Nonclassicality in weak measurements

Abstract

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 quasiprobability 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 non-negative. 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 contradict 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.

Nonclassical polarization dynamics in classical-like states

“…Nonetheless, there are some quantum approaches where these states also display nonclassical polarization features, as discussed in [54][55][56]. In this regard, a natural question that arises here is whether there is any relationship between the manifestation of nonclassical polarization in these approaches and the one discussed here within the Bohmian framework.…”

“…The Wigner distribution for Glauber coherent states is classical (it is everywhere positive definite), and consequently, one should go to nonlinear functions of the trajectories. This is because nonlinear local moments are related exclusively to Terletsky-Margenau-Hill [62], which is nonclassical for Glauber coherent states [54][55][56]. Regarding SU(2) coherent states, their characteristic trait is the presence of vortices governing the topology of the trajectories.…”

“…(7) provides the local value of a linear momentum. This can be suitably expressed as a local mean value of the momentum either via Wigner-Moyal phase-space distributions or via Terletsky-Margenau-Hill ones [57][58][59][60][61][62], which are the ones displaying nonclassical behavior in [54][55][56]. Trajectories displaying strange behaviors might then be regarded as the result of quantum polarization distributions incompatible with classical physics.…”

Linear response theory for open quantum systems within the framework of the ABL formalism

“…Furthermore, the weak value of an observable [9] has been found within the framework of the ABL formalism. The weak value has been attracted much attention and studied extensively due to the peculiarity and the potential applicability [10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Weak Values Influenced by Environment

“…It is surprising that the weak value may take a complex value or a value outside the range of the eigenvalues of an observable. After the discovery of the weak value of an observable, many works have been performed for understanding and generalizing weak values [3][4][5][6][7][8][9][10][11][12][13][14], and furthermore the weak value has been observed experimentally [15,16].…”