Weekly Papers on Quantum Foundations (35)

Authors: Xiao-Kan Guo

We study the $S$-matrix interpretation of quantum theory in light of Categotical Quantum Mechanics. The $S$-matrix interpretation of quantum theory is shown to be a functorial semantics relating the algebras of quantum theory to the effective $S$-matrix formalism. Consequently, issues such as state reduction and entanglement generation can be depicted in a simple manner. Moreover, this categorical $S$-matrix interpretation does not have the alleged thermodynamic cost.

Publication date: Available online 31 August 2017
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Author(s): Tomasz Bigaj
One of the key philosophical questions regarding quantum field theory is whether it should be given a particle or field interpretation. The particle interpretation of QFT is commonly viewed as being undermined by the well-known no-go results, such as the Malament, Reeh-Schlieder and Hegerfeldt theorems. These theorems all focus on the localizability problem within the relativistic framework. In this paper I would like to go back to the basics and ask the simple-minded question of how the notion of quanta appears in the standard procedure of field quantization, starting with the elementary case of the finite numbers of harmonic oscillators, and proceeding to the more realistic scenario of continuous fields with infinitely many degrees of freedom. I will try to argue that the way the standard formalism introduces the talk of field quanta does not justify treating them as particle-like objects with well-defined properties.

Author(s): Borivoje Dakić and Milan Radonjić

We study the question of what kind of a macroscopic superposition can(not) naturally exist as a ground state of some gapped local many-body Hamiltonian. We derive an upper bound on the energy gap of an arbitrary physical Hamiltonian provided that its ground state is a superposition of two well-disti...
[Phys. Rev. Lett. 119, 090401] Published Fri Sep 01, 2017

Author(s): Patrick P. Hofer, Jonatan Bohr Brask, Martí Perarnau-Llobet, and Nicolas Brunner

We propose the use of a quantum thermal machine for low-temperature thermometry. A hot thermal reservoir coupled to the machine allows for simultaneously cooling the sample while determining its temperature without knowing the model-dependent coupling constants. In its most simple form, the proposed...
[Phys. Rev. Lett. 119, 090603] Published Fri Sep 01, 2017

Abstract

Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity (QG), where novel empirical data is lacking. One principle widely adopted in the search for QG is UV completion: the idea that a theory should (formally) hold up to all possible high energies. We arguecontra standard scientific practicethat UVcompletion is poorly-motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we explore the reasons for expecting, or desiring, a UV-complete theory, as well as analyse how UV completion is used, and how it should be used, in various specific approaches to QG.

Abstract

We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being iA_{\mu } rather than A_{\mu } itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.

Abstract

As expressed in terms of classical coordinates, the inertial spacetime metric that contains quantum corrections deriving from a quantum potential defined from the quantum probability amplitude is obtained to be given as an elliptic integral of the second kind that does not satisfy Lorentz transformations but a generalised invariance quantum group. Based on this result, we introduce a new, alternative procedure to quantise Einstein general relativity where the metric is also given in terms of elliptic integrals and is free from the customary problems of the current quantum models. We apply the procedure to Schwarzschild black holes and briefly analyse the results.

Authors: Benito A. Juárez-AubryBernard S. KayDaniel Sudarsky

We recall and review earlier work on dynamical reduction models, both non-relativistic and relativistic, and discuss how they may relate to suggestions which have been made (including the matter-gravity entanglement hypothesis of one of us) for how quantum gravity could be connected to the resolution of the quantum-mechanical measurement problem. We then provide general guidelines for generalizing dynamical reduction models to curved spacetimes and propose a class of generally covariant relativistic versions of the GRW model. We anticipate that the collapse operators of our class of models may play a r\^ole in a yet-to-be-formulated theory of semiclassical gravity with collapses. We show explicitly that the collapse operators map a dense domain of states that are initially Hadamard to final Hadamard states -- a property that we expect will be needed for the construction of such a semiclassical theory. Finally, we provide a simple example in which we explicitly compute the violations in energy-momentum due to the state reduction process and conclude that this violation is of the order of a parameter of the model -- supposed to be small. We briefly discuss how this work may, upon further development of a suitable semiclassical gravity theory with collapses, enable further progress to be made on earlier work one of us and collaborators on the explanation of structure-formation in a homogeneous and isotropic quantum universe and on a possible resolution of the black hole information loss puzzle.

Szabo, Laszlo E. (2017) Meaning, Truth, and Physics. In G. Hofer-Szabó, L. Wronski (eds.) Making it Formally Explicit.
Cuffaro, Michael E. (2017) Information Causality, the Tsirelson Bound, and the 'Being-Thus' of Things. [Preprint]
Sam, Baron (2017) Mathematical Explanation by Law. The British Journal for the Philosophy of Science.

Authors: Dale Hodgson

We consider typical experiments that use Bell-inequalities to test local-realist theories of quantum mechanics and gain insight into how certain results can be obtained. We see that results against local-realism arise from some `quantum skew' of the correlation between entangled qubit pairs. Furthermore, we find some conditions necessary for a conclusion against local-realism. Finally we show that the problem of `no-signalling' that arises in these experiments cannot be reduced to arbitrary experimental accuracy.

Author(s): Holger F. Hofmann

Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit ...
[Phys. Rev. A 96, 020101(R)] Published Mon Aug 28, 2017

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.

Authors: Alastair A. AbbottJulian WechsFabio CostaCyril Branciard

The study of correlations with no definite causal order has revealed a rich structure emerging when more than two parties are involved. This motivates the consideration of multipartite "noncausal" correlations that cannot be realised even if noncausal resources are made available to a smaller number of parties. Here we formalise this notion: genuinely N-partite noncausal correlations are those that cannot be produced by grouping N parties into two or more subsets, where a causal order between the subsets exists. We prove that such correlations can be characterised as lying outside a polytope, whose vertices correspond to deterministic strategies and whose facets define what we call "2-causal" inequalities. We show that genuinely multipartite noncausal correlations arise within the process matrix formalism, where quantum mechanics holds locally but no global causal structure is assumed, although for some inequalities no violation was found. We further introduce two refined definitions that allow one to quantify, in different ways, to what extent noncausal correlations correspond to a genuinely multipartite resource.

Authors: Anirudh DasarthyJoshua P. IsaacsonKatherine Jones-SmithJason TabachnikHarsh Mathur

In PT quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time reversal. Here we study the role of boundary conditions in PT quantum mechanics by constructing a simple model that is the PT symmetric analog of a particle in a box. The model has the usual particle in a box Hamiltonian but boundary conditions that respect PT symmetry rather than hermiticity. We find that for a broad class of PT-symmetric boundary conditions the model respects the condition of unbroken PT-symmetry, namely that the Hamiltonian and the symmetry operator PT have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is self-adjoint under the PT inner product. Thus we obtain a simple soluble model that fulfils all the requirements of PT quantum mechanics. In the second part of this paper we formulate a variational principle for PT quantum mechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the PT-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a Breit-Wigner lineshape in transmission and a Fano lineshape in reflection; by contrast in the corresponding hermitian case the lineshapes always have a Breit-Wigner form in both transmission and reflection.

Publication date: 25 September 2017
Source:Physics Letters A, Volume 381, Issue 36
Author(s): Maurice A. de Gosson
Recent cosmological measurements tend to confirm that the fine structure constant α is not immutable and has undergone a tiny variation since the Big Bang. Choosing adequate units, this could also reflect a variation of Planck's constant h. The aim of this Letter is to explore some consequences of such a possible change of h for the pure and mixed states of quantum mechanics. Surprisingly enough it is found that not only is the purity of a state extremely sensitive to such changes, but that quantum states can evolve into classical states, and vice versa. A complete classification of such transitions is however not possible for the moment being because of yet unsolved mathematical difficulties related to the study of positivity properties of trace class operators.

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