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arXiv:1608.03602

Experimental verification of a quantumness criterion for single systems based on a Bell-like inequality

Jhonny Castrillón, Omar Calderón-Losada, Guzmán, David A., Alejandra Valencia, Boris A. Rodrguez

Published Aug 11, 2016• 0 citations
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Abstract

In this letter, we propose and experimentally test a quantumness criterion for single systems. The criterion is based on the violation of an already reported classical inequality. This inequality is expressed in terms of joint probabilities that we identify as realizations of preparation-and-measurement schemes. Our analysis points out that superposition is the key notion to grasp the quantum nature of physical systems. We verify our criterion in an all-optical experimental setup with heralded single photons generated via spontaneous parametric down conversion and use exclusively projective preparations and projective measurements.

DOI
10.48550/arxiv.1608.03602

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In this letter, we propose and experimentally test a quantumness criterion for single systems. The criterion is based on the violation of an already reported classical inequality. This inequality is expressed in terms of joint probabilities that we identify as realizations of preparation-and-measurement schemes. Our analysis points out that superposition is the key notion to grasp the quantum nature of physical systems. We verify our criterion in an all-optical experimental setup with heralded single photons generated via spontaneous parametric down conversion and use exclusively projective preparations and projective measurements.
We report the first experimental violation of Bell's inequality in the spatial domain using the Einstein-Podolsky-Rosen state. Two-photon states generated via optical spontaneous parametric down-conversion are shown to be entangled in the parity of their one-dimensional transverse spatial profile. Superpositions of Bell states are prepared by manipulation of the optical pump's transverse spatial parity-a classical parameter. The Bell-operator measurements are made possible by devising simple optical arrangements that perform rotations in the one-dimensional spatial-parity space of each photon of an entangled pair and projective measurements onto a basis of even-odd functions. A Bell-operator value of 2.389+/-0.016 is recorded, a violation of the inequality by more than 24 standard deviations.
Different degrees of freedom of single photons have been entangled and are used as a resource for various quantum technology applications. We present a simple scheme to perform Bell's test and show the violation of CHSH inequality in a path-entangled single photon state using interferometric and its equivalent non-interferometric approach in beam splitter setting. We demonstrate this experimentally by generating and controlling path-entangled state using both, heralded and un-heralded single photons from spontaneous parametric down-conversion. The experimental results we present show the transition to violation of CHSH inequality when the purity of single photons state visibility increase above 70\% , P>0.7\mathcal{P} > 0.7P>0.7. Our procedure using single beam splitter and two detector module for un-heralded single photon source allows a simple way to test for purity of any single photon source and to study quantum correlations on systems driven by dynamics where single particle entanglement with position space is prominent.
Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of constructing joint probability distribution for all values of all the different properties observed in Bell inequality tests. Physically, the impossibility of measuring such distribution experimentally, as set of relative frequencies, is due to the quantum back-action of projective measurements. Weakly coupling to quantum probe, however, produces minimal back-action, and so enables weak measurement of the projector of one observable, followed by projective measurement of non-commuting observable. By this technique it is possible to empirically measure probabilities for all of the values of the observables relevant to Bell test. The marginals of this joint distribution, which we experimentally determine, reproduces all of the observable quantum statistics including violation of the Bell inequality, which we independently measure. This is possible because our distribution, like the weak values for projectors on which it is built, is not constrained to the interval [0, 1]. It was first pointed out by Feynman that, for explaining singlet-state correlations within a [local] hidden variable view of nature ... everything works fine if we permit negative probabilities. However, there are infinitely many such theories. Our method, involving weak-valued singles out unique set of probabilities, and moreover does so empirically.
Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of constructing a joint probability distribution for all values of all the different properties observed in Bell inequality tests. Physically, the impossibility of measuring such a distribution experimentally, as a set of relative frequencies, is due to the quantum back-action of projective measurements. Weakly coupling to a quantum probe, however, produces minimal back-action, and so enables a weak measurement of the projector of one observable, followed by a projective measurement of a noncommuting observable. By this technique it is possible to empirically measure weak-valued probabilities for all of the values of the observables relevant to a Bell test. The marginals of this joint distribution, which we experimentally determine, reproduces all of the observable quantum statistics including a violation of the Bell inequality, which we independently measure. This is possible because our distribution, like the weak values for projectors on which it is built, is not constrained to the interval [0,1][0,1][0,1]. It was first pointed out by Feynman that, for explaining singlet-state correlations within ``a [local] hidden variable view of nature \dots{} everything works fine if we permit negative probabilities.'' However, there are infinitely many such theories. Our method, involving ``weak-valued probabilities,'' singles out a unique set of probabilities, and moreover does so empirically.
We demonstrate hybrid entanglement of photon pairs via the experimental violation of a Bell inequality with two different degrees of freedom (DOF), namely, the path (linear momentum) of one photon and the polarization of the other photon. Hybrid entangled photon pairs are created by spontaneous parametric down conversion and coherent polarization to path conversion for one photon. For that photon, path superposition is analyzed, and polarization superposition for its twin photon. The correlations between these two measurements give an SSS parameter of $S=2.653\ifmmode\pm\else\textpm\fi{}0.027$ in a Clauser-Horne-Shimony-Holt inequality and thus violate local realism for two different DOF by more than 24 standard deviations. This experimentally supports the idea that entanglement is a fundamental concept which is indifferent to the specific physical realization of Hilbert space.
Recent experiments to test Bell's inequality using entangled photons and ions aimed at tests of basic quantum mechanical principles. Interesting results have been obtained and many loopholes could be closed. In this paper we want to point out that tests of Bell's inequality also play an important role in verifying atom entanglement schemes. We describe as an example a scheme to prepare arbitrary entangled states of N two-level atoms using a leaky optical cavity and a scheme to entangle atoms inside a photonic crystal. During the state preparation no photons are emitted and observing a violation of Bell's inequality is the only way to test whether a scheme works with a high precision or not.