arXiv:quant-ph/0302080quant-ph
Quantum Trajectories and Quantum Measurement Theory
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Abstract
Beyond their use as numerical tools, quantum trajectories can be ascribed a degree of reality in terms of quantum measurement theory. In fact, they arise naturally from considering continuous observation of a damped quantum system. A particularly useful form of quantum trajectories is as linear (but non-unitary) stochastic Schrodinger equations. In the limit where a strong local oscillator is used in the detection, and where the system is not driven, these quantum trajectories can be solved. This gives an alternate derivation of the probability distributions for completed homodyne and heterodyne detection schemes. It also allows the previously intractable problem of real-time adaptive measurements to be treated. The results for an analytically soluble example of adaptive phase measurements are presented, and future developments discussed.
You're confusing quantum trajectories for classical ones. The latter are what we use in path-integral formulations, and constitute a single path through spacetime. No such path exists for quantum states, since that would be a local hidden-variable theory (which has been…
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