# Weekly Papers on Quantum Foundations (7)

Observing a Topological Transition in Weak-Measurement-Induced Geometric Phases. (arXiv:2102.05660v1 [quant-ph])

Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements in particular, through their back-action on the system, may enable various levels of coherent control. The latter ranges from observing quantum trajectories to state dragging and steering. Furthermore, just like the adiabatic evolution of quantum states that is known to induce the Berry phase, sequential weak measurements may lead to path-dependent geometric phases. Here we measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. This connection between weak measurement induced quantum dynamics and topological transitions reveals subtle topological features in measurement-based manipulation of quantum systems. Our protocol could be implemented for classes of operations (e.g. braiding) which are topological in nature. Furthermore, our results open new horizons for measurement-enabled quantum control of many-body topological states.

Measuring Topological Order. (arXiv:2102.05677v1 [cond-mat.str-el])

The topological order of a (2+1)D topological phase of matter is characterized by its chiral central charge and a unitary modular tensor category that describes the universal fusion and braiding properties of its anyonic quasiparticles. I discuss the topologically invariant quantities associated with these and identify ones that are useful for determining the topological order. I propose a variety of physical experiments that probe these quantities and detail the relation of the measured data to the topological invariants.

What makes a particle detector click. (arXiv:2102.05734v1 [quant-ph])

We highlight fundamental differences in the models of light-matter interaction between the behaviour of Fock state detection in free space versus optical cavities. To do so, we study the phenomenon of resonance of detectors with Fock wavepackets as a function of their degree of monochromaticity, the number of spatial dimensions, the linear or quadratic nature of the light-matter coupling, and the presence (or absence) of cavity walls in space. In doing so we show that intuition coming from quantum optics in cavities does not straightforwardly carry to the free space case. For example, in $(3+1)$ dimensions the detector response to a Fock wavepacket will go to zero as the wavepacket is made more and more monochromatic and in coincidence with the detector’s resonant frequency. This is so even though the energy of the free-space wavepacket goes to the expected finite value of $\hbar\Omega$ in the monochromatic limit. This is in contrast to the behaviour of the light-matter interaction in a cavity (even a large one) where the probability of absorbing a Fock quantum is maximized when the quantum is more monochromatic at the detector’s resonance frequency. We trace this crucial difference to the fact that monochromatic Fock states are not normalizable in the continuum, thus physical Fock states need to be constructed out of normalizable wavepackets whose energy density goes to zero in the monochromatic limit as they get spatially delocalized.

Witnessing Wigner Negativity. (arXiv:2102.06193v1 [quant-ph])

Negativity of the Wigner function is arguably one of the most striking non-classical features of quantum states. Beyond its fundamental relevance, it is also a necessary resource for quantum speedup with continuous variables. As quantum technologies emerge, the need to identify and characterize the resources which provide an advantage over existing classical technologies becomes more pressing. Here we derive witnesses for Wigner negativity of quantum states, based on fidelities with Fock states, which can be reliably measured using standard detection setups. They possess a threshold expected value indicating whether the measured state exhibits the desired property or not. We phrase the problem of finding the threshold values for our witnesses as an infinite-dimensional linear optimisation. By relaxing and restricting the corresponding linear programs, we derive two hierarchies of semidefinite programs, which provide numerical sequences of increasingly tighter upper and lower bounds for the threshold values. We further show that both sequences converge to the threshold value. Moreover, our witnesses form a complete family – each Wigner negative state is detected by at least one witness – thus providing a reliable method for experimentally witnessing Wigner negativity of quantum states from few measurements. From a foundational perspective, our work provides insights on the set of positive Wigner functions which still lacks a proper characterisation.

Positivity Bounds without Boosts. (arXiv:2102.05683v1 [hep-th])

Authors: Tanguy GrallScott Melville

We derive the first positivity bounds for low-energy Effective Field Theories (EFTs) that are not invariant under Lorentz boosts. “Positivity bounds” are the low-energy manifestation of certain fundamental properties in the UV — to date they have been used to constrain a wide variety of EFTs, however since all of the existing bounds require Lorentz invariance they are not directly applicable when this symmetry is broken, such as for most cosmological and condensed matter systems. From the UV axioms of unitarity, causality and locality, we derive an infinite family of bounds which (derivatives of) the $2\to2$ EFT scattering amplitude must satisfy even when Lorentz boosts are broken (either spontaneously or explicitly). We apply these bounds to the leading-order EFT of both a superfluid and the scalar fluctuations produced during inflation, comparing in the latter case with the current observational constraints on primordial non-Gaussianity.

No-boundary solutions are robust to quantum gravity corrections. (arXiv:2008.04134v2 [hep-th] UPDATED)

Authors: Caroline JonasJean-Luc Lehners

The no-boundary proposal is a theory of the initial conditions of the universe formulated in semi-classical gravity, and relying on the existence of regular (complex) solutions of the equations of motion. We show by explicit computation that regular no-boundary solutions are modified, but not destroyed, upon inclusion of expected quantum gravity corrections that involve higher powers of the Riemann tensor as well as covariant derivatives thereof. We illustrate our results with examples drawn from string theory. Our findings provide a crucial self-consistency test of the no-boundary framework.

An order-unity correction to Hawking radiation. (arXiv:2102.04930v2 [hep-th] UPDATED)

Authors: Eanna E Flanagan

When a black hole first forms, the properties of the emitted radiation as measured by observers near future null infinity are very close to the 1974 prediction of Hawking. However, deviations grow with time, and become of order unity after a time $t \sim M_i^{7/3}$, where $M_i$ is the initial mass in Planck units. After an evaporation time the corrections are large: the angular distribution of the emitted radiation is no longer dominated by low multipoles, with an exponential fall off at high multipoles. Instead, the radiation is redistributed as a power law spectrum over a broad range of angular scales, all the way down to the scale $\Delta \theta \sim 1/M_i$, beyond which there is exponential falloff. This effect is is a quantum gravitational effect, whose origin is the spreading of the wavefunction of the black hole’s center of mass location caused by the kicks of the individual outgoing quanta, discovered by Page in 1980. The modified angular distribution of the Hawking radiation has an important consequence: the number of soft hair modes that can effectively interact with outgoing Hawking quanta increases from the handful of modes at low multipoles $l$, to a large number of modes, of order $\sim M_i^2$. We argue that this change unlocks the Hawking-Perry-Strominger mechanism for purifying the Hawking radiation.

A pragmatic approach to the ontology of models

Antoniou, Antonis (2021) A pragmatic approach to the ontology of models. [Preprint]

Is the problem of molecular structure just the quantum measurement problem?

Fortin, Sebastian and Lombardi, Olimpia (2021) Is the problem of molecular structure just the quantum measurement problem? [Preprint]

Predictably random

Nature Physics, Published online: 11 February 2021; doi:10.1038/s41567-021-01177-4

Two experiments using entangled photons have successfully generated more randomness than consumed — at a level of security that is all but certain. They did so by exploiting non-locality, one of the most counterintuitive aspects of quantum mechanics.

On Mach On Time

Thebault, Karim P Y (2021) On Mach On Time. [Preprint]

Book Review: French, S., & Saatsi, J. (Eds.). (2020). Scientific Realism and the Quantum. Oxford University Press

Glick, David (2021) Book Review: French, S., & Saatsi, J. (Eds.). (2020). Scientific Realism and the Quantum. Oxford University Press. [Preprint]

Why Humean explanations are not circular

Duguid, Callum (2021) Why Humean explanations are not circular.

On French on Theories and Representation

Lutz, Sebastian (2021) On French on Theories and Representation. [Preprint]

Postselection-Free Entanglement Dynamics via Spacetime Duality

Author(s): Matteo Ippoliti and Vedika Khemani

A protocol based on space-time duality is used to find the purity of a quantum state for simulations of a class of nonunitary circuits, without any postselection.

[Phys. Rev. Lett. 126, 060501] Published Tue Feb 09, 2021

Why understanding-why is contrastive

Abstract

Contrastivism about interrogative understanding is the view that ‘S understands why p’ posits a three-place epistemic relation between a subject S, a fact p, and an alternative to pq. This thesis stands in stark opposition to the natural idea that a subject S can be said to understand why p simpliciter. I argue that contrastivism offers the best explanation for the fact that evaluations of the form ‘S understands why p’ vary depending on the alternatives to p under consideration. I also show that contrastivism offers valuable resources with which to explain the gradability of interrogative understanding attributions, as well as the sensitivity of these attributions to the perceived degree of epistemic demandingness of different contexts.

On the possibility of non-eternalism without absolute simultaneity

Abstract

It has been argued that the standard formulation of the Special Theory of Relativity (hereafter STR) is not only incompatible with presentism, but also strongly indicates the truth of eternalism. We should, however, distinguish two claims concerning the ontological implications of STR: (1) STR is inconsistent with every ontology which requires an absolute relation of simultaneity; and (2) STR implies that eternalism is the only possible ontology of time. There have been a wide range of responses designed to reject these claims, both jointly and independently. For example, one way of rejecting claim (2) is by rejecting claim (1): thus, one would argue that STR can be revised or interpreted in such a way that it allows an absolute relation of simultaneity. Another way of rejecting claim (2) is by questioning the equivalency of the relation ‘being real as of’ (a relation known in the literature as relation R). The main purpose of this paper is to raise a new line of objection against concluding eternalism from the relativity of simultaneity. I argue that there is a way to deny claim (2) without denying claim (1) and also without denying the equivalency of relation R. The argument which I present rests on a metaphysical assumption concerning the relation of simultaneity (hereafter the SIM): the assumption that the SIM holds basically between space–time points as opposed to holding basically between events.

Why Newton’s G is not a universal Constant of Nature A reanalysis of Cavendish’s experiment to determine the density of the Earth

Heinrich, Werner F. (2021) Why Newton’s G is not a universal Constant of Nature A reanalysis of Cavendish’s experiment to determine the density of the Earth. [Preprint]

Expanding the Empirical Realm: Constructive Empiricism and Augmented Observation

Dellsén, Finnur (2021) Expanding the Empirical Realm: Constructive Empiricism and Augmented Observation. [Preprint]

Are there really no such things as theories?

Dellsén, Finnur (2021) Are there really no such things as theories? [Preprint]

Identical Particles in Quantum Mechanics: Against the Received View

Dieks, Dennis (2020) Identical Particles in Quantum Mechanics: Against the Received View. [Preprint]