Complementarity and duality relations for finite-dimensional systems

Luis, Alfredo

doi:10.1103/physreva.67.032108

Cited by 39 publications

(32 citation statements)

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“…The weak value of an observable is also the optimal estimator of the observable between preselection and postselection [26]. The relation between the optimal estimator of an observable and phase-space distributions was examined in [27].…”

Section: Weak Measurementsmentioning

confidence: 99%

Nonclassicality in weak measurements

Johansen

Luis

2004

Phys. Rev. A

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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.

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Section: Weak Measurementsmentioning

confidence: 99%

Nonclassicality in weak measurements

Johansen

Luis

2004

Phys. Rev. A

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“…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.…”

Section: Final Remarksmentioning

confidence: 99%

“…(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.…”

Section: Final Remarksmentioning

confidence: 99%

Nonclassical polarization dynamics in classical-like states

Luis

Sanz

2015

Phys. Rev. A

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Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely, Glauber and SU(2) coherent states. Although these states are often regarded as classical, the analysis here shows that the corresponding electric-field polarization trajectories display topologies very different from those expected from classical electrodynamics. Rather than incompatibility with the usual classical model, this result demonstrates the dynamical richness of quantum motions, determined by local variations of the system quantum phase in the corresponding (polarization) configuration space, absent in classical-like models. These variations can be related to the evolution in time of the phase, but also to its dependence on configurational coordinates, which is the crucial factor to generate motion in the case of stationary states like those considered here. In this regard, for completeness these results are compared with those obtained from nonclassical NOON states.

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“…Barbieri et al (2009) recently verified Englert's duality relationship experimentally. The study of the canonical position and momentum operators has been extended to general canonically conjugate observables (Pegg et al 1990), and their properties explored using entropic uncertainty relations (Maassen & Uffink 1988;Rojas Gonzalez et al 1995) and other measures (Luis 2003). The related study of the approximate simultaneous measurement of non-commuting observables has also a long history (Arthurs & Kelly 1965;Luis 2004;Ozawa 2004 and references therein).…”

Section: Introductionmentioning

confidence: 99%

Particle-wave duality: a dichotomy between symmetry and asymmetry

Vaccaro

2011

Proc. R. Soc. A.

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Symmetry plays a central role in many areas of modern physics. Here, we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry, whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D), where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus a more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.

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Complementarity and duality relations for finite-dimensional systems

Cited by 39 publications

References 50 publications

Nonclassicality in weak measurements

Nonclassicality in weak measurements

Nonclassical polarization dynamics in classical-like states

Particle-wave duality: a dichotomy between symmetry and asymmetry

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