305 research outputs found
Reconstructing weak values without weak measurements
I propose a scheme for reconstructing the weak value of an observable without
the need for weak measurements. The post-selection in weak measurements is
replaced by an initial projector measurement. The observable can be measured
using any form of interaction, including projective measurements. The
reconstruction is effected by measuring the change in the expectation value of
the observable due to the projector measurement. The weak value may take
nonclassical values if the projector measurement disturbs the expectation value
of the observable.Comment: 6 pages. Accepted in Phys. Lett.
Quantum Mechanics of Successive Measurements with Arbitrary Meter Coupling
We study successive measurements of two observables using von Neumann's
measurement model. The two-pointer correlation for arbitrary coupling strength
allows retrieving the initial system state. We recover Luders rule, the Wigner
formula and the Kirkwood-Dirac distribution in the appropriate limits of the
coupling strength
Nonclassicality in Weak Measurements
We examine weak measurements of arbitrary observables where the object is
prepared in a mixed state and on which measurements with imperfect detectors
are made. The weak value of an observable can be expressed as a conditional
expectation value over an infinite class of different generalized Kirkwood
quasi-probability distributions. "Strange" weak values for which the real part
exceeds the eigenvalue spectrum of the observable can only be found if the
Terletsky-Margenau-Hill distribution is negative, or, equivalently, if the real
part of the weak value of the density operator is negative. We find that a
classical model of a weak measurement exists whenever the
Terletsky-Margenau-Hill representation of the observable equals the classical
representation of the observable and the Terletsky-Margenau-Hill distribution
is nonnegative. Strange weak values alone are not sufficient to obtain a
contradiction with classical models.
We propose feasible weak measurements of photon number of the radiation
field. Negative weak values of energy contradicts all classical stochastic
models, whereas negative weak values of photon number contradict all classical
stochastic models where the energy is bounded from below by the zero-point
energy. We examine coherent states in particular, and find negative weak values
with probabilities of 16% for kinetic energy (or squared field quadrature), 8%
for harmonic oscillator energy and 50% for photon number. These experiments are
robust against detector inefficiency and thermal noise.Comment: 12 pages, 8 figure
Nonclassical Properties of Coherent States
It is demonstrated that a weak measurement of the squared quadrature
observable may yield negative values for coherent states. This result cannot be
reproduced by a classical theory where quadratures are stochastic -numbers.
The real part of the weak value is a conditional moment of the Margenau-Hill
distribution. The nonclassicality of coherent states can be associated with
negative values of the Margenau-Hill distribution. A more general type of weak
measurement is considered, where the pointer can be in an arbitrary state, pure
or mixed.Comment: 4 pages. Some arguments rewritten, reference added to
quant-ph/0402050. Conclusion unchange
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