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.
The trouble with orbits: The Stark effect in the old and the new quantum theory
on 2014-9-26 8:30pm GMT
Publication date: Available online 26 September 2014
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Author(s): Anthony Duncan , Michel Janssen
The old quantum theory and Schrödinger׳s wave mechanics (and other forms of quantum mechanics) give the same results for the line splittings in the first-order Stark effect in hydrogen, the leading terms in the splitting of the spectral lines emitted by a hydrogen atom in an external electric field. We examine the account of the effect in the old quantum theory, which was hailed as a major success of that theory, from the point of view of wave mechanics. First, we show how the new quantum mechanics solves a fundamental problem that one runs into in the old quantum theory with the Stark effect. It turns out that, even without an external field, it depends on the coordinates in which the quantum conditions are imposed which electron orbits are allowed in a hydrogen atom. The allowed energy levels and hence the line splittings are independent of the coordinates used but the size and eccentricity of the orbits are not. In the new quantum theory, this worrisome non-uniqueness of orbits turns into the perfectly innocuous non-uniqueness of bases in Hilbert space. Second, we review how the so-called WKB (Wentzel–Kramers–Brillouin) approximation method for solving the Schrödinger equation reproduces the quantum conditions of the old quantum theory amended by some additional half-integer terms. These extra terms remove the need for some arbitrary extra restrictions on the allowed orbits that the old quantum theory required over and above the basic quantum conditions.
A categorial approach to relativistic locality
on 2014-9-26 8:30pm GMT
Publication date: Available online 26 September 2014
Source:Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Author(s): Miklós Rédei
Relativistic locality is interpreted in this paper as a web of conditions expressing the compatibility of a physical theory with the underlying causal structure of spacetime. Four components of this web are distinguished: spatiotemporal locality, along with three distinct notions of causal locality, dubbed CL-Independence, CL-Dependence, and CL-Dynamic. These four conditions can be regimented using concepts from the categorical approach to quantum field theory initiated by Brunetti, Fredenhagen, and Verch (2003). A covariant functor representing a general quantum field theory is defined to be causally local if it satisfies the three CL conditions. Any such theory is viewed as fully compliant with relativistic locality. We survey current results indicating the extent to which an algebraic quantum field theory satisfying the Haag–Kastler axioms is causally local.
Detection of nonlocal superpositions
on 2014-9-26 2:00pm GMT
Author(s): A. J. Gutiérrez-Esparza, W. M. Pimenta, B. Marques, A. A. Matoso, J. Sperling, W. Vogel, and S. Pádua
We study in theory and experiment the verification of the Schmidt number of quantum correlated radiation fields. This measure of entanglement counts the number of global superpositions of product states which are needed to describe a compound quantum system. For unraveling a certain value of this me…
[Phys. Rev. A 90, 032328] Published Fri Sep 26, 2014
on 2014-9-26 6:53am GMT
Wigner’s form of the local realist inequality is used to derive its temporal version for a single two-level system involving two-time joint probabilities. Such an equality may be regarded as a novel form of the Leggett-Garg inequality (LGI)constituting a necessary condition for macrorealism. The robustness of its quantum mechanical (QM) violation against unsharpness of measurement is investigated. It is found that there exists a range of values of the unsharpness parameter (characterizing imprecision of the relevant measurements) for which the usual LGI is satisfied, but Wigner’s form of LGI (WLGI) is violated, thereby implying that the QM violation of macrorealism cannot be tested using the usual LGI, but can be tested using WLGI. In showing this, we take into account the general form of usual LGI involving an arbitrary number of pairs of two-time correlation functions. A recently proposed another necessary condition for macrorealism, called `no-signalling in time’, is also probed, showing that its QM violation persists for arbitrarily unsharp measurements.
Schroedinger vs. Navier-Stokes. (arXiv:1409.7036v1 [math-ph] CROSS LISTED)
on 2014-9-26 6:53am GMT
Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier-Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck’s constant, while the volume density of entropy is proportional to Boltzmann’s constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier-Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation).
on 2014-9-26 6:53am GMT
Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that the correlations observed for some entangled quantum states can be explained within the framework of local models, thus proving that these resources are inequivalent in this scenario. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such relation in multipartite systems. We provide a general construction of genuinely multipartite entangled states that do not display genuinely multipartite nonlocality, thus proving that entanglement and nonlocality are inequivalent for any number of particles.
Entropic Version of the Greenberger-Horne-Zeilinger Paradox. (arXiv:1409.7290v1 [quant-ph])
on 2014-9-26 6:53am GMT
Consider four binary +-1 variables A, B, C and D for which classical reasoning implies ABCD = 1. In this case the knowledge of A, B, C automatically provides knowledge of D because D = ABC. However, the Greenberger-Horne-Zeilinger paradox shows that despite classical prediction one can find quantum states and observables with well defined outcomes for which D = -ABC. In this work we formulate an information-theoretic version of this paradox. We show that for a tripartite quantum system one can find a set of four properties for which classical reasoning implies that D = ABC, yet quantum theory predicts that one can know everything about A, B, C and nothing about D.
Quantum Support Vector Machine for Big Data Classification
PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.
on 2014-9-25 2:00pm GMT
Author(s): Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd
Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the…
[Phys. Rev. Lett. 113, 130503] Published Thu Sep 25, 2014
on 2014-9-25 4:12am GMT
Baryon Acoustic Oscillations (BAO) allow us to determine the expansion history of the Universe, thereby shedding light on the nature of dark energy. Recent observations of BAO’s in the SDSS DR9 and DR11 have provided us with statistically independent measurements of $H(z)$ at redshifts of 0.57 and 2.34, respectively. We show that these measurements can be used to test the cosmological constant hypothesis in a model independent manner by means of an improved version of the $Om$ diagnostic. Our results indicate that the SDSS DR11 measurement of $H(z) = 222 \pm 7$ km/sec/Mpc at $z = 2.34$, when taken in tandem with measurements of $H(z)$ at lower redshifts, imply considerable tension with the standard $\Lambda$CDM model. Our estimation of the new diagnostic $Omh^2$ from SDSS DR9 and DR11 data, namely $Omh^2 \approx 0.122 \pm 0.01$, which is equivalent to $\Omega_{0m}h^2$ for the spatially flat $\Lambda$CDM model, is in tension with the value $\Omega_{0m}h^2 = 0.1426 \pm 0.0025$ determined for $\Lambda$CDM from Planck+WP. This tension is alleviated in models in which the cosmological constant was dynamically screened (compensated) in the past. Such evolving dark energy models display a pole in the effective equation of state of dark energy at high redshifts, which emerges as a smoking gun test for these theories.
Protective measurements and the reality of the wave function
PhilSci-Archive: No conditions. Results ordered -Date Deposited.
on 2014-9-24 6:08pm GMT
Gao, Shan (2014) Protective measurements and the reality of the wave function. [Preprint]
Violation of Hudson’s theorem in relativistic quantum mechanics
on 2014-9-24 2:00pm GMT
Author(s): Andre G. Campos, Renan Cabrera, Denys I. Bondar, and Herschel A. Rabitz
In nonrelativistic quantum mechanics, Hudson’s theorem states that a Gaussian wave function is the only pure state corresponding to a positive Wigner function (WF). We explicitly construct non-Gaussian Dirac spinors with positive relativistic WFs. These pure relativistic states are coherent superpos…
[Phys. Rev. A 90, 034102] Published Wed Sep 24, 2014
A holographic proof of the averaged null energy condition. (arXiv:1408.3566v2 [gr-qc] UPDATED)
on 2014-9-24 2:48am GMT
The averaged null energy conditions (ANEC) states that, along a complete null curve, the negative energy fluctuations of a quantum field must be balanced by positive energy fluctuations. We use the AdS/CFT correspondence to prove the ANEC for a class of strongly coupled conformal field theories in flat spacetime. A violation of the ANEC in the field theory would lead to acausal propagation of signals in the bulk.
Is String Interaction the Origin of Quantum Mechanics?. (arXiv:1407.6833v3 [hep-th] UPDATED)
on 2014-9-24 2:48am GMT
String theory developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend open string field theory is a fully consistent definition of the theory – it is at least a self consistent sector. Then we find in its structure that the rules of quantum mechanics emerge from the non-commutative nature of the basic string joining/splitting interactions, thus deriving rather than assuming the quantum commutation rules among the usual canonical quantum variables for all physical systems derivable from open string field theory. Morally we would apply such an argument to M-theory to cover all physics. If string or M-theory really underlies all physics, it seems that the door has been opened to an understanding of the origins of quantum mechanics.
on 2014-9-24 2:45am GMT
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat’s principle in many-dimensional spaces describing dynamical systems (i.e., the quantum Hilbert space and the classical phase and configuration space). We propose that if the notion of a metric distance is well defined in that space and the velocity of the representative point of the system is an invariant of motion, then a generalized version of Fermat’s principle will hold. We substantiate this conjecture for time-independent quantum systems and for a classical system consisting of coupled harmonic oscillators. An exception to this principle is the configuration space of a charged particle in a constant magnetic field; in this case the principle is valid in a frame rotating by half the Larmor frequency, not the stationary lab frame.
Quantum optics: Photons made to dance together
Nature – Issue – nature.com science feeds
on 2014-9-24 12:00am GMT
Quantum optics: Photons made to dance together
Nature 513, 7519 (2014). doi:10.1038/513463a
Physicists have made two beams of light interact at the level of individual photons.Getting photons to interact is important for all-optical computation and for producing new quantum states of light. Kristin Beck at the Massachusetts Institute of Technology in Cambridge and her colleagues crossed
PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.
on 2014-9-23 2:00pm GMT
Author(s): Yeong-Cherng Liang, Florian John Curchod, Joseph Bowles, and Nicolas Gisin
We investigate the phenomenon of anonymous quantum nonlocality, which refers to the existence of multipartite quantum correlations that are not local in the sense of being Bell-inequality-violating but where the nonlocality is—due to its biseparability with respect to all bipartitions—seemingly nowh…
[Phys. Rev. Lett. 113, 130401] Published Tue Sep 23, 2014
on 2014-9-23 3:02am GMT
The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with non-commuting coordinates. This demonstrates that the algebraic extension keeps the simple structure of Quantum Mechanics, while it also introduces an effective quite involved structure in the 4-dimensional sub-space. The similarities to H. S. Snyder’s work, a former proposal to include the effects of a minimal length, are exposed. The first steps to pseudo-complex Quantum Mechanics in 1-dimension are outlined, awaiting still the interpretation of some new emerging structures. As an example, two waves, out of phase by 90 degrees, are added which classically annihilate each other, while in the pseudo-complex description there is a non-zero amplitude.
A quantum of history. (arXiv:1409.5956v1 [physics.hist-ph])
physics.hist-ph updates on arXiv.org
on 2014-9-23 3:02am GMT
With reference to primary sources it is shown that key claims made regarding the history of the pilot wave theory in Quantum Theory at the Crossroads are not supported by the historical record. It is also argued that the association of de Broglie with just a first-order law of particle motion, and Bohm with a second-order one, has no historical basis.
on 2014-9-23 3:02am GMT
Within the class of ontological interpretations of quantum theory where a physical system comprises a particle and a field (wavefunction) guiding it, an empty wave is a segment of the wavefunction not containing the particle. We examine the impact of this concept on the debate between the epistemological and ontological viewpoints. The theoretical merits of the empty wave in avoiding the wavefunction collapse hypothesis, and in supplying conceptual precision in the application of quantum mechanics, are emphasized. Particular reference is made to path detection in interferometry and it is shown how a consistent application of the particle and empty wave concepts dispels the suggestion that this is a <surrealist> theory. The problem of how the reality of an empty wave might be demonstrated by its effect on other systems is examined and general arguments advanced against this possibility. However, these arguments are not conclusive and we describe how the technique of protective measurement suggests a method to probe the empirical implications of empty waves and potentially distinguish between the epistemological and ontological perspectives.
on 2014-9-23 3:02am GMT
The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum measurement theory based on completely positive map-valued measures, a universally valid new formulation of the uncertainty principle for error and disturbance in quantum measurements, the Wigner-Araki-Yanase limit of quantum measurements, the accuracy limit of quantum computing based on conservation laws, and a quantum interpretation based on quantum set theory.
on 2014-9-23 3:02am GMT
The ontic breakthrough in quantum foundations, consisting of three theo- rems, that of Pusey, Barrett, and Rudolph (PBR), the Colbeck-Renner one, and Hardy’s one, is shortly presented, together with various reactions. Some of the ideas involved are explained and/or commented upon. Thus, the wave- function is proved real in three independent ways. Each of the theorems rests on more or less plausible assumptions, but they require more in-depth anal- yses.
on 2014-9-22 1:47am GMT
The gravitational interaction is generally considered to be too weak to be easily submitted to systematic experimental investigation in the quantum, microscopic, domain. In this paper we attempt to remedy this situation by considering the gravitational influence exerted by a crystalline nanosphere of mesoscopic size on itself, in the semi-classical, mean field, regime. We study in depth the self-localisation process induced by the corresponding non-linear potential of (gravitational) self-interaction. In particular, we characterize the stability of the associated self-collapsed ground state and estimate the magnitude of the corrections that are due to the internal structure of the object (this includes size-effects and corrections due to the discrete, atomic, structure of the sphere). Finally, we derive an approximated, gaussian, dynamics which mimics several essential features of the self-gravitating dynamics and, based on numerical results derived from this model, we propose a concrete experimental setting which we believe might, in the foreseeable future, reveal the existence of gravitational self-interaction effects.
Ambiguity in quantum-theoretical descriptions of experiments. (arXiv:1409.5678v1 [quant-ph])
on 2014-9-22 1:47am GMT
This paper contributes to a burgeoning area of investigation, the ambiguity inherent in mathematics and the implications for physics of this ambiguity. To display the mathematical form of equations of quantum theory used to describe experiments, we make explicit the knobs by which the devices of an experiment are arranged and adjusted. A quantum description comes in two parts: (1) a statement of results of an experiment, expressed by probabilities of detections as functions of knob settings, and (2) an explanation of how we think these results come about, expressed by linear operators, also as functions of knob settings. Because quantum mechanics separates the two parts of any description, it is known that between the statements of results and the explanations lurks a logical gap: given any statement of results one has a choice of explanations.
Here we work out some consequences of this openness to choice. We show how quantum theory as mathematical language in which to describe experiments necessarily involves multiple descriptions: multiple explanations of a given result, as well as multiple statements of results and multiple arrangement of knobs. Appreciating these multiplicities resolves what otherwise is a confusion in the concept of invariance. Implications of multiplicity of description for the security of quantum key distribution are noted.
