Weekly Papers on Quantum Foundations (42)

Authors: Richard LoppEduardo Martin-Martinez

We study how quantum randomness generation based on unbiased measurements on a hydrogen-like atom can get compromised by virtue of the unavoidable coupling of the atom with the electromagnetic field. Concretely, we show that an adversary with access to the quantum EM field, but not the atom, can perform an attack on the randomness of a set of unbiased quantum measurements. We analyze the light-atom interaction in 3+1 dimensions with no single-mode or rotating-wave approximations. In our study, we also take into account the non-pointlike nature of the atom and the exchanges of angular momentum between atom and field and compare with previous results obtained under scalar approximations. We show that preparing the atom in the ground state in the presence of no field excitations is, in general, not the safest state to generate randomness in atomic systems (such as trapped ions or optical lattices).

Authors: G. A. BrawleyM. R. VannerP. E. LarsenS. SchmidA. BoisenW. P. Bowen

Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of non-linear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic non-linearity of the radiation pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100~pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications.

Authors: Veronika BaumannStefan Wolf

There is yet no satisfying, agreed-upon interpretation of the quantum-mechanical formalism. Discussions of different interpretations are ongoing and sometimes hotheaded. In this note, we want to make a clear distinction between the (mathematical) quantum formalism -- and show that there is actually more than one -- and its interpretation. We further propose a novel (somewhat minimalistic) reading of the relative-state formalism and argue that the formalism is different from the standard Born and measurement-update rule, regardless of its interpretation. To do so we consider observations of observers -- Wigner's-friend-type experiments -- the feasibility of which remains an open question.

Laudisa, Federico (2017) Open Problems in Relational Quantum Mechanics. [Preprint]

Abstract

Recently I published an article in this journal entitled “Less interpretation and more decoherence in quantum gravity and inflationary cosmology” (Crull in Found Phys 45(9):1019–1045, 2015). This article generated responses from three pairs of authors: Vassallo and Esfeld (Found Phys 45(12):1533–1536, 2015), Okon and Sudarsky (Found Phys 46(7):852–879, 2016) and Fortin and Lombardi (Found Phys, 2017). In what follows, I reply to the criticisms raised by these authors.

Abstract

The difficult issues related to the interpretation of quantum mechanics and, in particular, the “measurement problem” are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary cosmology. The unessential mathematical complexity of the particular problem is bypassed, facilitating the discussion of the conceptual issues, by considering, within the paradigm set up by the cosmological problem, another problem where symmetry serves as a focal point: a simplified version of Mott’s problem.

de Ronde, Christian (2016) Unscrambling the Omelette of Quantum Contextuality (Part I): Preexistent Properties or Measurement Outcomes? [Preprint]
Butterfield, Jeremy (2017) Peaceful Coexistence: Examining Kent's Relativistic Solution to the Quantum Measurement Problem. [Preprint]

Authors: Christian de Ronde

In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper "scrambling" of two different meanings of quantum contextuality. While the first one, introduced by Bohr, is related to an epistemic interpretation of contextuality which stresses the incompatibility (or complementarity) of certain measurement situations described in classical terms; the second meaning of contextuality is related to a purely formal understanding of contextuality as exposed by the Kochen-Specker (KS) theorem which focuses instead on the constraints of the orthodox quantum formalism in order to interpret projection operators as preexistent or actual (definite valued) properties. We will show how these two notions have been scrambled together creating an "omelette of contextuality" which has been fully widespread through a popularized "epistemic explanation" of the KS theorem according to which: The measurement outcome of the observable A when measured together with B or together with C will necessarily differ in case [A, B] = [A, C] = 0, and [B, C] /= 0. We will show why this statement is not only improperly scrambling epistemic and formal perspectives, but is also physically and philosophically meaningless. Finally, we analyze the consequences of such widespread epistemic reading of KS theorem as related to statistical statements of measurement outcomes.

Authors: Akira MatsumuraTaishi IkedaShingo Kukita

When individual particles pass through a double slit, a fringe pattern appears on a screen. If an observer detects the path of the particle, the interference fringes disappear. This is called the quantum decoherence. In this paper, we discuss a parameter estimation problem using the quantum decohenrece in the double-slit experiment. As a simple model, we consider a massive scalar field interacting with the particle which have passed through the double slit. The scalar field, as well as the observer, can induce the loss of the fringe pattern of the particle. Because the interference fringes of the particle depend on the field mass and coupling, we can estimate the field parameters from the fringes. For qualitative analysis, we introduce the interferometric visibility of the fringe pattern and the Fisher information (FI) matrix of the field mass and coupling. Using the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the FI matrix. Also if we focus on FI of the mass, then we find that FI characterizes the wave-particle duality in the double-slit experiment.

Authors: Matteo Lugli

This work discloses some inconsistencies of quantum mechanics (QM) in two different contexts. On the one hand the equivalence principle in his two formulations is the starting point of all gravitational theories; yet there is no way to make it consistent with the non-relativistic formulation of QM. Moreover, the evaluation of the Schr\"odinger equation for a particle in an accelerated reference frame sheds light on a trajectory-dependent phase term subject to proper time. On the other hand, the Bargmann theorem unmistakably proves that the Schr\"odinger equation does not admit any superposition of different masses if the symmetry chosen for the system is the Galilean one. However, this is incompatible with relativity, since mass and energy are equivalent and one can certainly superimpose different energies. Both inconsistencies support the hypothesis that mass and proper time could be treated as variables. In the third chapter we will describe a theory in which the Galilean symmetry is extended by assuming particle mass and proper time as canonically conjugated classical variables, or conjugated observables in the quantum theory.

The first three chapters discuss subjects illustrated in several articles of the professor Daniel M. Greenberger, which are listed in the bibliography. Whereas in the last chapter the results of a recent theory on QW, say a discrete model for quantum particle evolution, will be examined. In particular, the striking result is that, in the most natural physical interpretation of QW dynamics, it is not possible to have a constant and invariant mass in any manner. The long term aim of this work is indeed to study the reasons and consequences of a theory of particles with variable mass in the context of wider studies still in progress on QW.

The Quantum Labyrinth is an interesting look at the working relationship between the “calm and elegant Wheeler” and the “flamboyant, excitable Feynman”, writes Philip Ball

Authors: H. Dieter Zeh

The role attributed to the observer in various interpretations of quantum mechanics as well as in classical statistical mechanics is discussed, with particular attention being paid to the Everett interpretation. In this context, the important difference between "quasi-classical" (robust against decoherence) and "macroscopic" or "physically given" (redundantly documented in the environment) is pointed out.

Authors: Mark Davidson

Complex space-time has proven useful in general relativity, and in Bohmian mechanics. Complexified Li\.enard-Wiechert potentials simplify the mathematics of Kerr-Newman particles. Here we constrain them to move along Bohmian trajectories. A covariant theory due to Stueckelberg is used. The trajectories typically become multi-valued. A tractable Gaussian wave is analyzed. A single trajectory is replaced by two trajectories on different Riemann sheets which are connected by analytical continuation in the world-time variable. An extension of analytic continuation that adds different Riemann sheets of a function together with complex weighting factors is applied. Whereas there are only two Bohmian trajectories connected by standard analytic continuation, there are an infinite number of trajectories that are connected by this generalized analytic continuation (GAN). Moreover, all the Bohmian trajectories can be derived from just a single one by applying GAN to it. This is suggestive of wave-particle duality. Maxwell's equations in complex space-time are different in that rather than a single retarded time solution contributing in a field calculation for a timelike trajectory in real space-time, there are multiple null roots. In the Bohmian case studied here there are an infinite number of retarded times associated with a single trajectory through the GAN continuation, and when one adds up their contribution weighted naturally by the Bohmian weighting factors, one finds the total radiated power goes to zero for a free particle. This is a major improvement over traditional Bohm models where even free charged particles would radiate if coupled classically. Thus a major point of this paper is to allow Bohmian particles to interact with classical electromagnetic fields without producing obviously unphysical effects. Some implications of these results are discussed.

A technique that combines machine learning and quantum computing has been used to identify the particles known as Higgs bosons. The method could find applications in many areas of science. See Letter p.375

Nature 550 339 doi: 10.1038/550339a

Authors: R. Srikanth

Quantum bit commitment (QBC) is insecure in the standard non-relativistic quantum cryptographic framework, essentially because Alice can exploit quantum steering to defer making her commitment. Two assumptions in this framework are that: (a) Alice knows the ensembles of evidence $E$ corresponding to either commitment; and (b) system $E$ is quantum rather than classical. Here, we show how relaxing assumption (a) or (b) can render her malicious steering operation indeterminable or inexistent, respectively. Finally, we present a secure protocol that relaxes both assumptions in a quantum teleportation setting. Without appeal to an ontological framework, we argue that the protocol's security entails the reality of the quantum state, provided retrocausality is excluded.

Authors: G. EngelhardtG. Schaller

The long-standing paradigm of Maxwell's demon is till nowadays a frequently investigated issue, which still provides interesting insights into basic physical questions. Considering a single-electron transistor, where we implement a Maxwell demon by a piecewise-constant feedback protocol, we investigate quantum implications of the Maxwell demon. To this end, we harness a dynamical coarse-graining method, which provides a convenient and accurate description of the system dynamics even for high measurement rates. In doing so, we are able to investigate the Maxwell demon in a quantum-Zeno regime leading to transport blockade. We argue that there is a measurement rate providing an optimal performance. Moreover, we find that besides building up a chemical gradient, there can be also a regime where additionally the system under consideration provides energy to the demon due to the quantum measurement.

Authors: Sam AltermanJaeho ChoiRebecca DurstSarah M. FlemingWilliam K. Wootters

In this paper we explore the following question: can the probabilities constituting the quantum Boltzmann distribution, $P^B_n \propto e^{-E_n/kT}$, be derived from a requirement that the quantum configuration-space distribution for a system in thermal equilibrium be very similar to the corresponding classical distribution? While it is certainly to be expected that the quantum distribution in configuration space will approach the classical distribution as the temperature approaches infinity, the high degree of agreement between the two distributions, even at modest temperatures, depends on a certain coordination between the shapes of the squares of the energy eigenfunctions (in the position representation) and the Boltzmann weights with which these functions are averaged in thermal equilibrium. We ask whether this agreement itself might provide an alternative way of generating the probabilities $P^B_n$. For two of the simple examples we consider--a particle in a one-dimensional box and a simple harmonic oscillator--this approach leads to probability distributions that provably approach the Boltzmann probabilities at high temperature, in the sense that the Kullback-Liebler divergence between the distributions approaches zero.

Authors: Michael D. MazurekMatthew F. PuseyKevin J. ReschRobert W. Spekkens

Many experiments in the field of quantum foundations seek to adjudicate between quantum theory and speculative alternatives to it. To do so, one must analyse the experimental data in a manner that does not presume the correctness of the quantum formalism. The mathematical framework of generalized probabilistic theories (GPTs) provides a means of doing so. We present a scheme for determining what GPTs are consistent with a given set of experimental data. It proceeds by performing tomography on the preparations and measurements in a self-consistent manner, i.e., without presuming a prior characterization of either. We illustrate the scheme by analyzing experimental data for a large set of preparations and measurements on the polarization degree of freedom of a single photon. We find that the smallest and largest GPT state spaces consistent with our data are a pair of polytopes, each approximating the shape of the Bloch Sphere and having a volume ratio of $0.977 \pm 0.001$, which provides a quantitative bound on the scope for deviations from quantum theory. We also demonstrate how our scheme can be used to bound the extent to which nature might be more nonlocal than quantum theory predicts, as well as the extent to which it might be more or less contextual. Specifically, we find that the maximal violation of the CHSH inequality can be at most $1.3\% \pm 0.1$ greater than the quantum prediction, and the maximal violation of a particular noncontextuality inequality can not differ from the quantum prediction by more than this factor on either side.

Publication date: 29 November 2017
Source:Physics Letters A, Volume 381, Issue 44
Author(s): Shovon Biswas
Bohr–van Leeuwen theorem has been studied in non-commutative space where the space coordinates do not commute. It has been found that in non-commutative space Bohr–van Leeuwen theorem, in general, is not satisfied and a classical treatment of the partition function of charged particles in a magnetic field gives rise to non zero magnetization.
Author: Anthony Duncan
ISBN: 9780198807650
Binding: Paperback
Publication Date: 17 October 2017
Price: $55.00

Authors: Gabriel R. BengocheaGabriel León

Within the framework of inflationary models that incorporate a spontaneous reduction of the wave function for the emergence of the seeds of cosmic structure, we study the effects on the primordial scalar power spectrum by choosing a novel initial quantum state that characterizes the perturbations of the inflaton. Specifically, we investigate under which conditions one can recover an essentially scale free spectrum of primordial inhomogeneities when the standard Bunch-Davies vacuum is replaced by another one that minimizes the renormalized stress-energy tensor via a Hadamard procedure. We think that this new prescription for selecting the vacuum state is better suited for the self-induced collapse proposal than the traditional one in the semiclassical gravity picture. We show that the parametrization for the time of collapse, considered in previous works, is maintained. Also, we obtain an angular spectrum for the CMB temperature anisotropies consistent with the one that best fits the observational data. Therefore, we conclude that the collapse mechanism might be of a more fundamental character than previously suspected.

Cuffaro, Michael E. (2017) Information Causality, the Tsirelson Bound, and the 'Being-Thus' of Things. [Preprint]

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