Weak Measurements with Arbitrary Pointer States

The exact conditions on valid pointer states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any pointer state with vanishing probability current density. This condition is found both for weak measurements of noncommuting observables and for $c$-number observables. In addition, the interaction between pointer and object must be sufficiently weak. There is no restriction on the purity of the pointer state. For example, a thermal pointer state is fully valid.Comment: 4 page

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

Nonclassicality of Thermal Radiation

It is demonstrated that thermal radiation of small occupation number is strongly nonclassical. This includes most forms of naturally occurring radiation. Nonclassicality can be observed as a negative weak value of a positive observable. It is related to negative values of the Margenau-Hill quasi-probability distribution.Comment: 3 pages, 3 figure

Quantum theory of successive projective measurements

We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The complex modification term is a measure of measurement disturbance. A selective phase rotation is needed to obtain the imaginary part. This leads to a complex quasiprobability, the Kirkwood distribution. We show that the Kirkwood distribution contains full information about the state if the two observables are maximal and complementary. The Kirkwood distribution gives a new picture of state reduction. In a nonselective measurement, the modification term vanishes. A selective measurement leads to a quantum state as a nonnegative conditional probability. We demonstrate the special significance of the Schwinger basis.Comment: 6 page

Practical schemes for the measurement of angular-momentum covariance matrices in quantum optics

Original article can be found at: http://pra.aps.org/ Copyright American Physical Society. DOI: 10.1103/PhysRevA.78.043814We develop practical schemes for the measurement of the covariance matrix for intrinsic angular-momentum variables in quantum optics. We particularize this approach to two-beam polarimetry and interferometry, as well as to ensembles of two-level atoms interacting with classical fields. We show the practical advantages of noisy simultaneous measurements.Peer reviewe