arXiv subjects

Kristel Michielsen

Publications and source records attributed to Kristel Michielsen.

At least 109 records · Page 6Linked to original sources

arXiv2015

Quantum theory as a description of robust experiments: derivation of the Pauli equation

It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schrödinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern-Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments.

quant-ph↗

arXiv2014

Event-by-event simulation of a quantum delayed-choice experiment

The quantum delayed-choice experiment of Tang et al. [Nature Photonics 6 (2012) 600] is simulated on the level of individual events without making reference to concepts of quantum theory or without solving a wave equation. The simulation results are in excellent agreement with the quantum theoretical predictions of this experiment. The implication of the work presented in the present paper is that the experiment of Tang et al. can be explained in terms of cause-and-effect processes in an event-by-event manner.

quant-ph↗

arXiv2014

Event-based simulation of quantum physics experiments

We review an event-based simulation approach which reproduces the statistical distributions of wave theory not by requiring the knowledge of the solution of the wave equation of the whole system but by generating detection events one-by-one according to an unknown distribution. We illustrate its applicability to various single photon and single neutron interferometry experiments and to two Bell test experiments, a single-photon Einstein-Podolsky-Rosen experiment employing post-selection for photon pair identification and a single-neutron Bell test interferometry experiment with nearly $100\%$ detection efficiency.

quant-ph↗

arXiv2014

Macroscopically deterministic, Markovian thermalization in finite quantum spin systems

A key feature of non-equilibrium thermodynamics is the Markovian, deterministic relaxation of coarse observables such as, for example, the temperature difference between two macroscopic objects which evolves independently of almost all details of the initial state. We demonstrate that the unitary dynamics for moderately sized spin-1/2 systems may yield the same type of relaxation dynamics for a given magnetization difference. This observation might contribute to the understanding of the emergence of thermodynamics within closed quantum systems.

quant-ph↗

arXiv2014

Event-based simulation of neutron experiments: interference, entanglement and uncertainty relations

We discuss a discrete-event simulation approach, which has been shown to give a unified cause-and-effect description of many quantum optics and single-neutron interferometry experiments. The event-based simulation algorithm does not require the knowledge of the solution of a wave equation of the whole system, yet reproduces the corresponding statistical distributions by generating detection events one-by-one. It is showm that single-particle interference and entanglement, two important quantum phenomena, emerge via information exchange between individual particles and devices such as beam splitters, polarizers and detectors. We demonstrate this by reproducing the results of several single-neutron interferometry experiments, including one that demonstrates interference and one that demonstrates the violation of a Bell-type inequality. We also present event-based simulation results of a single neutron experiment designed to test the validity of Ozawa's universally valid error-disturbance relation, an uncertainty relation derived using the theory of general quantum measurements.

quant-ph↗

arXiv2014

Discrete-event simulation of uncertainty in single-neutron experiments

A discrete-event simulation approach which provides a cause-and-effect description of many experiments with photons and neutrons exhibiting interference and entanglement is applied to a recent single-neutron experiment that tests (generalizations of) Heisenberg's uncertainty relation. The event-based simulation algorithm reproduces the results of the quantum theoretical description of the experiment but does not require the knowledge of the solution of a wave equation nor does it rely on concepts of quantum theory. In particular, the data satisfies uncertainty relations derived in the context of quantum theory.

quant-ph↗

arXiv2013

Quantum Decoherence Scaling with Bath Size: Importance of Dynamics, Connectivity, and Randomness

The decoherence of a quantum system $S$ coupled to a quantum environment $E$ is considered. For states chosen uniformly at random from the unit hypersphere in the Hilbert space of the closed system $S+E$ we derive a scaling relationship for the sum of the off-diagonal elements of the reduced density matrix of $S$ as a function of the size $D_E$ of the Hilbert space of $E$. This sum decreases as $1/\sqrt{D_E}$ as long as $D_E\gg 1$. This scaling prediction is tested by performing large-scale simulations which solve the time-dependent Schr{ö}dinger equation for a ring of spin-1/2 particles, four of them belonging to $S$ and the others to $E$. Provided that the time evolution drives the whole system from the initial state toward a state which has similar properties as states belonging to the class of quantum states for which we derived the scaling relationship, the scaling prediction holds. For systems which do not exhibit this feature, it is shown that increasing the complexity (in terms of connections) of the environment or introducing a small amount of randomness in the interactions in the environment suffices to observe the predicted scaling behavior.

quant-ph↗

arXiv2012

Equilibration and Thermalization of Classical Systems

It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that this conclusion holds for both integrable or nonintegrable systems even though the whole system may contain as little as a few thousand particles. In other words, we demonstrate that the canonical distribution holds for subsystems of experimentally relevant sizes and observation times.

cond-mat.stat-mech↗

arXiv2012

Event-by-event simulation of quantum phenomena

A discrete-event simulation approach is reviewed that does not require the knowledge of the solution of the wave equation of the whole system, yet reproduces the statistical distributions of wave theory by generating detection events one-by-one. The simulation approach is illustrated by applications to a two-beam interference experiment and two Bell test experiments, an Einstein-Podolsky-Rosen- Bohm experiment with single photons employing postselection for pair identification and a single-neutron Bell test interferometry experiment with nearly 100% detection efficiency.

quant-ph↗

arXiv2012

Event-based simulation of neutron interferometry experiments

A discrete-event approach, which has already been shown to give a cause-and-effect explanation of many quantum optics experiments, is applied to single-neutron interferometry experiments. The simulation algorithm yields a logically consistent description in terms of individual neutrons and does not require the knowledge of the solution of a wave equation. It is shown that the simulation method reproduces the results of several single-neutron interferometry experiments, including experiments which, in quantum theoretical language, involve entanglement. Our results demonstrate that classical (non-Hamiltonian) systems can exhibit correlations which in quantum theory are associated with interference and entanglement, also when all particles emitted by the source are accounted for.

quant-ph↗

arXiv2012

Corpuscular Event-by-Event Simulation of Quantum Optics Experiments: Application to a Quantum-Controlled Delayed-Choice Experiment

A corpuscular simulation model of optical phenomena that does not require the knowledge of the solution of a wave equation of the whole system and reproduces the results of Maxwell's theory by generating detection events one-by-one is discussed. The event-based corpuscular model gives a unified description of multiple-beam fringes of a plane parallel plate and single-photon Mach-Zehnder interferometer, Wheeler's delayed choice, photon tunneling, quantum eraser, two-beam interference, Einstein-Podolsky-Rosen-Bohm and Hanbury Brown-Twiss experiments. The approach is illustrated by application to a recent proposal for a quantum-controlled delayed choice experiment, demonstrating that also this thought experiment can be understood in terms of particle processes only.

quant-ph↗

arXiv2012

Event-by-event simulation of nonclassical effects in two-photon interference experiments

A corpuscular simulation model for second-order intensity interference phenomena is discussed. It is shown that both the visibility ${\cal V}=1/2$ predicted for two-photon interference experiments with two independent sources and the visibility ${\cal V}=1$ predicted for two-photon interference experiments with a parametric down-conversion source can be explained in terms of a locally causal, modular, adaptive, corpuscular, classical (non-Hamiltonian) dynamical system. Hence, there is no need to invoke quantum theory to explain the so-called nonclassical effects in the interference of signal and idler photons in parametric-down conversion. A revision of the commonly accepted criterion of the nonclassical nature of light is needed.

quant-ph↗

arXiv2011

Hidden assumptions in the derivation of the Theorem of Bell

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.

quant-ph↗

arXiv2011

Multi-order interference is generally nonzero

It is demonstrated that the third-order interference, as obtained from explicit solutions of Maxwell's equations for realistic models of three-slit devices, including an idealized version of the three-slit device used in a recent three-slit experiment with light (U. Sinha et al., Science 329, 418 (2010)), is generally nonzero. The hypothesis that the third-order interference should be zero is shown to be fatally flawed because it requires dropping the one-to-one correspondence between the symbols in the mathematical theory and the different experimental configurations.

physics.optics↗

arXiv2010

Event-based simulation of light propagation in lossless dielectric media

We describe an event-based approach to simulate the propagation of an electromagnetic plane wave through dielectric media. The basic building block is a deterministic learning machine that is able to simulate a plane interface. We show that a network of two of such machines can simulate the propagation of light through a plane parallel plate. With properly chosen parameters this setup can be used as a beam splitter. The modularity of the simulation method is illustrated by constructing a Mach-Zehnder interferometer from plane parallel plates, the whole system reproducing the results of wave theory. A generalization of the event-based model of the plane parallel plate is also used to simulate a periodically stratified medium.

physics.comp-ph↗

arXiv2010

Approach to equilbrium in nano-scale systems at finite temperatur

We study the time evolution of the reduced density matrix of a system of spin-1/2 particles interacting with an environment of spin-1/2 particles. The initial state of the composite system is taken to be a product state of a pure state of the system and a pure state of the environment. The latter pure state is prepared such that it represents the environment at a given finite temperature in the canonical ensemble. The state of the composite system evolves according to the time-dependent Schr{ö}dinger equation, the interaction creating entanglement between the system and the environment. It is shown that independent of the strength of the interaction and the initial temperature of the environment, all the eigenvalues of the reduced density matrix converge to their stationary values, implying that also the entropy of the system relaxes to a stationary value. We demonstrate that the difference between the canonical density matrix and the reduced density matrix in the stationary state increases as the initial temperature of the environment decreases. As our numerical simulations are necessarily restricted to a modest number of spin-1/2 particles ($<36$), but do not rely on time-averaging of observables nor on the assumption that the coupling between system and environment is weak, they suggest that the stationary state of the system directly follows from the time evolution of a pure state of the composite system, even if the size of the latter cannot be regarded as being close to the thermodynamic limit.

quant-ph↗

arXiv2010

Reply to the Comment by A.J. Leggett and Anupam Garg

In their comment[1] on our Letter [arXiv:0907.0767], Leggett and Garg claim that they have introduced in their original paper (LG1) a dependence on measurement times. They also claim that Eqs.(HMDR1) and (LG2a) can therefore not be linked in such a way that the arguments of [arXiv:0907.0767] can be transcribed. However, (LG1) distinguishes only three time differences, and all experimental results corresponding to the same time differences are identically labeled and therefore treated as mathematically identical. We therefore cannot agree with the argumentation of Leggett and Garg: except for a change of nomenclature Eqs.(HMDR1) and (LG2a) are the same. A more extensive discussion of this point can be found in [arXiv:0901.2546].

quant-ph↗

arXiv2010

Corpuscular model of two-beam interference and double-slit experiments with single photons

We introduce an event-based corpuscular simulation model that reproduces the wave mechanical results of single-photon double slit and two-beam interference experiments and (of a one-to-one copy of an experimental realization) of a single-photon interference experiment with a Fresnel biprism. The simulation comprises models that capture the essential features of the apparatuses used in the experiment, including the single-photon detectors recording individual detector clicks. We demonstrate that incorporating in the detector model, simple and minimalistic processes mimicking the memory and threshold behavior of single-photon detectors is sufficient to produce multipath interference patterns. These multipath interference patterns are built up by individual particles taking one single path to the detector where they arrive one-by-one. The particles in our model are not corpuscular in the standard, classical physics sense in that they are information carriers that exchange information with the apparatuses of the experimental set-up. The interference pattern is the final, collective outcome of the information exchanges of many particles with these apparatuses. The interference patterns are produced without making reference to the solution of a wave equation and without introducing signalling or non-local interactions between the particles or between different detection points on the detector screen.

quant-ph↗