Weekly Papers on Quantum Foundations (45)

Authors: Zhikuan ZhaoRobert PisarczykJayne ThompsonMile GuVlatko VedralJoseph F. Fitzsimons

The traditional formalism of non-relativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial and temporal quantum correlations. Here we unify the geometrical description of two-point quantum correlations in space-time. Our study presents the geometry of correlations between two sequential Pauli measurements on a single qubit undergoing an arbitrary quantum channel evolution together with two-qubit spatial correlations under a common framework. We establish a symmetric structure between quantum correlations in space and time. This symmetry is broken in the presence of non-unital channels, which further reveals a set of temporal correlations that are indistinguishable from correlations found in bipartite entangled states.

Authors: Don N. Page

In ordinary situations involving a small part of the universe, Born’s rule seems to work well for calculating probabilities of observations in quantum theory. However, there are a number of reasons for believing that it is not adequate for many cosmological purposes. Here a number of possible generalizations of Born’s rule are discussed, explaining why they are consistent with the present statistical support for Born’s rule in ordinary situations but can help solve various cosmological problems.

Authors: D. Jaffino StargenV. SreenathL. Sriramkumar

The perturbations in the early universe are generated as a result of the interplay between quantum field theory and gravitation. Since these primordial perturbations lead to the anisotropies in the cosmic microwave background and eventually to the inhomogeneities in the Large Scale Structure (LSS), they provide a unique opportunity to probe issues which are fundamental to our understanding of quantum physics and gravitation. One such fundamental issue that remains to be satisfactorily addressed is the transition of the primordial perturbations from their quantum origins to the LSS which can be characterized completely in terms of classical quantities. Bouncing universes provide an alternative to the more conventional inflationary paradigm as they can help overcome the horizon problem in a fashion very similar to inflation. While the problem of the quantum-to-classical transition of the primordial perturbations has been investigated extensively in the context of inflation, we find that there has been a rather limited effort towards studying the issue in bouncing universes. In this work, we analyze certain aspects of this problem with the example of tensor perturbations produced in bouncing universes. We investigate the issue mainly from two perspectives. Firstly, we approach the problem by examining the extent of squeezing of a quantum state associated with the tensor perturbations with the help of the Wigner function. Secondly, we analyze this issue from the perspective of the quantum measurement problem. In particular, we study the effects of wave function collapse, using a phenomenological model known as continuous spontaneous localization, on the tensor power spectra. We conclude with a discussion of results.

Authors: S. O. AlexeyevX. CalmetB. N. Latosh

We show that the non-locality recently identified in quantum gravity using resummation techniques propagates to the matter sector of the theory. We describe these non-local effects using effective field theory techniques. We derive the complete set of non-local effective operators at order $N G^2$ for theories involving scalar, spinor, and vector fields. We then use recent data from the Large Hadron Collider to set a bound on the scale of space-time non-locality and find $M_\star> 3 \times 10^{-11}$ GeV.

Authors: Giulio GasbarriMarko TorošSandro DonadiAngelo Bassi

Starting from an idea of S.L. Adler~\cite{Adler2015}, we develop a novel model of gravity-induced spontaneous wave-function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength $\xi$ of the complex metric fluctuations with available experimental data. We show that $\xi\geq 10^{-26}$ in order for the model to guarantee classicality of macro-objects, and at the same time $\xi \leq 10^{-20}$ in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of $\xi \sim 10^{-21}$.

Authors: Leonardo Pedro

One attractive interpretation of quantum mechanics is the ensemble interpretation, where Quantum Mechanics merely describes a statistical ensemble of systems rather than individual systems. However, such interpretation does not address why the wave-function plays a central role in the calculations of probabilities, unlike most other interpretations of quantum mechanics. We first show that for a quantum system defined in a 2-dimensional real Hilbert space, the role of the wave-function is identical to the role of the Euler’s formula in engineering, while the collapse of the wave-function is identical to selecting the real part of a complex number. We will then show that the wave-function is merely one possible parametrization of any probability distribution describing an ensemble: a surjective map from an hypersphere to the set of all possible probability distributions. The fact that the hypersphere is a surface of constant radius reflects the fact that the integral of the probability distribution is always 1. Any transformation of a probability distribution is represented by a rotation of the hypersphere. It is thus a very good parametrization which allows us to apply group theory to the hypersphere, despite the fact that a stochastic process is not always a Markov process. The collapse of the wave-function is required to compensate the fact that physical transformations on the probability distribution are not linear transformations.

Authors: Bob CoeckeStefano GogiosoJohn H. Selby

We consider a very general class of theories, process theories, which capture the underlying structure common to most theories of physics as we understand them today (be they established, toy or speculative theories). Amongst these theories, we will be focusing on those which are `causal’, in the sense that they are intrinsically compatible with the causal structure of space-time — as required by relativity. We demonstrate that there is a sharp contrast between these theories and the corresponding time-reversed theories, where time is taken to flow backwards from the future to the past. While the former typically feature a rich gamut of allowed states, the latter only allow for a single state: eternal noise. We illustrate this result by considering of the time-reverse of quantum theory. We also derive a strengthening of the result in PRL 108, 200403 on signalling in time-reversed theories.

Authors: Craig HoganOhkyung Kwon

A Lorentz invariant framework is developed to interpret exotic cross-correlations in the signals of two separate interferometers, associated with the emergence of space-time and inertial frames from a Planck scale quantum system. The framework extends our earlier models of exotic autospectra based on invariant causal structure. Space-time relationships between world lines are modeled as antisymmetric cross-correlations on past and future light cones between sequences in proper time with Planck bandwidth, arising from nonlocal entanglement information in geometrical states. These exotic correlations of a flat space-time are normalized to have the same holographic information content as black holes. Simple models of interferometer response are shown to produce a unique signature: a broad band imaginary cross spectrum, with a frequency structure determined by the layout of the apparatus. The framework will be useful for interpreting data in the bent reconfiguration of the Fermilab Holometer, and for conceptual design of future experiments.

The effort to reconcile general relativity with quantum mechanics always hits one snag: gravity. An experiment could finally tell us if it is a quantum force
Flash Physics: need-to-know updates from the world of physics

Author(s): Tim Thomay, Sergey V. Polyakov, Olivier Gazzano, Elizabeth Goldschmidt, Zachary D. Eldredge, Tobias Huber, Vivien Loo, and Glenn S. Solomon

Advances in quantum optics and quantum information technologies increasingly require a way to fully understand the state of single indistinguishable photons. While previous approaches have needed two or more measurements, a new experiment demonstrates a way to characterize single-photon states with just one measurement.

[Phys. Rev. X 7, 041036] Published Wed Nov 15, 2017

Authors: Alejandro PerezDaniel Sudarsky

We argue that discreteness at the Planck scale (naturally expected to arise from quantum gravity) might manifest in the form of minute violations of energy-momentum conservation of the matter degrees of freedom when described in terms of (idealized) smooth fields on a smooth spacetime. In the context of applications to cosmology such `energy diffusion’ from the low energy matter degrees of freedom to the discrete structures underlying spacetime leads to the emergence of an effective dark energy term in Einstein’s equations. We estimate this effect using a (relational) hypothesis about the materialization of discreteness in quantum gravity which is motivated by the strict observational constraints supporting the validity of Lorentz invariance at low energies. The predictions coming from simple dimensional analysis yield a cosmological constant of the order of magnitude of the observed value without fine tuning.

Authors: Djamil BouazizTolga Birkandan

The problem of a particle of mass m in the field of the inverse square potential is studied in quantum mechanics with a generalized uncertainty principle, characterized by the existence of a minimal length. Using the coordinate representation, for a specific form of the generalized uncertainty relation, we solve the deformed Schr\”odinger equation analytically in terms of confluent Heun functions. We explicitly show the regularizing effect of the minimal length on the singularity of the potential. We discuss the problem of bound states in detail and we derive an expression for the energy spectrum in a natural way from the square integrability condition; the results are in complete agreement with the literature.

Authors: Saul RodriguezDaniel Sudarsky

In this work we consider the Higgs inflation scenario, but in contrast with past works, the present analysis is done in the context of a spontaneous collapse theory for the quantum state of the inflaton field. In particular we will rely on a previously studied adaptation of the Continuous Spontaneous Localization model for the treatment of inflationary cosmology. We will show that with the introduction of the dynamical collapse hypothesis, some of the most serious problems of the Higgs inflation proposal, can be evaded in a natural way.

Feintzeig, Benjamin H. (2017) The classical limit of a state on the Weyl algebra. [Preprint]
John Wheeler tried to help his heroes see eye to eye on quantum physics

— Read more on ScientificAmerican.com


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Ruyant, Quentin (2017) Structural Realism or Modal Empiricism? The British Journal for the Philosophy of Science.
Barbar, Ahmed (2017) The Kochen-Specker and Conway-Kochen Theorems. [Preprint]

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One Response

  1. Ruth Kastner
    Ruth Kastner at |

    Hi, I’d like to note the following 2 papers that seem to have been left off the list (apologies if I’ve overlooked them):

    https://arxiv.org/abs/1709.09367 “On the status of the Measurement Problem: Recalling the Relativistic Transactional Interpretation” (Kastner, R.)


    https://arxiv.org/abs/1711.04501 “Quantifying Absorption in the Transactional interpretation” (Kastner, R. and Cramer, J.)

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