Optimization of a Pulsed Source of Entangled Photons for the Violation of the CHSH Inequality
This thesis focuses on my work carried out in the Quantum Communications laboratory with the Quantum Future research group of the Department of Information Engeneering, in which I worked on the creation and optimization of a pulsed source of polarization entangled photons. The main focus in the laboratory was to optimize the experimental setup to prove the entangled nature of the photons produced. This was done by violating the Bell inequality in the form presented by Clauser, Horne, Shimony and Holt (CHSH) in 1969. The present work's objective is to provide an overview of all the crucial physical phenomena exploited in the experiment to obtain the wanted results.
In section 1 a presentation of the phenomenon of entanglement and of Bell's argument proving the incapability to describe its properties with a both real and local theory is given, along with the derivation of the ``CHSH inequality and the possibility to violate it with polarization entangled photons. Sections 2 and 3 focus on the properties of the Gaussian beam used in the experiment and its source: the mode-locked Mira laser. A brief discussion about mode-locked lasers and their properties is provided. In section 4 the nonlinear optical phenomena of second harmonic generation and spontaneous parametric down conversion are discussed, the former from a classical standpoint and the latter with a few quantum mechanical considerations. Section 5 focuses on polarization optics and the both classical and quantum mechanical formalism of the Jones vectors. A discussion of the effects of the birefringent devices used in the experiment on the photons' state is provided. Finally, sections 6 and 7 display a complete overview of the experimental setup and the results obtained for the violation of the inequality. A systematic explanation of the experimental optimization procedure is provided in section 6 as it may be useful for the future experimenters, since it proved to be tricky.
Throughout all the work, various characteristics of the devices used in the experimental setup are given, hopefully making the most important and peculiar aspects of the experiment clear.
Optimization of a Pulsed Source of Entangled Photons for the Violation of the CHSH Inequality
This thesis focuses on my work carried out in the Quantum Communications laboratory with the Quantum Future research group of the Department of Information Engeneering, in which I worked on the creation and optimization of a pulsed source of polarization entangled photons. The main focus in the laboratory was to optimize the experimental setup to prove the entangled nature of the photons produced. This was done by violating the Bell inequality in the form presented by Clauser, Horne, Shimony and Holt (CHSH) in 1969. The present work's objective is to provide an overview of all the crucial physical phenomena exploited in the experiment to obtain the wanted results.
In section 1 a presentation of the phenomenon of entanglement and of Bell's argument proving the incapability to describe its properties with a both real and local theory is given, along with the derivation of the ``CHSH inequality and the possibility to violate it with polarization entangled photons. Sections 2 and 3 focus on the properties of the Gaussian beam used in the experiment and its source: the mode-locked Mira laser. A brief discussion about mode-locked lasers and their properties is provided. In section 4 the nonlinear optical phenomena of second harmonic generation and spontaneous parametric down conversion are discussed, the former from a classical standpoint and the latter with a few quantum mechanical considerations. Section 5 focuses on polarization optics and the both classical and quantum mechanical formalism of the Jones vectors. A discussion of the effects of the birefringent devices used in the experiment on the photons' state is provided. Finally, sections 6 and 7 display a complete overview of the experimental setup and the results obtained for the violation of the inequality. A systematic explanation of the experimental optimization procedure is provided in section 6 as it may be useful for the future experimenters, since it proved to be tricky.
Throughout all the work, various characteristics of the devices used in the experimental setup are given, hopefully making the most important and peculiar aspects of the experiment clear.
We theoretically and experimentally investigate the optimal conditions for the Bell experiment using spontaneous parametric down-conversion (SPDC) sources. In theory, we show that a relatively large average photon number (typically $\ensuremath{\sim}0.5$) is desirable to observe the maximum violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. Moreover, we show that the violation converges to 0.27 in the limit of large average photon number. In experiment, we perform the Bell experiment without postselection using polarization-entangled photon pairs at 1550-nm telecommunication wavelength generated from SPDC sources. While the violation of the CHSH inequality is not directly observed due to the overall detection efficiencies of our system, the experimental values agree well with those obtained by the theory with experimental imperfections. Furthermore, in the range of small average photon numbers ($\ensuremath{\le}0.1$), we propose and demonstrate a method to estimate the ideal CHSH value intrinsically contained in the tested state from the lossy experimental data without assuming the input quantum state.
In this thesis activity the candidate has explored the main aspects of Bell Inequalities
theory and eventually executed an experimental Violation test.
This work contains a brief overview of the theoretical aspects around Bell Inequalities:
the doubts arisen by Einstein, Podolski and Rosen about Quantum Theory completeness;
the hidden variable theories and the bounds on classical correlations; quantum
correlations and violation of Bell inequalities; the response given by Bell to the EPR
paradox by introducing its famous theorem. In addition, the entanglement phenomenon
has been studied, in particular in those dof that are given an important role in the violation
of Bell Inequalities. Some documentation work was also done on non linear optics
in order to understand fundamental effects that is common practice to exploit in the
photon entanglement generation: SHG for the pump photons, SPDC in non-linear crystals.
Moreover, the candidate also explored in this thesis some issues more closely related
to the experimental aspect:loopholes that could affect the integrity of Bell inequalities
proofs; efficiency threshold estimates regarding detection loophole; loophole-free configurations.
Eventually, here in this report are also showed, along with the experimental
setup brief description and some comments on the apparatus and its setting, the results
of an experimental test of the CHSH inequality violation using photons entangled at first
in polarization and then in a time-bin entanglement configuration.
Quantum mechanics is undoubtedly a weird field of science, which violates many deep conceptual tenets of classical physics, requiring reconsideration of the concepts on which classical physics is based. For instance, it permits persistent correlations between classically separated systems, that are termed as entanglement. To circumvent these problems and explain entanglement, hidden variables theories--based on undiscovered parameters--have been devised. However, John S. Bell and others invented inequalities that can distinguish between the predictions of local hidden variable (LHV) theories and quantum mechanics. The CHSH-inequality (formulated by J. Clauser, M. Horne, A. Shimony and R. A. Holt), is one of the most famous among these inequalities. In the present work, we found that this inequality actually contains an even simpler logical structure, which can itself be described by an inequality and will be violated by quantum mechanics. We found 3 simpler inequalities and were able to violate them experimentally. Furthermore, the CHSH inequality can be used to devise games that can outperform classical strategies. We explore CHSH-games for biased and unbiased cases and present their experimental realizations. We also found a remarkable application of CHSH-games in real life, namely in the card game of duplicate Bridge. In this thesis, we have described this application along with its experimental realization. Moreover, non-local games with quantum inputs can be used to certify entanglement in a measurement device independent manner. We implemented this method and detected entanglement in a set of two-photon Werner states. Our results are in good agreement with theory. A peculiar form of entanglement that is not distillable through local operations and classical communication (LOCC) is known as bound entanglement (BE). In the present work, we produced and studied BE in four-partite Smolin states and present an experimental violation of a Bell inequality by such states. Moreover we produced a three-qubit BE state, which is also the first experimental realization of a tripartite BE state. We also present its activation, where we experimentally demonstrate super additivity of quantum information resources.
Verifying the violation of Bell's inequality is one of the most representative methods to demonstrate that entangled photon pairs prepared in a quantum optics-based system exhibit quantum properties. While experiments on Bell inequality violations have been theoretically well-established and extensively conducted to implement various quantum information technologies in laboratory settings, mathematical modeling for systematically describing the distribution of high-brightness entangled photon pairs in high-loss environments remains an issue that requires further research. As the brightness of the entangled photon pairs increases, the influence of multi-photon effects becomes more significant, leading to a decrease in the CHSH valueSand also a reduction in the standard deviation of the CHSH valueΔS. Therefore, a new analysis of the(S−2)/ΔSvalue is required to more precisely confirm the degree of CHSH inequality violation including the reliability ofS. In this paper, we propose a mathematical model to predict the(S−2)/ΔSvalue as a function of the brightness of the entangled photon pair source, and we also suggest the need to optimize the brightness of this source. Additionally, we provide experimental evidence supporting this model. The experiment confirms that when the mean photon number isμ=0.026in an entanglement distribution setup with a total loss of−19.03dB, the CHSH value drops to 2.69, while the(S−2)/ΔSvalue increases to 60.95.
Verifying the violation of Bell's inequality is one of the most representative methods to demonstrate that entangled photon pairs prepared in a quantum optics-based system exhibit quantum properties. While experiments on Bell inequality violations have been theoretically well-established and extensively conducted to implement various quantum information technologies in laboratory settings, mathematical modeling for accurately predicting the distribution of high-intensity entangled photon pairs in high-loss environments remains an issue that requires further research. As the brightness of the entangled photon pairs increases, the influence of multi-photon effects becomes more significant, leading to a decrease in the CHSH value S and also a reduction in the standard deviation of the CHSH value ΔS. Therefore, a new analysis of the (S−2)/ΔS value is required to more precisely confirm the degree of CHSH inequality violation including the reliability of S. In this paper, we propose a mathematical model to predict the (S−2)/ΔS value as a function of the brightness of the entangled photon pair source, and we also suggest the need to optimize the brightness of this source. Additionally, we provide experimental evidence supporting this model. The experiment confirms that when the mean photon number is μ=0.026 in an entanglement distribution setup with a total loss of −19.03 dB, the CHSH value drops to 2.69, while the (S−2)/ΔS value increases to 60.95.