Weak measurement

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Weak measurement

Weak Measurements are a type of Quantum measurement , where the measured system is very weakly coupled to the measuring device. After the measurement the measuring device is shifted by what is called the "weak value". The system is not disturbed by the measurement. Although this may seem to contradict some basic aspects of quantum theory, the formalism lies within the boundaries of the theory and does not contradict any fundamental concept.

The idea of weak measurements and weak values, first developed by Yakir Aharonov, David Albert and Lev Vaidman [Y Aharonov, DZ Albert, L Vaidman, "How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100," Physical Review Letters, 1988.] is especially useful for gaining information about pre- and post-selected systems described by the two state vector formalism [Y. Aharonov and L. Vaidmanin Time in Quantum Mechanics, J.G. Muga et al. eds., (Springer) 369-412 (2002) [http://il.arxiv.org/abs/quant-ph/0105101 quant-ph/0105101] ] .Since a "strong" perturbative measurement can both upset the outcome of the post-selection and tamper with all subsequent measurement, weak nonperturbative measurements may be used to learn about such systems during their evolution.

If $|phi_1 angle$ and $|phi_2 angle$ are the pre- and post-selected quantum mechanical states, the "weak value" of the observable $hat\left\{mathbf\left\{A$ is defined as :$A_w = frac\left\{langlephi_1|hat\left\{mathbf\left\{A|phi_2 angle\right\}\left\{langlephi_1|phi_2 angle\right\}.$

The weak value of the observable becomes large when the post-selected state, $|phi_2 angle$, approaches being orthogonal to the pre-selected state, $|phi_1 angle$. In this way, by properly choosing the two states, the weak value of the operator can be made arbitrarily large, and otherwise small effects can be amplified [O. Hosten and P. Kwiat "Observation of the spin Hall effect of light via weak measurements" Science 319 787 (2008) [http://www.sciencemag.org/cgi/content/full/sci;319/5864/787?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&andorexacttitleabs=and&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&volume=319&firstpage=787&resourcetype=HWCIT] ] .

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