Pragya Shukla, Indian Institute of Technology Kharagpur
Abstract
All measurement begins with an inter action between the system under consideration and a measuring device. For quantum mechanical devices however the measurement is a two-way street: any such interaction must also disturb the system being measured. ‘Weak measurement’, a technique invented by Aharonov and co-workers about 20 years ago, is a way of probing a quantum system so gently that the measurement disturbance (due to Heisenberg’s uncertainty principle) becomes negligible. The most interesting features of weak measurement is revealed when it is subjected to conditions, involving pre-selection and post-selection of the state of the quantum system. It was predicted that for a very low probability post-selection (that is, if the measurement is conditioned on finding the system in a very unlikely final state) the measurement outcome can be unexpectedly large, larger than any ‘legal’ value for the property being measured.
Weak values, resulting from the action of an operator on a preselected state when measured after postselection by a different state, can lie outside the spectrum of eigenvalues of the operator: they can be ‘superweak’. This phenomenon can be quantified by averaging over an ensemble of the two states, and calculating the probability distribution of the weak values. Our main results indicate an unanticipated universality in the distribution of weak and superweak values. If there are many eigenvalues, distributed within a finite range, this distribution takes a simple universal generalized Lorentzian form, and the ‘superweak probablility’, of weak values outside the spectrum, can be as large as 0.293 (almost 30% chance of a weak value being superweak). By contrast, the familiar expectation values always lie within the spectral range, and their distribution, although approximately Gaussian for many eigenvalues, is not universal.
Reference:
(i) M.V. Berry and P. Shukla, J. Phys. A: Math. & Theo., 43, 354024, (2010) (ii) M.V. Berry, M R Dennis, B. Mcroberts and P. Shukla, J. Phys. A. Math. & Theo. 44,
(2011), 20530 (iii) M V Berry1, N Brunner1, S Popescu1 and P Shukla2J. Phys. A: Math. Theor. 44
(2011) 492001