# Weekly Papers on Quantum Foundations (49)

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.

Convergence of empirical distributions in an interpretation of quantum mechanics. (arXiv:1412.1563v1 [quant-ph])

on 2014-12-05 11:44am GMT

Authors: Ian W. McKeagueBruce Levin

From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the interaction of finitely many classical “worlds.” The wave function is then recovered (as a secondary object) from observations of particles in these worlds, without knowing the world from which any particular observation originates. Hall, Deckert and Wiseman [Physical Review X 4 (2014) 041013] have introduced an explicit many-interacting-worlds harmonic oscillator model to provide support for this approach. In this note we provide a proof of their claim that the particle configuration is asymptotically Gaussian, thus matching the ground-state solution of Schrodinger’s equation when the number of worlds goes to infinity.

John Bell’s varying interpretations of quantum mechanics. (arXiv:1402.5498v7 [quant-ph] UPDATED)

on 2014-12-05 11:44am GMT

Authors: H. Dieter Zeh

Various interpretations of quantum mechanics, favored (or neglected) by John Bell in the context of his non-locality theorem, are compared and discussed.

Communication complexity and the reality of the wave-function. (arXiv:1412.1723v1 [quant-ph])

on 2014-12-05 11:44am GMT

Authors: Alberto Montina

In this review, we discuss a relation between quantum communication complexity and a long-standing debate in quantum foundation concerning the interpretation of the quantum state. Is the quantum state a physical element of reality as originally interpreted by Schrodinger? Or is it an abstract mathematical object containing statistical information about the outcome of measurements as interpreted by Born? Although these questions sound philosophical and pointless, they can be made precise in the framework of what we call classical theories of quantum processes, which are a reword of quantum phenomena in the language of classical probability theory. In 2012, Pusey, Barrett and Rudolph (PBR) proved, under an assumption of preparation independence, a theorem supporting the original interpretation of Schrodinger in the classical framework. Recently, we showed that these questions are related to a practical problem in quantum communication complexity, namely, quantifying the minimal amount of classical communication required in the classical simulation of a two-party quantum communication process. In particular, we argued that the statement of the PBR theorem can be proved if the classical communication cost of simulating the communication of n qubits grows more than exponentially in ‘n’. Our argument is based on an assumption that we call probability equipartition property. This property is somehow weaker than the preparation independence property used in the PBR theorem, as the former can be justified by the latter and the asymptotic equipartition property of independent stochastic sources. The equipartition property is a general and natural hypothesis that can be assumed even if the preparation independence hypothesis is dropped. In this review, we further develop our argument into the form of a theorem.

Superselection rule for the cosmological constant in three-dimensional spacetime. (arXiv:1412.1492v1 [hep-th])

on 2014-12-05 11:41am GMT

Authors: Claudio BunsterAlfredo Perez

Efforts to understand the origin of the cosmological constant {\Lambda} and its observed value have led to consider it as a dynamical field rather than as a universal constant. Then the possibility arises that the universe, or regions of it, might be in a superposition of quantum states with different values of {\Lambda}, so that its actual value would not be definite. There appears to be no argument to rule out this possibility for a generic spacetime dimension D. However, as proved herein, for D=3 there exists a superselection rule that forbids such superpositions. The proof is based on the asymptotic symmetry algebra.

Local hidden variable models for entangled quantum states using finite shared randomness. (arXiv:1412.1416v1 [quant-ph])

on 2014-12-04 9:15am GMT

The statistics of local measurements performed on certain entangled states can be reproduced using a local hidden variable (LHV) model. While all known models make use of an infinite amount of shared randomness—the physical relevance of which is questionable—we show that essentially all entangled states admitting a LHV model can be simulated with finite shared randomness. Our most economical model simulates noisy two-qubit Werner states using only 3.58 bits of shared randomness. We also discuss the case of POVMs, and the simulation of nonlocal states with finite shared randomness and finite communication. Our work represents a first step towards quantifying the cost of LHV models for entangled quantum states.

An Evolutionary Formalism for Weak Quantum Measurements. (arXiv:1412.1312v1 [quant-ph])

on 2014-12-04 9:15am GMT

Authors: Apoorva PatelParveen Kumar

Unitary evolution and projective measurement are fundamental axioms of quantum mechanics. Even though projective measurement yields one of the eigenstates of the measured operator as the outcome, there is no theory that predicts which eigenstate will be observed in which experimental run. There exists only an ensemble description, which predicts probabilities of various outcomes over many experimental runs. We propose a dynamical evolution equation for the projective collapse of the quantum state in individual experimental runs, which is consistent with the well-established framework of quantum mechanics. In case of gradual weak measurements, its predictions for ensemble evolution are different from those of the Born rule. It is an open question whether or not suitably designed experiments can observe this alternate evolution.

The informationally-complete quantum theory. (arXiv:1412.1079v1 [quant-ph])

on 2014-12-04 9:15am GMT

Authors: Zeng-Bing Chen

Quantum mechanics is a cornerstone of our current understanding of nature and extremely successful in describing physics covering a huge range of scales. However, its interpretation remains controversial for a long time, from the early days of quantum mechanics to nowadays. What does a quantum state really mean? Is there any way out of the so-called quantum measurement problem? Here we present an informationally-complete quantum theory (ICQT) and the trinary property of nature to beat the above problems. We assume that a quantum system’s state provides an informationally-complete description of the system in the trinary picture. We give a consistent formalism of quantum theory that makes the informational completeness explicitly and argue that the conventional quantum mechanics is an approximation of the ICQT. We then show how our ICQT provides a coherent picture and fresh angle of some existing problems in physics. The computational content of our theory is uncovered by defining an informationally-complete quantum computer.

The Casimir effect from the point of view of algebraic quantum field theory. (arXiv:1412.1409v1 [math-ph])

on 2014-12-04 9:13am GMT

We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize these two systems within the algebraic approach to quantum field theory using the so-called functional formalism. As a first step we construct a suitable unital *-algebra of observables whose generating functionals are characterized by a labeling space which is at the same time optimal and separating. Subsequently we give a definition for these systems of Hadamard states and we investigate explicit examples. In the case of a single plate, it turns out that one can build algebraic states via a pull-back of those on the whole Minkowski spacetime, moreover inheriting from them the Hadamard property. When we consider instead two plates, algebraic states can be put in correspondence with those on flat spacetime via the so-called method of images, which we translate to the algebraic setting. For a massless scalar field we show that this procedure works perfectly for a large class of quasi-free states including the Poincar\’e vacuum and KMS states. Eventually we use our results in both systems to introduce the notion of Wick polynomials, showing that a global extended algebra does not exist. Furthermore we construct explicitly the two-point function and the regularized energy density, showing, moreover, that the outcome is consistent with the standard results of the Casimir effect.

Theory-independent limits on correlations from generalised Bayesian networks. (arXiv:1405.2572v2 [quant-ph] UPDATED)

on 2014-12-03 10:16am GMT

Authors: Joe HensonRaymond LalMatthew F. Pusey

Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities. Inspired by this connection, we generalise the formalism of classical Bayesian networks in order to investigate non-classical correlations in arbitrary causal structures. Our framework of generalised Bayesian networks’ replaces latent variables with the resources of any generalised probabilistic theory, most importantly quantum theory, but also, for example, Popescu-Rohrlich boxes. We obtain three main sets of results. Firstly, we prove that all of the observable conditional independences required by the classical theory also hold in our generalisation; to obtain this, we extend the classical $d$-separation theorem to our setting. Secondly, we find that the theory-independent constraints on probabilities can go beyond these conditional independences. For example we find that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes. Finally, we begin a classification of those causal structures, such as the Bell scenario, that may yield a separation between classical, quantum and general-probabilistic correlations.

Quantum Trajectories based on the Weak Value. (arXiv:1412.0916v1 [quant-ph])

on 2014-12-03 10:16am GMT

Authors: Takuya MoriIzumi Tsutsui

The notion of trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any quantum observable, can offer a possible description of trajectory on account of its statistical nature of the value. In this paper, we explore the physical significance provided by this weak trajectory by considering various situations where interference takes place simultaneously with the observation of particles, that is, in prototypical quantum situations for which no classical treatment is available. These include the double slit experiment and Lloyd’s mirror, where in the former case it is argued that the real part of the weak trajectory describes an average over the possible classical trajectories involved in the process, and that the imaginary part is related to the variation of interference. It is shown that this average interpretation of the weak trajectory holds universally under the complex probability defined from the given transition process. These features remain essentially unaltered in the case of Lloyd’s mirror where interference occurs with a single slit.

Reality of the Quantum State: A Stronger Psi-ontology Theorem. (arXiv:1412.0669v1 [quant-ph])

on 2014-12-03 10:16am GMT

Authors: Shane Mansfield

The Pusey-Barrett-Rudolph no-go theorem provides an argument for the reality of the quantum state based on certain assumptions, most of which are common to the familiar no-go theorems of Bell, Kochen & Specker, etc. The exception is their assumption of preparation independence, which has been subject to a number of criticisms. We propose a much weaker, physically motivated notion of independence, which merely prohibits the possibility of super-luminal causal influences in the preparation process. This is a minimum requirement for maintaining a reasonable notion of subsystem. Under the weaker assumption, it is shown that the argument of PBR becomes invalid. We propose an experiment involving randomly sampled preparations that realises an approximation of the result, which becomes exact in the limit as the sample space of preparations becomes infinite, thereby proving a stronger theorem asserting the reality of the quantum state. The theorem holds even if there are non-local correlations in the global ontic state. Conceptually, it shows that the degree to which the quantum state may be statistical is limited by the degree to which (sub)systems may be composed.

Physics: Quantum computer quest

Nature – Issue – nature.com science feeds

on 2014-12-03 12:00am GMT

Physics: Quantum computer quest

Nature 516, 7529 (2014). http://www.nature.com/doifinder/10.1038/516024a

Author: Elizabeth Gibney

After a 30-year struggle to harness quantum weirdness for computing, physicists finally have their goal in reach.

Derivation of the Dirac equation from principles of information processing

PRA: Fundamental concepts

on 2014-12-02 3:00pm GMT

Author(s): Giacomo Mauro D’Ariano and Paolo Perinotti

Without using the relativity principle, we show how the Dirac equation in three space dimensions emerges from the large-scale dynamics of the minimal nontrivial quantum cellular automaton satisfying unitarity, locality, homogeneity, and discrete isotropy. The Dirac equation is recovered for small wa…

[Phys. Rev. A 90, 062106] Published Tue Dec 02, 2014

Does it Make Sense to Speak of Self-Locating Uncertainty in the Universal Wave Function? Remarks on Sebens and Carroll. (arXiv:1408.1944v3 [gr-qc] UPDATED)

on 2014-12-02 12:32pm GMT

Authors: Adrian Kent (Centre for Quantum Information and Foundations, DAMTP, University of Cambridge, Perimeter Institute)

Following a proposal of Vaidman, Sebens and Carroll have argued that in Everettian (i.e. purely unitary) quantum theory, observers are uncertain, before they complete their observation, about which Everettian branch they are on. They argue further that this solves the problem of making sense of probabilities within Everettian quantum theory, even though the theory itself is deterministic. We note some problems with these arguments.

Newton-Wigner position operator and its corresponding spin operator in relativistic quantum mechanics. (arXiv:1412.0351v1 [quant-ph])

on 2014-12-02 12:32pm GMT

Authors: Taeseung Choi

A relativistic spin operator is to be the difference between the total and orbital angular momentum. As the unique position operator for a localized state, the remarkable Newton-Wigner position operator, which has all desirable commutation relations as a position operator, can give a proper spin operator. Historically important three spin operators respectively proposed by Bogolubov et al., Pryce, and Foldy-Woutheysen are investigated to manifest a corresponding spin operator to the Newton-Wigner position operator. We clarify a unique spin operator in relativistic quantum mechanics described by the Dirac Hamiltonian.

Some Personal Reflections on Quantum Non-locality and the Contributions of John Bell. (arXiv:1412.0594v1 [physics.hist-ph])

on 2014-12-02 12:32pm GMT

Authors: B. J. Hiley

I present the background of the Bohm approach that led John Bell to a study of quantum non-locality from which his famous inequalities emerged. I recall the early experiments done at Birkbeck with an aim to explore the possibility of spontaneous collapse’, a way suggested by Schr\”{o}dinger to avoid the conclusion that quantum mechanics was grossly non-local. I also review some of the work that John did which directly impinged on my own investigations into the foundations of quantum mechanics and report some new investigations towards a more fundamental theory.

Derivation of the Born rule from the unitarity of quantum evolution. (arXiv:1411.6992v2 [quant-ph] UPDATED)

on 2014-12-02 12:31pm GMT

Authors: G.B. Lesovik

In order to make the quantum mechanics a closed theory one has to derive the Born rule from the first principles, like the Schroedinger equation, rather than postulate it. The Born rule was in certain sense derived in several articles, e.g. in [D. Deutsch, Proc. R. Soc. Lond. A455, 3129 (1999)] and [W. H. Zurek, Phys. Rev. Lett. 90, 120404 (2003)]. In this work some arguments of previous authors are simplified and made more “physical”. It is shown how to derive the Born rule using the conservation of quantum state norm $\langle\Psi|\Psi\rangle$ that is the unitary evolution property determined by the Schroedinger equation. It is this property that makes the probability equal to the square of the amplitude modulus. We also present arguments in the spirit of the Many-World Interpretation to explain the origin of probabilistic behavior. Simply speaking, the randomness appears as a result of representing the wave function by using a detector of discrete nature that is found only in one state at a time, out of two or more possible states.

Leggett-Garg Inequalities, Pilot Waves and Contextuality. (arXiv:1409.4104v2 [quant-ph] UPDATED)

on 2014-12-02 12:31pm GMT

Authors: Guido Bacciagaluppi

In this paper we first analyse Leggett and Garg’s argument to the effect that macroscopic realism contradicts quantum mechanics. After making explicit all the assumptions in Leggett and Garg’s reasoning, we argue against the plausibility of their auxiliary assumption of non-invasive measurability, using Bell’s construction of stochastic pilot-wave theories as a counterexample. Violations of the Leggett-Garg inequality thus do not provide a good argument against macrorealism per se. We then apply Dzhafarov and Kujala’s analysis of contextuality in the presence of signalling to the case of the Leggett-Garg inequalities, with rather surprising results. An analogy with pilot-wave theory again helps to clarify the situation.

Quantum Mechanics and Quantum Information Science: The Nature of $\Psi$. (arXiv:1412.0192v1 [quant-ph])

on 2014-12-02 12:31pm GMT

Authors: Partha Ghose

An overview is given of the nature of the quantum mechanical wave function.

Logical Entropy for Quantum States. (arXiv:1412.0616v1 [quant-ph])

on 2014-12-02 12:31pm GMT

Authors: Boaz TamirEliahu Cohen

The novel concept of quantum logical entropy is presented. We prove several basic properties of this entropy with regard to density matrices. The properties are similar to those of the familiar von Neumann entropy, but it turns out that some of the proofs are easier using logical entropy. We thereby motivate a different approach for the assignment of quantum entropy to density matrices.

A solution to the problem of time. (arXiv:1411.8006v1 [gr-qc])

on 2014-12-01 4:46am GMT

Authors: Benjamin Shlaer

Despite the severe ultraviolet problems with quantum gravity, infrared phenomena such as eternal inflation and black hole evaporation should enjoy fully quantum mechanical unitary time evolution. Currently this is not possible, the impediment being what is known as the problem of time. Here, we provide a solution by promoting the cosmological constant \Lambda to a Lagrange multiplier constraining the metric volume element to be manifestly a total derivative. Because \Lambda appears linearly in the Hamiltonian constraint, it unitarily generates time evolution, yielding a functional Schroedinger equation for gravity. Two pleasant side effects of this construction are that vacuum energy is completely sequestered from the cosmological constant problem, much like in unimodular gravity, and the natural foliation provided by the time variable defines a sensible solution to the measure problem.

Bohm’s approach and Individuality. (arXiv:1405.4772v3 [quant-ph] UPDATED)

on 2014-12-01 4:46am GMT

Authors: P. PylkkänenB. J. HileyI. Pättiniemi

Ladyman and Ross (LR) argue that quantum objects are not individuals (or are at most weakly discernible individuals) and use this idea to ground their metaphysical view, ontic structural realism, according to which relational structures are primary to things. LR acknowledge that there is a version of quantum theory, namely the Bohm theory (BT), according to which particles do have definite trajectories at all times. However, LR interpret the research by Brown {\em et al.} as implying that “raw stuff” or {\em haecceities} are needed for the individuality of particles of BT, and LR dismiss this as idle metaphysics. In this paper we note that Brown {\em et al.}’s research does not imply that {\em haecceities} are needed. Thus BT remains as a genuine option for those who seek to understand quantum particles as individuals. However, we go on to discuss some problems with BT which led Bohm and Hiley to modify it. This modified version underlines that, due to features such as context-dependence and non-locality, Bohmian particles have a very limited autonomy in situations where quantum effects are non-negligible. So while BT restores the possibility of quantum individuals, it also underlines the primacy of the whole over the autonomy of the parts. The later sections of the paper also examine the Bohm theory in the general mathematical context of symplectic geometry. This provides yet another way of understanding the subtle, holistic and dynamic nature of Bohmian individuals. We finally briefly consider Bohm’s other main line of research, the “implicate order”, which is in some ways similar to LR’s structural realism.

The physics and metaphysics of primitive stuff. (arXiv:1411.7545v1 [physics.hist-ph])

on 2014-12-01 4:46am GMT

The paper sets out a primitive ontology of the natural world in terms of primitive stuff, that is, stuff that has as such no physical properties at all, but that is not a bare substratum either, being individuated by metrical relations. We focus on quantum physics and employ identity-based Bohmian mechanics to illustrate this view, but point out that it applies all over physics. Properties then enter into the picture exclusively through the role that they play for the dynamics of the primitive stuff. We show that such properties can be local (classical mechanics), as well as holistic (quantum mechanics), and discuss two metaphysical options to conceive them, namely Humeanism and modal realism in the guise of dispositionalism.

Quantum Gravity models – brief conceptual summary. (arXiv:1404.6797v2 [hep-th] UPDATED)

on 2014-12-01 4:46am GMT

Authors: Jerzy Lukierski

After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We present briefly three proposals: loop quantum gravity (LQG), the field-theoretic framework on noncommutative space-time and QG models formulated on discretized (triangularized) space-time. We evaluate these models as realizing expected important properties of QG: background independence, consistent quantum diffeomorphisms, noncommutative or discrete structure of space-time at very short distances, finite/renormalizable QG corrections. We only briefly outline an important issue of embedding QG into larger geometric and dynamical frameworks (e.g. supergravity, (super)strings, p-branes, M-theory), with the aim to achieve full unification of all fundamental interactions.

A measure of physical reality. (arXiv:1411.7811v1 [quant-ph])