.03050v1 [hep-th])

We determine the inner product on the Hilbert space of wavefunctions of the universe by imposing the Hermiticity of the quantum Hamiltonian in the context of the minisuperspace model. The corresponding quantum probability density reproduces successfully the classical probability distribution in the $\hbar \to 0$ limit, for closed universes filled with a perfect fluid of index $w$. When $-1/3<w\le 1$, the wavefunction is normalizable and the quantum probability density becomes vanishingly small at the big bang/big crunch singularities, at least at the semi-classical level. Quantum expectation values of physical geometrical quantities, which diverge classically at the singularities, are shown to be finite.

Emergence of Minkowski-Spacetime by Simple Deterministic Graph Rewriting. (arXiv:2110.03388v1 [gr-qc])

Authors: Gabriel Leuenberger

The causal set program as well as the Wolfram physics project leave open the problem of how a graph that is a (3+1)-dimensional Minkowski-spacetime according to its simple geodesic distances, could be generated solely from simple deterministic rules. This paper provides a solution by describing simple rules that characterize discrete Lorentz boosts between 4D lattice graphs, which combine further to form Wigner rotations that produce isotropy and lead to the emergence of the continuous Lorentz group and the (3+1)-dimensional Minkowski-spacetime. On such graphs, the speed of light, the proper time interval, as well as the proper length are all shown to be highly accurate.

Hints for a gravitational constant transition in Tully-Fisher data. (arXiv:2104.14481v3 [astro-ph.CO] UPDATED)

We use an up to date compilation of Tully-Fisher data to search for transitions in the evolution of the Tully-Fisher relation. Using an up to date data compilation, we find hints at $\approx 3\sigma$ level for a transition at critical distances $D_c \simeq 9 Mpc$ and $D_c \simeq 17 Mpc$. We split the full sample in two subsamples according to the measured galaxy distance with respect to a splitting distance $D_c$ and identify the likelihood of the best fit slope and intercept of one sample with respect to the best fit corresponding values of the other sample. For $D_c \simeq 9 Mpc$ and $D_c \simeq 17 Mpc$ we find a tension between the two subsamples at a level of $\Delta \chi^2 > 17\; (3.5\sigma)$. Using a Monte-Carlo simulation we demonstrate that this result is robust with respect to random statistical and systematic variations of the galactic distances. If the tension is interpreted as due to a gravitational strength transition, it would imply a shift of the effective gravitational constant to lower values for distances larger than $D_c$ by $\frac{\Delta G}{G}\simeq -0.1$. Such a shift is of the anticipated sign and magnitude but at somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions ($\frac{\Delta G}{G}\simeq -0.1$ at transition redshift $z_t\lesssim 0.01$ ($D_c\lesssim 40 Mpc$)).

Carroll symmetry, dark energy and inflation. (arXiv:2110.02319v1 [hep-th] CROSS LISTED)

Carroll symmetry arises from Poincar\’e symmetry upon taking the limit of vanishing speed of light. We determine the constraints on the energy-momentum tensor implied by Carroll symmetry and show that for energy-momentum tensors of perfect fluid form, these imply an equation of state ${\cal E}+P=0$ for energy density plus pressure. Therefore Carroll symmetry might be relevant for dark energy and inflation. In the Carroll limit, the Hubble radius goes to zero and outside it recessional velocities are naturally large compared to the speed of light. The de Sitter group of isometries, after the limit, becomes the conformal group in Euclidean flat space. We also study the Carroll limit of chaotic inflation, and show that the scalar field is naturally driven to have an equation of state with $w=-1$. Finally we show that the freeze-out of scalar perturbations in the two point function at horizon crossing is a consequence of Carroll symmetry.

To make the paper self-contained, we include a brief pedagogical review of Carroll symmetry, Carroll particles and Carroll field theories that contains some new material as well. In particular we show, using an expansion around speed of light going to zero, that for scalar and Maxwell type theories one can take two different Carroll limits at the level of the action. In the Maxwell case these correspond to the electric and magnetic limit. For point particles we show that there are two types of Carroll particles: those that cannot move in space and particles that cannot stand still.

Analyzing Nonequilibrium Quantum States through Snapshots with Artificial Neural Networks

Author(s): A. Bohrdt, S. Kim, A. Lukin, M. Rispoli, R. Schittko, M. Knap, M. Greiner, and J. Léonard

Current quantum simulation experiments are starting to explore nonequilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and timescales. Therefore, the question emerges as to which observables are best suited to study the dynamics in such quantum many-body systems…

[Phys. Rev. Lett. 127, 150504] Published Thu Oct 07, 2021

The statistical interpretation: Born, Heisenberg and von Neumann, 1926-27

Bacciagaluppi, Guido (2021) The statistical interpretation: Born, Heisenberg and von Neumann, 1926-27. [Preprint]

The Double Nature of Maxwell’s Physical Analogies

Nappo, Francesco (2021) The Double Nature of Maxwell’s Physical Analogies. [Preprint]

The duality of a multitude

Nature Physics, Published online: 06 October 2021; doi:10.1038/s41567-021-01389-8

The duality of a multitude