# Weekly Papers on Quantum Foundations (42)

This is a list of this week’s papers on quantum foundations published in the various journals or uploaded to the preprint servers such as arxiv.org and PhilSci Archive.

Inhomogeneities from quantum collapse scheme without inflation. (arXiv:1410.4212v1 [gr-qc])

on 2014-10-18 8:32am GMT

In this work, we consider the problem of the emergence of seeds of cosmic structure in the framework of the non-inflationary model proposed by Hollands and Wald. In particular, we consider a modification to that proposal designed to account for breaking the symmetries of the initial quantum state, leading to the generation of the primordial inhomogeneities. This new ingredient is described in terms of a spontaneous reduction of the wave function. We investigate under which conditions one can recover an essentially scale free spectrum of primordial inhomogeneities, and which are the dominant deviations that arise in the model as a consequence of the introduction of the collapse of the quantum state into that scenario.

Casimir effect in a quantum space-time. (arXiv:1410.4479v1 [gr-qc])

on 2014-10-18 8:32am GMT

We apply quantum field theory in quantum space-time techniques to study the Casimir effect for large spherical shells. As background we use the recently constructed exact quantum solution for spherically symmetric vacuum space-time in loop quantum gravity. All calculations are finite and one recovers the usual results without the need of regularization or renormalization. This is an example of how loop quantum gravity provides a natural resolution to the infinities of quantum field theories.

In Quantum Computing Speedup Illusory?: The False Coin of “Counting Function Evaluations”. (arXiv:1407.4345v2 [quant-ph] UPDATED)

on 2014-10-18 8:32am GMT

By using a new way to encode Boolean functions in a reversible gate, an algorithm is developed in quantum computing over Z_2, symbolized QC/2, (as opposed to QC over C) that needs only one function evaluation to solve the Grover Database Search Problem of finding a designated record among 2^m records for any m. In the usual Grover algorithm in quantum computing over C, one needs essentially Sqrt(2^m) function evaluations as opposed to the average of (2^m)/2 functions evaluations needed in the classical algorithm. The one function evaluation of the QC/2 algorithm (for any m) represents such a super speedup, even over the Grover algorithm in QC/C, that one feels something has gone awry. Indeed, our analysis of the transparent calculations of Boolean functions over Z_2 shows that the classical algorithm is just repackaged in a rather obvious way in the single function evaluation of the QC/2 algorithm–whereas the calculations are hidden and non-transparent in the Grover QC/C algorithm using C. The conclusion in both cases (which is rather obvious in the QC/2 case) is that “counting function evaluations” is a false coin to measure speedup in the comparison between quantum and classical computing.

Matrix-Product Operators and States: NP-Hardness and Undecidability

PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

on 2014-10-16 2:00pm GMT

Author(s): M. Kliesch, D. Gross, and J. Eisert

Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely correlated states or matrix-product operators, designed to capt…

[Phys. Rev. Lett. 113, 160503] Published Thu Oct 16, 2014

A possible correspondence between Ricci identities and Dirac equations in the Newman-Penrose formalism: towards an understanding of gravity induced collapse of the wave-function?. (arXiv:1403.2231v2 [gr-qc] UPDATED)

on 2014-10-16 3:27am GMT

It is well-known that in the Newman-Penrose formalism the Riemann tensor can be expressed as a set of eighteen complex first-order equations, in terms of the twelve spin coefficients, known as Ricci identities. The Ricci tensor herein is determined via the Einstein equations. It is also known that the Dirac equation in a curved spacetime can be written in the Newman-Penrose formalism as a set of four first-order coupled equations for the spinor components of the wave-function. In the present article we suggest that it might be possible to think of the Dirac equations in the N-P formalism as a special case of the Ricci identities, after an appropriate identification of the four Dirac spinor components with four of the spin coefficients, provided torsion is included in the connection, and after a suitable generalization of the energy-momentum tensor. We briefly comment on similarities with the Einstein-Cartan-Sciama-Kibble theory. The motivation for this study is to take some very preliminary steps towards developing a rigorous description of the hypothesis that dynamical collapse of the wave-function during a quantum measurement is caused by gravity.

Short-time quantum propagator and Bohmian trajectories

ScienceDirect Publication: Physics Letters A

on 2014-10-15 7:26pm GMT

Publication date: 6 December 2013
Source:Physics Letters A, Volume 377, Issue 42
Author(s): Maurice de Gosson , Basil Hiley
We begin by giving correct expressions for the short-time action following the work Makri–Miller. We use these estimates to derive an accurate expression modulo Δ t 2 for the quantum propagator and we show that the quantum potential is negligible modulo Δ t 2 for a point source, thus justifying an unfortunately largely ignored observation of Holland made twenty years ago. We finally prove that this implies that the quantum motion is classical for very short times.

Can the wave function in configuration space be replaced by single-particle wave functions in physical space?. (arXiv:1410.3676v1 [quant-ph])

on 2014-10-15 1:00am GMT

The ontology of Bohmian mechanics includes both the universal wave function (living in 3N-dimensional configuration space) and particles (living in ordinary 3-dimensional physical space). Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated — replaced by a set of single-particle pilot-wave fields living in ordinary physical space. Such a re-formulation of the Bohmian pilot-wave theory can exactly reproduce the statistical predictions of ordinary quantum theory. But this comes at the rather high ontological price of introducing an infinite network of interacting potential fields (living in 3-dimensional space) which influence the particles’ motion through the pilot-wave fields. We thus introduce an alternative approach which aims at achieving empirical adequacy (like that enjoyed by GRW type theories) with a more modest ontological complexity, and provide some preliminary evidence for optimism regarding the (once popular but prematurely-abandoned) program of trying to replace the (philosophically puzzling) configuration space wave function with a (totally unproblematic) set of fields in ordinary physical space.

Joint Measurability of Generalized Measurements Implies Classicality

PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

on 2014-10-14 2:00pm GMT

Author(s): Roope Uola, Tobias Moroder, and Otfried Gühne

The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and is responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements, quantum behavior can be characte…

[Phys. Rev. Lett. 113, 160403] Published Tue Oct 14, 2014

Solvable Models on Noncommutative Spaces with Minimal Length Uncertainty Relations. (arXiv:1410.3193v1 [hep-th])

on 2014-10-14 2:01am GMT

Our main focus is to explore different models in noncommutative spaces in higher dimensions. We provide a procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing non-commutative spaces. The representations for the corresponding operators obey algebras whose uncertainty relations lead to minimal length, areas and volumes in phase space, which are in principle natural candidates of many different approaches of quantum gravity. We study some explicit models on these types of noncommutative spaces, first by utilising the perturbation theory, later in an exact manner. In many cases the operators are not Hermitian, therefore we use PT -symmetry and pseudo-Hermiticity property, wherever applicable, to make them self-consistent. Apart from building mathematical models, we focus on the physical implications of noncommutative theories too. We construct Klauder coherent states for the perturbative and nonperturbative noncommutative harmonic oscillator associated with uncertainty relations implying minimal lengths. In both cases, the uncertainty relations for the constructed states are shown to be saturated and thus imply to the squeezed coherent states. They are also shown to satisfy the Ehrenfest theorem dictating the classical like nature of the coherent wavepacket. The quality of those states are further underpinned by the fractional revival structure. More investigations into the comparison are carried out by a qualitative comparison between the dynamics of the classical particle and that of the coherent states based on numerical techniques. The qualitative behaviour is found to be governed by the Mandel parameter determining the regime in which the wavefunctions evolve as soliton like structures.

Unitary Inequivalent Representations in Quantum Physics. (arXiv:1312.3239v2 [quant-ph] UPDATED)

on 2014-10-14 2:01am GMT

First the existence of different unitary inequivalent representations in the Quantum Field Theory(QFT) is discussed. Then it is shown that how they can play a major role for us to understand some phenomena such as Hawking effect.

Generalized von Neumann measurement with Hermite-Gaussian and Laguerre-Gaussian pointer states. (arXiv:1410.3189v1 [quant-ph])

on 2014-10-14 2:01am GMT

Using post-selection followed by von Neumann interaction, we can extract not only an eigenvalue of an observable on the measured system but also an off-diagonal element of the observable such as the weak value. In this generalized von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaussian wave function. Considering the optical implementation of the generalized von Neumann measurement, higher-order Gaussian modes can be used. In this paper, we consider the Hermite-Gaussian (HG) and the Laguerre-Gaussian (LG) modes as pointer states. We calculate the average shift of the pointer states of the generalized von Neumann measurement assuming the system observable $\hat{A}$ with $\hat{A}^{2}=\hat{I}$ and $\hat{A}^{2}=\hat{A}$ for an arbitrary interaction strength, where $\hat{I}$ represents the identity operator. Our results show that the HG and LG pointer states for a given coupling direction have no advantages over the fundamental Gaussian mode for improving the signal-to-noise ratio (SNR). However, because the LG pointer state is not factorized in the two-dimensional plane, the pointer state can be shifted orthogonally along the coupling direction. In the weak coupling regime, we find that the SNR for this orthogonal direction can be drastically improved by increasing the azimuthal indices $l$ in the $\hat{A}^{2}=\hat{A}$ case; however, the SNR has an upper bound in the $\hat{A}^{2}=\hat{I}$ case.

Quantization as a Guide to Ontic Structure

The British Journal for the Philosophy of Science – Advance Access

on 2014-10-13 12:58pm GMT

The ontic structural realist stance is motivated by a desire to do philosophical justice to the success of science, whilst withstanding the metaphysical undermining generated by the various species of ontological underdetermination. We are, however, as yet in want of general principles to provide a scaffold for the explicit construction of structural ontologies. Here we will attempt to bridge this gap by utilizing the formal procedure of quantization as a guide to ontic structure of modern physical theory. The example of non-relativistic particle mechanics will be considered and, for that case, it will be shown that a viable candidate for an ontic structural realism framework can be constituted in terms of the combination of a state-space with Poisson bracket structure, and a set of observables, with Lie algebra structure.

• 1 Introduction
• 2 Formulation Underdetermination and Structural Ontologies
• 3 Quantization and Structural Ontologies
• 4 The Case of Non-relativistic Particle Mechanics
•   4.1 Formulation underdetermination
•   4.2 The classical ontology
•   4.3 Quantum theory and the generalized structural ontology
•   4.4 Interpretation of results
• 5 Conclusion and Prospects

Treating Time Travel Quantum Mechanically. (arXiv:1401.4933v3 [quant-ph] UPDATED)

on 2014-10-13 2:50am GMT

The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and “postselected” CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the “equivalent circuit model”—which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory—is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of “transition probability” CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features—such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states—that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.

Bell’s inequality and extremal nonlocal box from Hardy’s test for nonlocality. (arXiv:1403.0790v2 [quant-ph] UPDATED)

on 2014-10-13 2:50am GMT

Bell showed 50 years ago that quantum theory is nonlocal via his celebrated inequalities, turning the issue of quantum nonlocality from a matter of taste into a matter of test. Years later, Hardy proposed a test for nonlocality without inequality, which is a kind of “something-versus-nothing” argument. Hardy’s test for $n$ particles induces an $n$-partite Bell’s inequality with two dichotomic local measurements for each observer, which has been shown to be violated by all entangled pure states. Our first result is to show that the Bell-Hardy inequality arising form Hardy’s nonlocality test is tight for an arbitrary number of parties, i.e., it defines a facet of the Bell polytope in the given scenario. On the other hand quantum theory is not that nonlocal since it forbids signaling and even not as nonlocal as allowed by non-signaling conditions, i.e., quantum mechanical predictions form a strict subset of the so called non-signaling polytope. In the scenario of each observer measuring two dichotomic observables, Fritz established a duality between the Bell polytope and the non-signaling polytope: tight Bell’s inequalities, the facets of the Bell polytope, are in a one-to-one correspondence with extremal non-signaling boxes, the vertices of the non-signaling polytope. Our second result is to provide an alternative and more direct formula for this duality. As an example, the tight Bell-Hardy inequality gives rise to an extremal non-signaling box that serves as a natural multipartite generalization of Popescu-Rohrlich box.

Physical Properties as Modal Operators in the Topos Approach to Quantum Mechanics

Latest Results for Foundations of Physics

on 2014-10-12 12:00am GMT

Abstract

In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.