In this letter, we present a new procedure to determine completely the complex modular values of arbitrary observables of pre-and post-selected ensembles, which works experimentally for all measurement strengths and all post-selected states. This procedure allows us to discuss the physics of modular and weak values in interferometric experiments involving a qubit meter. We determine both the modulus and the argument of the modular value for any measurement strength in a single step, by controlling simultaneously the visibility and the phase in a quantum eraser interference experiment. Modular and weak values are closely related. Using entangled qubits for the probed and meter systems, we show that the phase of the modular and weak values has a topological origin. This phase is completely defined by the intrinsic physical properties of the probed system and its time evolution. The physical significance of this phase can thus be used to evaluate the quantumness of weak values.In 1988, Aharonov, Albert, and Vaidman (AAV) introduced the weak value of a quantum observable from an extension of the von Neumann measurement scheme [1]. They pointed out that the result of a measurement involving a weak coupling between a meter and the observable of a system with a pre-selected initial state |ψ i , and a post-selected final state |ψ f depends directly on the weak value:an unbounded complex number. In particular, they showed that the shift of the average detected position due to post-selection is proportional to the real part of the weak value. Since for weak measurements in the absence of post-selection, this shift is proportional to the average of the observable ψ i |Â|ψ i / ψ i |ψ i , a direct but bold physical interpretation of the weak value assumes it represents somehow the average of in the pre-and post-selected ensemble. They also related the imaginary part of the weak value to the shift of the average impulsion. Beside the AAV approach, weak values may also appear using a meter strongly coupled to the observablê A [2][3][4][5][6][7]. In these instances, the effective weak interaction is achieved by selecting particular initial states of the meter system, so that the probability of actually measurinĝ A is low and the probed system is left unperturbed most of the time. Therefore, both methods transform the standard von Neumann procedure to a weak measurement with a high incertitude. Weak values and weak measurements proved useful in many fields of physics and chemistry [8][9][10][11][12][13][14][15][16][17][18][19][20]. Nevertheless, the proper physical interpretation of weak values remains highly debated. For example, weak values were used to develop a time-symmetrized approach to standard quantum theory, the two-state vector formalism [21], where they appear as purely quantum objects.Oppositely, a purely classical view of the occurrence of unbounded, real weak values -and possibly of complex ones -was proposed recently [22] (which is criticizable though [23-25]).In this letter, we uncover a physical interpretati...

Abstract. We express modular and weak values of observables of three-and higherlevel quantum systems in their polar form. The Majorana representation of N -level systems in terms of symmetric states of N − 1 qubits provides us with a description on the Bloch sphere. With this geometric approach, we find that modular and weak values of observables of N -level quantum systems can be factored in N −1 contributions. Their modulus is determined by the product of N −1 ratios involving projection probabilities between qubits, while their argument is deduced from a sum of N − 1 solid angles on the Bloch sphere. These theoretical results allow us to study the geometric origin of the quantum phase discontinuity around singularities of weak values in three-level systems. We also analyze the three-box paradox [1] from the point of view of a bipartite quantum system. In the Majorana representation of this paradox, an observer comes to opposite conclusions about the entanglement state of the particles that were successfully preand postselected.arXiv:1612.07023v2 [quant-ph]

Insertion of 2D materials in optical systems modifies their electrodynamical response. In particular, the Brewster angle undergoes an up-shift if a substrate is covered with a conducting 2D material. This work theoretically and experimentally investigates this effect related to the 2D induced current at the interface. The shift is predicted for all conducting 2D materials and tunability with respect to the Fermi level of graphene is evidenced. Analytical approximations for high and low 2D conductivities are proposed and avoid cumbersome numerical analysis of experimental data. Experimental demonstration using spectroscopic ellipsometry has been performed in UV to NIR range on mono-, bi-and trilayer graphene samples. The non-contact measurement of this modified Brewster angle allows to deduce the optical conductivity of 2D materials. Applications to telecommunication technologies can be considered thanks to the tunability of the shift at 1.55 µm.

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We performed quantum tomography to reveal the robustness of quantum correlations of photons entangled in polarisation after their interaction with plasmonic and nonplasmonic environments at normal incidence. The experimental findings clearly show that the visibility of quantum correlations survives the interaction, and that the presence of plasmonic resonances has not any significant influence on the survival of polarisation correlations for transmitted photon pairs. The results indicate that quantum states can be encoded into the multiple motions of a many-body electronic system without demolishing their quantum nature. The plasmonic structures and their resonances only enhance the overall transmission. Thus, they could benefit the pair detection rate, that is the number of coincidences per unit of time, but they do not affect the visibility of quantum correlations. We also performed quantum tomography of the entangled pairs after interaction with the continuous planar gold film as a function of the incidence angle. The latter illustrates the loss of polarization correlations that arises from the partially polarizing properties of the isotropic sample out of normal incidence. Our work shows that plasmonic structures are not needed to exploit quantum entanglement if the rate of coincidence counting is sufficient.

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Heterostructures combining graphene layers, dielectric slabs and even metallic substrates are interesting systems to look at in view of their potential applications in microwaves and terahertz. A short review of their properties is presented, together with possible applications such as shielding layers, polarizers and plasmonic devices. In the near infrared and visible range, a graphene layer modifies the Brewster angle of the substrate that supports it. This effect leads to a non-destructive technique to count the number of atomic planes the graphene is made of.