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An Evolutionary Formalism for Weak Quantum Measurements
Unitary evolution and projective measurement are fundamental axioms of quantum mechanics. Even though projective measurement yields one of the eigenstates of the measured operator as the outcome, there is no theory that predicts which eigenstate will be observed in which experimental run. There exists only an ensemble description, which predicts probabilities of various outcomes over many experimental runs. We propose a dynamical evolution equation for the projective collapse of the quantum state in individual experimental runs, which is consistent with the well-established framework of quantum mechanics. In case of gradual weak measurements, its predictions for ensemble evolution are different from those of the Born rule. It is an open question whether or not suitably designed experiments can observe this alternate evolution.
Keywords
Born Rule, Decoherence, Density Matrix, Fixed Point, Quantum Trajectory, State Collapse.
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- Lindblad, G., On the generators of quantum dynamical subgroups. Comm. Math. Phys., 1976, 48(2), 119–130.
- Gorini, V., Kossakowski, A. and Sudarshan, E. C. G., Completely positive semigroups of N-level systems. J. Math. Phys., 1976, 17(5), 821–825.
- Giulini, D., Joos, E., Kiefer, C., Kuptsch, J., Stamatescu, I.-O. and Zeh, H. D., Decoherence and the Appearance of a Classical World in Quantum Theory, Springer, 1996.
- Wiseman, H. M. and Milburn, G. J., Quantum Measurement and Control, Cambridge University Press, 2010.
- DeWitt, B. S. and Graham, N. (eds), The Many-Worlds Interpretation of Quantum Mechanics, Princeton University Press, 1973.
- Bengaluru is the capital of the state of Karnataka in India. See http://www.karnatakatourism.org/
- Aharonov, Y., Albert, D. Z. and Vaidman, L., How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett., 1988, 60(14), 1351–1354.
- Ghose, P., Measurement as spontaneous symmetry breaking, nonlocality and non-Boolean holism; arXiv:1008.2510[quant-ph].
- Korotkov, A. N., Continuous quantum measurement of a double dot. Phys. Rev. B, 1999, 60(8), 5737–5742; Selective quantum evolution of a qubit state due to continuous measurement. Phys. Rev. B, 2001, 63(11), 115403-1–115403-15.
- Vijay, R. et al., Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback. Nature, 2012, 490(7418), 77–80.
- Murch, K. W., Weber, S. J., Macklin, C. and Siddiqi, I., Observing single quantum trajectories of a superconducting quantum bit. Nature, 2013, 502(7470), 211–214.
- Gell-Mann, M. and Hartle, J. B., Classical equations for quantum systems. Phys. Rev. D, 1993, 47(8), 3345–3382.
- Penrose, R., On gravity’s role in quantum state reduction. Gen. Relativ. Gravit., 1996, 28(5), 581–600.
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