# Weekly Papers on Quantum Foundations (3)

Nonlocality via Entanglement-Swapping — a Bridge Too Far?. (arXiv:2101.05370v1 [quant-ph])

A 2015 experiment by Hanson and his Delft colleagues provided new confirmation that the quantum world violates the Bell inequalities, closing some loopholes left open by previous experiments. The experiment was also taken to provide new evidence of quantum nonlocality. Here we argue for caution about the latter claim. The Delft experiment relies on entanglement swapping, and our main point is that this introduces new loopholes in the argument from violation of the Bell inequalities to nonlocality. As we explain, the sensitivity of such experiments to these new loopholes depends on the temporal relation between the entanglement swapping measurement C and the two measurements A and B between which we seek to infer nonlocality. If the C is in the future of A and B, the loopholes loom large. If C is in the past, they are less of a threat. The Delft experiment itself is the intermediate case, in which the separation is spacelike. We argue that this still leaves it vulnerable to the new loopholes, unable to establish conclusively that it avoids them.

Quantum logics close to Boolean algebras. (arXiv:2101.05501v1 [quant-ph])

We consider orthomodular posets endowed with a symmetric difference. We call them ODPs. Expressed in the quantum logic language, we consider quantum logics with an XOR-type connective. We study three classes of “almost Boolean” ODPs, two of them defined by requiring rather specific behaviour of infima and the third by a Boolean-like behaviour of Frink ideals. We establish a (rather surprising) inclusion between the three classes, shadding thus light on their intrinsic properties. (More details can be found in the Introduction that follows.) Let us only note that the orthomodular posets pursued here, though close to Boolean algebras (i.e., close to standard quantum logics), still have a potential for an arbitrarily high degree of non-compatibility and hence they may enrich the studies of mathematical foundations of quantum mechanics.

Entangled Kernels — Beyond Separability. (arXiv:2101.05514v1 [cs.LG])

We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and entanglement, we propose a new view on operator-valued kernels and define a general family of kernels that encompasses previously known operator-valued kernels, including separable and transformable kernels. Within this framework, we introduce another novel class of operator-valued kernels called entangled kernels that are not separable. We propose an efficient two-step algorithm for this framework, where the entangled kernel is learned based on a novel extension of kernel alignment to operator-valued kernels. We illustrate our algorithm with an application to supervised dimensionality reduction, and demonstrate its effectiveness with both artificial and real data for multi-output regression.

Layers of classicality in the compatibility of measurements. (arXiv:2101.05752v1 [quant-ph])

The term “Layers of classicality” in the context of quantum measurements, is introduced in [T. Heinosaari, Phys. Rev. A \textbf{93}, 042118 (2016)]. The strongest layer among these consists of the sets of observables that can be broadcast and the weakest layer consists of the sets of compatible observables. There are several other layers in between those two layers. In this work, we show the differences and similarities in their mathematical and geometric properties. We also show the relations among these layers.

An experimental proposal to study collapse of the wave function in travelling-wave parametric amplifiers. (arXiv:1811.01698v6 [quant-ph] UPDATED)

The read-out of a microwave qubit state occurs using an amplification chain that enlarges the quantum state to a signal detectable with a classical measurement apparatus. However, at what point in this process is the quantum state really ‘measured’? In order to investigate whether the `measurement’ takes place in the amplification chain, in which a parametric amplifier is often chosen as the first amplifier, it is proposed to construct a microwave interferometer that has such an amplifier added to each of its arms. Feeding the interferometer with single photons, the interference visibility depends on the gain of the amplifiers and whether a measurement collapse has taken place during the amplification process. The visibility as given by standard quantum mechanics is calculated as a function of gain, insertion loss and temperature. We find a visibility of 1/3 in the limit of large gain without taking into account losses, which is reduced to 0.26 in case the insertion loss of the amplifiers is 2.2 dB at a temperature of 50 mK. It is shown that if the wave function collapses within the interferometer, the measured visibility is reduced compared to its magnitude predicted by standard quantum mechanics once this collapse process sets in.

Introducing the inverse hoop conjecture for black holes. (arXiv:2101.05290v1 [gr-qc])

Authors: Shahar Hod

It is conjectured that stationary black holes are characterized by the inverse hoop relation ${\cal A}\leq {\cal C}^2/\pi$, where ${\cal A}$ and ${\cal C}$ are respectively the black-hole surface area and the circumference length of the smallest ring that can engulf the black-hole horizon in every direction. We explicitly prove that generic Kerr-Newman-(anti)-de Sitter black holes conform to this conjectured area-circumference relation.

Generalized gravity theory with curvature, torsion and nonmetricity. (arXiv:2101.05318v1 [gr-qc])

In this article, the generalized gravity theory with the curvature, torsion and nonmetricy was studied. For the FRW spacetime case, in particular, the Lagrangian, Hamilatonian and gravitational equations are obtained. The particular case $F(R,T)=\alpha R+\beta T+\mu Q+\nu{\cal T}$ is investigated in detail. In quantum case, the corresponding Wheeler-DeWitt equation is obtained. Finally, some gravity theories with the curvature, torsion and nonmetricity are presented.

Gravitationally induced uncertainty relations in curved backgrounds. (arXiv:2101.05552v1 [gr-qc])

Authors: Luciano PetruzzielloFabian Wagner

This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like hypersurface whose radius is a measure of the position uncertainty. On the other hand, we concurrently work out a viable physical definition of the momentum operator and its standard deviation in the non-relativistic limit of the 3+1 formalism. Finally, we evaluate the uncertainty relation which to second order depends on the Ricci scalar of the effective 3-metric and the corresponding covariant derivative of the shift vector. For the sake of illustration, we apply our general result to a number of examples arising in the context of both general relativity and extended theories of gravity.

A cosmic shadow on CSL. (arXiv:1906.04405v4 [quant-ph] UPDATED)

Authors: Jerome MartinVincent Vennin

The Continuous Spontaneous Localisation (CSL) model solves the measurement problem of standard quantum mechanics, by coupling the mass density of a quantum system to a white-noise field. Since the mass density is not uniquely defined in general relativity, this model is ambiguous when applied to cosmology. We however show that most natural choices of the density contrast already make current measurements of the cosmic microwave background incompatible with other laboratory experiments.

IR dynamics and entanglement entropy. (arXiv:1910.07847v3 [hep-th] UPDATED)

Authors: Theodore N TomarasNicolaos Toumbas

We consider scattering of Faddeev-Kulish electrons in QED and study the entanglement between the hard and soft particles in the final state at the perturbative level. The soft photon spectrum naturally splits into two parts: i) soft photons with energies less than a characteristic infrared scale $E_d$ present in the clouds accompanying the asymptotic charged particles, and ii) sufficiently low energy photons with energies greater than $E_d$, comprising the soft part of the emitted radiation. We construct the density matrix associated with tracing over the radiative soft photons and calculate the entanglement entropy perturbatively. We find that the entanglement entropy is free of any infrared divergences order by order in perturbation theory. On the other hand infrared divergences in the perturbative expansion for the entanglement entropy appear upon tracing over the entire spectrum of soft photons, including those in the clouds. To leading order the entanglement entropy is set by the square of the Fock basis amplitude for real single soft photon emission, which leads to a logarithmic infrared divergence when integrated over the photon momentum. We argue that the infrared divergences in the entanglement entropy (per particle flux per unit time) in this latter case persist to all orders in perturbation theory in the infinite volume limit.

Conserved charges in general relativity. (arXiv:2005.13233v3 [gr-qc] UPDATED)

Authors: Sinya AokiTetsuya OnogiShuichi Yokoyama

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner-Sharp mass in the Oppenheimer-Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold.

The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions. (arXiv:2008.03280v2 [hep-th] UPDATED)

The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further we demonstrate an equivalent formalism of computation using a general time independent Hamiltonian having well defined eigenstate representation for integrable supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism we consider the two well known models viz. Harmonic Oscillator and one dimensional potential well within the framework of supersymmetry. For the Harmonic Oscillator case we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both micro-canonical and canonical ensembles in quantum mechanics without supersymmetry. On the other hand, for one dimensional potential well problem we found significantly different time scale and the other parameter dependence compared to the results obtained from non-supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model independent Hamiltonian along with the previously mentioned these well cited models.

Quantum Detection of Inertial Frame Dragging. (arXiv:2009.10584v3 [gr-qc] UPDATED)

A relativistic theory of gravity like general relativity produces phenomena differing fundamentally from Newton’s theory. An example, analogous to electromagnetic induction, is gravitomagnetism, or the dragging of inertial frames by mass-energy currents. These effects have recently been confirmed by classical observations. Here we show, for the first time, that they can be observed by a quantum detector. We study the response function of Unruh De-Witt detectors placed in a slowly rotating shell. We show that the response function picks up the presence of rotation even though the spacetime inside the shell is flat and the detector is locally inertial. The detector can distinguish between the static situation when the shell is non-rotating and the stationary case when the shell rotates and the dragging of inertial frames, i.e. gravitomagnetic effects, arise. Moreover, it can do so when the detector is switched on for a finite time interval within which a light signal cannot travel to the shell and back to convey the presence of rotation.

String Theory, the Dark Sector and the Hierarchy Problem. (arXiv:2010.15610v2 [hep-th] UPDATED)

Authors: Per BerglundTristan HübschDjordje Minic

We discuss dark energy, dark matter and the hierarchy problem in the context of a general non-commutative formulation of string theory. In this framework dark energy is generated by the dynamical geometry of the dual spacetime while dark matter, on the other hand, comes from the degrees of freedom dual to the visible matter. This formulation of string theory is sensitive both to the IR and UV scales and the Higgs scale is radiatively stable by being a geometric mean of radiatively stable UV and IR scales. We also comment on various phenomenological signatures of this novel approach to dark energy, dark matter and the hierarchy problem. We find that this new view on the hierarchy problem is realized in a toy model based on a non-holomorphic deformation of the stringy cosmic string. Finally, we discuss a proposal for a new non-perturbative formulation of string theory, which sheds light on M theory and F theory, as well as on supersymmetry and holography.

The history of LHCb. (arXiv:2101.05331v1 [physics.hist-ph])

In this paper we describe the history of the LHCb experiment over the last three decades, and its remarkable successes and achievements. LHCb was conceived primarily as a b-physics experiment, dedicated to CP violation studies and measurements of very rare b decays, however the tremendous potential for c-physics was also clear. At first data taking, the versatility of the experiment as a general-purpose detector in the forward region also became evident, with measurements achievable such as electroweak physics, jets and new particle searches in open states. These were facilitated by the excellent capability of the detector to identify muons and to reconstruct decay vertices close to the primary pp interaction region. By the end of the LHC Run 2 in 2018, before the accelerator paused for its second long shut down, LHCb had measured the CKM quark mixing matrix elements and CP violation parameters to world-leading precision in the heavy-quark systems. The experiment had also measured many rare decays of b and c quark mesons and baryons to below their Standard Model expectations, some down to branching ratios of order 10-9. In addition, world knowledge of b and c spectroscopy had improved significantly through discoveries of many new resonances already anticipated in the quark model, and also adding new exotic four and five quark states.

On the Relationship Between Modelling Practices and Interpretive Stances in Quantum Mechanics

Ruyant, Quentin (2021) On the Relationship Between Modelling Practices and Interpretive Stances in Quantum Mechanics. Foundations of Science. ISSN 1233-1821

Efficient Simulation of Loop Quantum Gravity: A Scalable Linear-Optical Approach

Author(s): Lior Cohen, Anthony J. Brady, Zichang Huang, Hongguang Liu, Dongxue Qu, Jonathan P. Dowling, and Muxin Han

The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theor…

[Phys. Rev. Lett. 126, 020501] Published Mon Jan 11, 2021

Truth and beauty in physics and biology

Nature Physics, Published online: 11 January 2021; doi:10.1038/s41567-020-01132-9

Physicists and biologists have different conceptions of beauty. A better appreciation of these differences may bring the disciplines closer and help develop a more integrated view of life.

No Time for Time from No-Time

Chua, Eugene Y. S. and Callender, Craig (2020) No Time for Time from No-Time. [Preprint]

Humean Laws of Nature: The End of the Good Old Days

Callender, Craig (2021) Humean Laws of Nature: The End of the Good Old Days. [Preprint]

Downward Causation Defended

Woodward, James (2021) Downward Causation Defended. [Preprint]