• Corpus ID: 6759536

QUANTUM CAUSALITY, DECOHERENCE, TRAJECTORIES AND INFORMATION

@inproceedings{Belavkin2005QUANTUMCD,
  title={QUANTUM CAUSALITY, DECOHERENCE, TRAJECTORIES AND INFORMATION},
  author={Viacheslav P. Belavkin},
  year={2005}
}

• V. Belavkin
• Published 2005
• Physics

A history of the discovery of “new” quantum mechanics and the paradoxes of its probabilistic interpretation are briefly reviewed from the modern point of view of quantum probability and information. The modern quantum theory, which has been developed during the last 20 years for treatment of quantum open systems including quantum noise, decoherence, quantum diffusions and spontaneous jumps occurring under continuous in time observation, is not yet a part of the standard curriculum of quantum physics. It is argued that the conventional formalism of quantum mechanics is insufficient for the description of quantum events, such as spontaneous decays say, and the new experimental phenomena related to individual quantum measurements, but they all have received an adequate mathematical treatment in quantum stochastics of open systems. Moreover, the only reasonable probabilistic interpretation of quantum mechanics put forward by Max Born was in fact in irreconcilable contradiction with traditional mechanical reality and causality. This led to numerous quantum paradoxes, some of them due to the great inventors of quantum theory such as Einstein and Schrödinger. They are reconsidered in this paper from the point of view of quantum information. The development of quantum measurement theory, initiated by von Neumann, indicated a possibility for resolution of this interpretational crisis by divorcing the algebra of the dynamical generators and the algebra of the actual observables, or beables. It is shown that within this approach quantum causality can be rehabilitated in the form of a superselection rule for compatibility of the past beables with the potential future. This rule, together with the self-compatibility of the measurements insuring the consistency of the histories, is called the nondemolition, or causality principle in modern quantum theory. The application of this rule in the form of the dynamical commutation relations leads to the derivation of the von Neumann projection postulate, and also to the more general reductions, instantaneous, spontaneous, and even continuous in time. This gives a quantum stochastic solution, in the form of the dynamical filtering equations, of the notorious measurement problem which was tackled unsuccessfully by many famous physicists starting with Schrödinger and Bohr. It has been recently proved that the quantum stochastic model for the continuous in time measurements is equivalent to a Dirac type boundary-value problem for the secondary quantized input ”offer waves from future” in one extra dimension, and to a reduction of the algebra of the consistent histories of past events to an Abelian subalgebra for the “trajectories of the output particles”. This supports the corpuscular-wave duality in the form of the thesis that everything in the future are quantized waves, everything in the past are trajectories of the recorded particles. http://www.maths.nott.ac.uk/personal/vpb/