# Weekly Papers on Quantum Foundations (1)

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.

A formal framework for the study of the notion of undefined particle number in quantum mechanics

Latest Results for Synthese

on 2015-2-01 12:00am GMT

Abstract

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions.

Dissipative extension of the Ghirardi-Rimini-Weber model

PRA: Fundamental concepts

on 2014-12-31 3:00pm GMT

Author(s): Andrea Smirne, Bassano Vacchini, and Angelo Bassi

In this paper, we present an extension of the Ghirardi-Rimini-Weber model for the spontaneous collapse of the wave function. Through the inclusion of dissipation, we avoid the divergence of the energy on the long-time scale, which affects the original model. In particular, we define jump operators, …

[Phys. Rev. A 90, 062135] Published Wed Dec 31, 2014

Stationary and uniformly accelerated states in nonlinear quantum mechanics

PRA: Fundamental concepts

on 2014-12-31 3:00pm GMT

Author(s): A. R. Plastino, A. M. C. Souza, F. D. Nobre, and C. Tsallis

We consider two kinds of solutions of a recently proposed field theory leading to a nonlinear Schrödinger equation exhibiting solitonlike solutions of the power-law form eqi(kx−wt), involving the q exponential function naturally arising within nonextensive thermostatistics [eqz≡[1+(1−q)z]1/(1−q), wi…

[Phys. Rev. A 90, 062134] Published Wed Dec 31, 2014

Implications of a deeper level explanation of the deBroglie-Bohm version of quantum mechanics. (arXiv:1412.8349v1 [quant-ph])

quant-ph updates on arXiv.org

on 2014-12-30 12:43pm GMT

Elements of a “deeper level” explanation of the deBroglie-Bohm (dBB) version of quantum mechanics are presented. Our explanation is based on an analogy of quantum wave-particle duality with bouncing droplets in an oscillating medium, the latter being identified as the vacuum’s zero-point field. A hydrodynamic analogy of a similar type has recently come under criticism by Richardson et al., because despite striking similarities at a phenomenological level the governing equations related to the force on the particle are evidently different for the hydrodynamic and the quantum descriptions, respectively. However, said differences are not relevant if a radically different use of said analogy is being made, thereby essentially referring to emergent processes in our model. If the latter are taken into account, one can show that the forces on the particles are identical in both the dBB and our model. In particular, this identity results from an exact matching of our emergent velocity field with the Bohmian “guiding equation”. One thus arrives at an explanation involving a deeper, i.e. subquantum, level of the dBB version of quantum mechanics. We show in particular how the classically-local approach of the usual hydrodynamical modeling can be overcome and how, as a consequence, the configuration-space version of dBB theory for $N$ particles can be completely substituted by a “superclassical” emergent dynamics of $N$ particles in real 3-dimensional space.

An operational approach to spacetime symmetries: Lorentz transformations from quantum communication. (arXiv:1412.8462v1 [quant-ph])

quant-ph updates on arXiv.org

on 2014-12-30 12:43pm GMT

Authors: Philipp A HoehnMarkus P Mueller

In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum gravity, which are seen as fundamental principles to which the final theory has to be adjusted. In this paper, we suggest within a much simpler setting that this kind of reasoning can actually be reversed, by taking an operational approach inspired by quantum information theory. We consider observers in distant laboratories, with local physics described by the laws of abstract quantum theory, and without presupposing a particular spacetime structure. We ask what information-theoretic effort the observers have to spend to synchronize their descriptions of local physics. If there are “enough” observables that can be measured jointly on different types of systems, we show that the observers’ descriptions are related by an element of the Lorentz group O^+(3,1), together with a global scaling factor. This operational derivation of the Lorentz transformations correctly describes the physics of relativistic Stern-Gerlach measurements in the WKB approximation, and predicts representations of different spin and Wigner little groups.

Proceedings of the 11th workshop on Quantum Physics and Logic. (arXiv:1412.8102v1 [cs.LO])

quant-ph updates on arXiv.org

on 2014-12-30 12:43pm GMT

Authors: Bob Coecke (University of Oxford), Ichiro Hasuo (The University of Tokyo), Prakash Panangaden (McGill University)

This volume contains the proceedings of the 11th International Workshop on Quantum Physics and Logic (QPL 2014), which was held from the 4th to the 6th of June, 2014, at Kyoto University, Japan.

The goal of the QPL workshop series is to bring together researchers working on mathematical foundations of quantum physics, quantum computing and spatio-temporal causal structures, and in particular those that use logical tools, ordered algebraic and category-theoretic structures, formal languages, semantic methods and other computer science methods for the study of physical behavior in general. Over the past few years, there has been growing activity in these foundational approaches, together with a renewed interest in the foundations of quantum theory, which complement the more mainstream research in quantum computation. Earlier workshops in this series, with the same acronym under the name “Quantum Programming Languages”, were held in Ottawa (2003), Turku (2004), Chicago (2005), and Oxford (2006). The first QPL under the new name Quantum Physics and Logic was held in Reykjavik (2008), followed by Oxford (2009 and 2010), Nijmegen (2011), Brussels (2012) and Barcelona (2013).

Comment on “Quantum Darwinism, Decoherence, and the Randomness of Quantum Jumps,” arXiv:1412.5206. (arXiv:1412.7950v1 [quant-ph])

quant-ph updates on arXiv.org

on 2014-12-30 12:43pm GMT

Authors: R. E. Kastner

This brief note points out an extant rebuttal in the literature to the claims made in a recent publication by Zurek.

A Review of Unitary Quantum Premeasurement Theory An Algebraic Study of Basic Kinds of Premeasurements. (arXiv:1412.7862v1 [quant-ph])

quant-ph updates on arXiv.org

on 2014-12-30 12:43pm GMT

Authors: Fedor Herbut

A detailed theory of quantum premeasurement dynamics is presented in which a unitary composite-system operator that contains the relevant object-measuring-instrument interaction brings about the final premeasurement state. It does not include collapse, and it does not consider the environment. It is assumed that a discrete degenerate or non-degenerate observable is measured. Premeasurement is defined by the calibration condition, which requires that every initially statistically sharp value of the measured observable has to be detected with statistical certainty by the measuring instrument. The entire theory is derived as a logical consequence of this definition using the standard quantum formalism. The study has a comprehensive coverage, hence the article is actually a topical review. Connection is made with results of other authors, particularly with basic works on premeasurement. The article is a conceptual review, not a historical one. General exact premeasurement is defined in 7 equivalent ways. Nondemolition premeasurement, defined by requiring preservation of any sharp value of the measured observable, is characterized in 10 equivalent ways. Overmeasurement, i. e., a process in which the observable is measured on account of being a function of a finer observable that is actually measured, is discussed. Disentangled premeasurement, in which, by definition, to each result corresponds only one pointer-observable state in the final composite-system state, is investigated. Ideal premeasurement, a special case of both nondemolition premeasurement and disentangled premeasurement, is defined, and its most important properties are discussed. Finally, disentangled and entangled premeasurements, in conjunction with nondemolition or demolition premeasurements, are used for classification of all premeasurements.

Experimental Proof of Nonlocal Wavefunction Collapse for a Single Particle Using Homodyne Measurement. (arXiv:1412.7790v1 [quant-ph])

quant-ph updates on arXiv.org

on 2014-12-30 12:43pm GMT

A single quantum particle can be described by a wavefunction that spreads over arbitrarily large distances, but it is never detected in two (or more) places. This strange phenomenon is explained in quantum theory by what Einstein repudiated as “spooky action at a distance”: the instantaneous nonlocal collapse of the wavefunction to wherever the particle is detected. We demonstrate this single-particle spooky action, for the first time with no efficiency loophole, by splitting a single photon between two laboratories and experimentally testing if the choice of measurement in one lab really causes a change in the local quantum state in the other lab. To this end, we use homodyne measurements with six different measurement settings and quantitatively verify Einstein’s spooky action by violating an Einstein-Podolsky-Rosen-steering inequality by $0.042 \pm 0.006$. Our experiment also verifies the entanglement of the split single photon even when one side is untrusted.

Black Hole Remnants and the Information Loss Paradox. (arXiv:1412.8366v1 [gr-qc])

gr-qc updates on arXiv.org

on 2014-12-30 12:41pm GMT

Authors: Pisin ChenYen Chin OngDong-han Yeom

Forty years after the discovery of Hawking radiation, its exact nature remains elusive. If Hawking radiation does not carry any information out from the ever shrinking black hole, it seems that unitarity is violated once the black hole completely evaporates. On the other hand, attempts to recover information via quantum entanglement lead to the firewall controversy. Amid the confusions, the possibility that black hole evaporation stops with a “remnant” has remained unpopular and is often dismissed due to some “undesired properties” of such an object. Nevertheless, as in any scientific debate, the pros and cons of any proposal must be carefully scrutinized. We fill in the void of the literature by providing a timely review of various types of black hole remnants, and provide some new thoughts regarding the challenges that black hole remnants face in the context of information loss paradox and its latest incarnation, namely the firewall controversy. The importance of understanding the role of curvature singularity is also emphasized, after all there remains a possibility that singularity cannot be cured even by quantum gravity. In this context a black hole remnant conveniently serves as a cosmic censor. We conclude that a remnant remains a possible end state of Hawking evaporation, and if it contains large interior geometry, may help to ameliorate information loss and the firewall paradox. We hope that this will raise some interests in the community to investigate remnants more critically but also more thoroughly.

LQG predicts the Unruh Effect. Comment to the paper “Absence of Unruh effect in polymer quantization” by Hossain and Sardar. (arXiv:1412.7827v1 [gr-qc])

gr-qc updates on arXiv.org

on 2014-12-30 12:41pm GMT

Authors: Carlo Rovelli

A recent paper claims that loop quantum gravity predicts the absence of the Unruh effect. I show that this is not the case, and take advantage of this opportunity to shed some light on some related issues.

Comment on “Quantum Darwinism, Decoherence, and the Randomness of Quantum Jumps,” arXiv:1412.5206. (arXiv:1412.7950v1 [quant-ph])

physics.hist-ph updates on arXiv.org

on 2014-12-30 12:41pm GMT

Authors: R. E. Kastner

This brief note points out an extant rebuttal in the literature to the claims made in a recent publication by Zurek.

Quantum Zeno effect for a free-moving particle

PRA: Fundamental concepts

on 2014-12-29 3:00pm GMT

Author(s): Miguel A. Porras, Alfredo Luis, and Isabel Gonzalo

Although the quantum Zeno effect takes its name from Zeno’s arrow paradox, the effect of frequently observing the position of a freely moving particle on its motion has not been analyzed in detail in the frame of standard quantum mechanics. We study the evolution of a moving free particle while moni…

[Phys. Rev. A 90, 062131] Published Mon Dec 29, 2014

A Relativistic Dynamical Collapse Model (arXiv:1412.6723 [quant-ph])

quant-ph updates on arXiv.org

on 21 Dec 2014 04:47:12 GMT

Authors: Philip Pearle

A model is discussed where all operators are constructed from a quantum scalar field whose energy spectrum takes on all real values. The Schr\”odinger picture wave function depends upon space and time coordinates for each particle, as well as an inexorably increasing evolution parameter s which labels a foliation of space-like hypersurfaces. The model is constructed to be manifestly Lorentz invariant in the interaction picture. Free particle states and interactions are discussed in this framework. Then, the formalism of the CSL (Continuous Spontaneous Localization) theory of dynamical collapse is applied. The collapse-generating operator is chosen to to be the particle number space-time density. Unlike previous relativistically invariant models, the vacuum state is not excited. The collapse dynamics depends upon two parameters, a parameter Λ which represents the collapse rate/volume and a scale factor ℓ. A common example of collapse dynamics, involving a clump of matter in a superposition of two locations, is analyzed. The collapse rate is shown to be identical to that of non-relativistic CSL when the GRW-CSL choice of ℓ=a=10−5cm, is made, along with Λ=λ/a3 (GRW-CSL choice λ=10−16s−1). However, it is also shown that the change of mass of a nucleon over the age of the universe is then unacceptably large. The case where ℓ is the size of the universe is then considered. It is shown that the collapse behavior is satisfactory and the change of mass over the age of the universe is acceptably small, when Λ=λ/ℓa2.