Quantum to Classical Transitions via Weak Measurements and Post-Selection

This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based on a very weak von Neumann coupling, is a unique kind of quantum measurement with numerous theoretical and practical applications. In contrast to other measurement techniques, it allows to gather a small amount of information regarding the quantum system, with only a negligible probability of collapsing it. A single weak measurement yields an almost random outcome, but when performed repeatedly over a large ensemble, the averaged outcome becomes increasingly robust and accurate. Importantly, a long sequence of weak measurements can be thought of as a single projective measurement. I claim in this work that classical variables appearing in the macro-world, such as centre of mass, moment of inertia, pressure and average forces, result from a multitude of quantum weak measurements performed in the micro-world. Here again, the quantum outcomes are highly uncertain, but the law of large numbers obliges their convergence to the definite quantities we know from our everyday lives. By augmenting this description with a final boundary condition and employing the notion of "classical robustness under time-reversal" I will draw a quantitative borderline between the classical and quantum regimes. I will conclude by analyzing the role of macroscopic systems in amplifying and recording quantum outcomes.Comment: To be published as a book chapter in "Quantum Structural Studies: Classical Emergence from the Quantum Level", R.E. Kastner, J. Jeknic-Dugic, G. Jaroszkiewicz (Eds.), World Scientific Publishing Co. arXiv admin note: substantial text overlap with arXiv:1406.638

The mean king's problem: Prime degrees of freedom

We show how one can ascertain the values of a complete set of mutually complementary observables of a prime degree of freedom.Comment: Originally submitted to Physical Review Letters; updated version now submitted to Physics Letters