Event-by-Event Simulation
of Quantum Phenomena


Quantum interference




Recent advances in nanotechnology are paving the way to attain control over individual microscopic objects. The ability to prepare, manipulate, couple and measure single microscopic systems facilitate the study of single quantum systems at the level of individual events. Such experiments address the most fundamental aspects of quantum theory.

Quantum theory gives us a recipe to compute the frequencies for observing events only. As is well known from the early days of its development, quantum theory does not describe individual events such as the arrival of a single electron at a particular position on the detection screen.

Reconciling the mathematical formalism (that does not describe single events) with the experimental fact that each observation yields a definite outcome is often referred to as the quantum measurement paradox. It is the most fundamental, unsolved problem in the foundation of quantum theory.

As the material presented on this web site demonstrates, it is possible to simulate quantum phenomena on the level of individual events, without invoking a single concept of quantum theory. This event-by-event simulation approach rigorously satisfies Einstein's criterion of local causality and builds up the final outcome that agrees with quantum theory event-by-event, just like in real experiments.

Our simulation approach does not resolve the quantum measurement paradox: It does not suffer from this problem. The averages that can be computed from quantum theory are obtained through a simulation of locally causal, classical (non-Hamiltonian) dynamical systems. The key point of these dynamical systems is that they are built from units that are adaptive. Phrased differently, these units have a very primitive form of learning capability and are called Deterministic Learning Machines (DLMs).


Evidence that our event-by-event simulation approach works is provided by the successful application, that is by reproducing the averages predicted by quantum theory, to:

  • Double-slit and two-beam interference experiments with single-photons
  • Single-photon beam-splitter and Mach-Zehnder interferometer experiments.
  • Universal quantum computation.
  • Quantum cryptography.
  • Wheeler’s delayed choice experiment.
  • Quantum eraser, single-photon quantum optics in general.
  • Einstein-Podolsky-Rosen-Bohm experiments with photons.
  • Einstein-Podolsky-Rosen-Bohm experiments with non-orthogonal detection planes.


  • We have invented a systematic, modular procedure to construct locally causal, classical (non-Hamiltonian) dynamical systems that can be used for a deterministic or pseudo-random (unpredictable) event-by-event simulation of real-time quantum phenomena.
  • Our simulation approach allows the modeling of nanoscale processes on the level of individual events without using concepts of quantum theory.


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Last updated: 31-Mar-11