# Weekly Papers on Quantum Foundations (52)

Quantum Ontology without Speculation

Egg, Matthias (2020) Quantum Ontology without Speculation. [Preprint]

Refining the general comparison theorem for Klein-Gordon equation. (arXiv:2012.13008v1 [math-ph])

By recasting the Klein–Gordon equation as an eigen-equation in the coupling parameter $v > 0,$ the basic Klein–Gordon comparison theorem may be written $f_1\leq f_2\implies G_1(E)\leq G_2(E)$, where $f_1$ and $f_2$, are the monotone non-decreasing shapes of two central potentials $V_1(r) = v_1\,f_1(r)$ and $V_2(r) = v_2\, f_2(r)$ on $[0,\infty)$. Meanwhile $v_1 = G_1(E)$ and $v_2 = G_2(E)$ are the corresponding coupling parameters that are functions of the energy $E\in(-m,\,m)$. We weaken the sufficient condition for the ground-state spectral ordering by proving (for example in $d=1$ dimension) that if $\int_0^x\big[f_2(t) – f_1(t)\big]\varphi_i(t)dt\geq 0$, the couplings remain ordered $v_1 \leq v_2$ where $i = 1\, {\rm or}\, 2,$ and $\{\varphi_1, \varphi_2\}$ are the ground-states corresponding respectively to the couplings $\{v_1,\, v_2\}$ for a given $E \in (-m,\, m).$. This result is extended to spherically symmetric radial potentials in $d > 1$ dimensions.

Quantum symmetry vs nonlocal symmetry. (arXiv:2012.13328v1 [math.QA])

We introduce the notion of nonlocal symmetry of a graph $G$, defined as a winning quantum correlation for the $G$-automorphism game that cannot be produced classically. Recent connections between quantum group theory and quantum information show that quantum correlations for this game correspond to tracial states on $C(\text{Qut}(G))$ — the algebra of functions on the quantum automorphism group of $G$. This allows us to also define nonlocal symmetry for any quantum permutation group. We investigate the differences and similarities between this and the notion of quantum symmetry, defined as non-commutativity of $C(\text{Qut}(G))$. Roughly speaking, quantum symmetry vs nonlocal symmetry can be viewed respectively as non-classicality of our model of reality vs non-classicality of our observation of reality.

We show that quantum symmetry is necessary but not sufficient for nonlocal symmetry. In particular, we show that the complete graph on five vertices is the only connected graph on five or fewer vertices with nonlocal symmetry, despite a dozen others having quantum symmetry. In particular this shows that the quantum symmetric group on four points, $S_4^+$, does not exhibit nonlocal symmetry, answering a question from the literature. In contrast to quantum symmetry, we show that two disjoint classical automorphisms do not guarantee nonlocal symmetry. However, three disjoint automorphisms do suffice. We also give a construction of quantum permutation matrices built from a finite abelian group $\Gamma$ and a permutation $\pi$ on $|\Gamma|$ elements. Computational evidence suggests that for cyclic groups of increasing size almost all permutations $\pi$ result in nonlocal symmetry. Surprisingly, the construction never results in nonlocal symmetry when $\mathbb{Z}_2^3$ is used. We also investigate under what conditions nonlocal symmetry arises when taking unions or products of graphs.

Decoherence from General Relativity. (arXiv:2012.12903v1 [gr-qc])

Authors: Itamar J. AllaliMark P. Hertzberg

It is of great interest to explore matter in nontrivial quantum arrangements, including Schrodinger cat-like states. Such states are sensitive to decoherence from their environment. Recently, in Ref. [1] we computed the rate of decoherence of a piece of superposed matter that primarily only interacts gravitationally, a dark-matter-Schrodinger-cat-state (DMSCS), within the nonrelativistic approximation. In this work we improve this to a general relativistic analysis. We firstly derive a single particle relativistic Schrodinger equation for a probe particle that passes through the DMSCS; the interaction is provided by the weak field metric of general relativity from the source. For a static DMSCS we find a neat generalization of our previous results. We then turn to the interesting new case of a time dependent DMSCS, which can be provided by a coherently oscillating axion field leading to superposed time dependent oscillations in the metric; a truly quantum-general relativistic phenomenon. We use scattering theory to derive the decoherence rate in all these cases. When the DMSCS is in a superposition of distinct density profiles, we find that the decoherence rate can be appreciable. We then consider the novel special case in which the density is not in a superposition, but the phase of its field oscillation is; this is a property that cannot be decohered within the nonrelativistic framework. We find that if the probe particle and/or the DMSCS’s velocity dispersion is slow, then the rate of decoherence of the phase is exponentially suppressed. However, if both the probe and the DMSCS’s velocity dispersion are relativistic, then the phase can decohere more rapidly. As applications, we find that diffuse galactic axions with superposed phases are robust against decoherence, while dense boson stars and regions near black hole horizons are not, and we discuss implications for experiment.

The gravitino problem in Extended Gravity cosmologies. (arXiv:2012.13205v1 [gr-qc])

The gravitino problem is investigated in the framework of Extended Gravity cosmologies. In particular, we consider $f(R)$ gravity, the most natural extension of the Hilbert-Einstein action, and $f(\cal T)$ gravity, the extension of teleparallel equivalent gravity. Since in these theories the expansion laws of the Universe are modified, as compared to the standard $\Lambda$CDM cosmology, it follows that also the thermal history of particles gets modified. We show that $f(R)$ models allow to avoid the late abundance of gravitinos. In particular, we found that for an appropriate choice of the parameters characterizing the $f(R)$ model, the gravitino abundance turns out to be independent of the reheating temperature. A similar behavior is achieved also in the context of $f(\cal T)$ gravity. In this perspective, we can conclude that geometric corrections to standard General Relativity (and to Teleparallel Equivalent of General Relativity) can improve shortcomings both in cosmology and in unified theories beyond the Standard Model of particles.

Prospects for testing the inverse-square law and gravitomagnetism using quantum interference. (arXiv:1910.13814v3 [gr-qc] UPDATED)

We examine a simple tabletop experimental setup for probing the inverse-square law of gravity and detecting eventual deviations therefrom. The nature of the setup allows indeed to effectively reach for shorter distances compared to what is allowed by other methods. Furthermore, we show that the same setup could also in principle be used to probe the interaction between gravitomagnetism and the intrinsic angular spin of quantum particles. Moreover, we show that the setup allows to have a gravitationally induced harmonic oscillator, introducing thus the possibility of studying in a novel way the interaction between gravity and quantum particles.

Constraints on variation of fine structure constant from joint SPT-SZ and XMM-Newton observations. (arXiv:2008.10541v2 [astro-ph.CO] UPDATED)

Authors: Kamal BoraShantanu Desai

We search for a variation of the electromagnetic fine structure constant ($\alpha \equiv e^2/\hbar c$) using a sample of 58 SZ selected clusters in the redshift range ($0.2<z<1.5$) detected by the South Pole Telescope, along with X-ray measurements using the XMM-Newton observatory. We use the ratio of the integrated SZ Compto-ionization to its X-ray counterpart as our observable for this search. We first obtain a model-independent constraint on $\alpha$ of about 0.7%, using the fact that the aforementioned ratio is constant as a function of redshift. We then look for a logarithmic dependence of $\alpha$ as a function of redshift: $\Delta \alpha/\alpha = -\gamma \ln(1+z)$, as this is predicted by runaway dilaton models. We find that $\gamma$ = $-0.046 \pm 0.1$, which indicates that there is no logarithmic variation of $\alpha$ as a function of redshift. We also search for a dipole variation of the fine structure constant using the same cluster sample. We do not find any evidence for such a spatial variation.

Hidden Variable Model for Universal Quantum Computation with Magic States on Qubits

Author(s): Michael Zurel, Cihan Okay, and Robert Raussendorf

Contrary to expectations, negativity in a quasiprobability function is not required for universal quantum computation.

[Phys. Rev. Lett. 125, 260404] Published Wed Dec 23, 2020

What Is Nonlocal in Counterfactual Quantum Communication?

Author(s): Yakir Aharonov and Daniel Rohrlich

We revisit the “counterfactual quantum communication” of Salih et al. [1], who claim that an observer “Bob” can send one bit of information to a second observer “Alice” without any physical particle traveling between them. We show that a locally conserved, massless current—specifically, a current of…

[Phys. Rev. Lett. 125, 260401] Published Mon Dec 21, 2020

Prediction of Short Time Qubit Readout via Measurement of the Next Quantum Jump of a Coupled Damped Driven Harmonic Oscillator

Author(s): Massimo Porrati and Seth Putterman

The dynamics of the next quantum jump for a qubit [two level system] coupled to a readout resonator [damped driven harmonic oscillator] is calculated. A quantum mechanical treatment of readout resonator reveals nonexponential short time behavior which could facilitate detection of the state of the q…

[Phys. Rev. Lett. 125, 260403] Published Mon Dec 21, 2020

Priority and privilege in scientific discovery

Rubin, Hannah and Schneider, Mike D. (2020) Priority and privilege in scientific discovery. [Preprint]

Theoretical Virtues and Theorizing in Physics: Against the Instrumentalist View of Simplicity

Mohammadian, Mousa (2020) Theoretical Virtues and Theorizing in Physics: Against the Instrumentalist View of Simplicity. [Preprint]