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...

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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