In this note, I analyze the data generated by M. Fodje's (2013, 2014) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions showed that they made use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signalling. His coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.
In this note, I analyze the data generated by M. Fodje's (2013, 2014) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions showed that they made use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signalling. His coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.
In this note, I analyze the data generated by M. Fodje's (2013) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions shows that they make use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signaling. Fodje's coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.
In this note, I analyze the data generated by M. Fodje's (2013) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions shows that they make use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signaling. Fodje's coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.
In this note, I analyze the code and the data generated by M. Fodje's (2013) simulation programs "epr-simple" and "epr-clocked". They were written in Python published on Github only, initially without any documentation at all of how they worked. Inspection of the code showed that they made use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signaling. The coincidence-loophole model is actually a clever modification of the detection-loophole model. Because of this, however, it cannot lead to optimal efficiency. Later versions of the programs included an explanation of how they worked, including formulas, though still no reference whatever to the literature on the two loopholes which Fodje exploits, not even to the concept of an experimental (i.e., in principle, avoidable) loophole. The documentation available now does make a lot of the "reverse engineering" in this paper superfluous. I plan to incorporate its results in a new paper with a wider focus.
The aim of this study is to produce a simulation of EPR experiments violating the CHSH-Bell inequalities using physically interpretable objects (properties defined before measurement) and interactions (no supraliminal communication), without influence from any theory. It turns out that the proposed model systematically violates the CHSH-Bell inequalities reaching all the values ( 2 ≤ S ≤ 4 ) . Our simulation reproduces experimental entanglements with greater efficiency. This approach has at least two consequences. First, it demonstrates that violations of the CHSH-Bell inequalities are possible while still verifying the principles of realism and locality, but in a different sense from that of Bell’s theorem. Therefore, Bell’s theorem itself is not called into question, nor are the results of the EPR experiments. However, it is the deduction that leads to the current interpretation (often described as strange because it does not follow one of the principles of realism and locality as defined by Bell’s theorem) that is challenged. Second, it challenges real-world EPR experiments to exceed the efficiency rates of our simulation. Our idealization demonstrates that, between the efficiency rates required to confirm the violation of Bell’s inequalities and the efficiency rates of our idealization, the interpretation of experiments remains possible within a framework of “classical” physical principles (properties defined before measurement and no supraliminal communication). Confirming the strangeness of quantum mechanics would therefore require obtaining efficiency rates higher than those of Bell’s theorem.
Let us imagine an experimentalist, who has maximally entangled photons and wants to violate Bell’s inequality in his laboratory. Among many obstacles he has to overcome, two of them are the most significant. Firstly, he has to avoid exchanging information about the measurement settings between the particles. Secondly, he has to detect particles with a high enough probability, because if the detection efficiency is too low, one can reproduce quantum correlations using a LHV (Local Hidden Variables) model. These two problems are known in the literature, respectively, as the locality loophole [1] and the detection loophole [2, 3]. Fortunately, it is possible to close the locality loophole using photons in the experiment [4, 5, 6, 7, 8]. However, closing the detection loophole is still an object of study. The authors of [9] showed that for the CHSH inequality, the lower bound for detector efficiency needed to close the loophole is 82.8% for maximally entangled states. This bound was lowered to 66.7% by Eberhard [10]. Furthermore, the detector efficiency has been studied for other Bell inequalities [11, 12, 13, 14, 15, 16]. In our research, we are trying to answer the following question: If we prepare a Bell experiment and we have two detectors, having different efficiencies both smaller than 100%, which detector should each party receive? And also: Which representation of the chosen Bell inequality should we consider? These are very crucial questions, which arise in laboratories. Hence, we hope that our results will be useful for experimentalists. We focus on the I3322 inequality [17], which is a natural candidate for testing, because of its asymmetry [14, 18]. We consider the case of a post-selection strategy, which consists in rejecting all the rounds in the Bell experiment when one of the detectors does not click. We used numerical optimisation methods to find both the best classical strategy for Alice and Bob and the best detector clicking strategy. Thus, we have found minimal efficiencies of the detectors of Alice and Bob needed to violate I3322. We made the same studies also for symmetric representations of I3322 [19]. Our results show that the minimal efficiencies of Alice and Bob’s detectors of the asymmetric representation of I3322 is lower than in case of the symmetric one [20]. It is work in progress, and we are examining other post-selection methods as well as other Bell inequalities. We want to consider also the case when non-maximally entangled states are used in Bell experiments.
A local hidden-variable model is constructed for the postselected correlations of nonmaximally entangled photon pairs in the states |Phi_r> and |Psi_r>, continuous in r over [-1,1] from the product state to the maximally entangled state. Its root-mean-square deviations from the quantum correlations and from the coincidence probabilities, averaged over a uniform grid of polarizer angles, are 0.0322 and 0.0233, smaller than those of the sigmoid-threshold model of Ref. [14] by factors of 2.7 to 3.5. The source emits a photon pair with a probability that depends on the hidden variable and on r; each station detects with a probability that depends on the local hidden variable and on the local polarizer angle. This dependence violates the fair-sampling assumption and exploits the detection loophole. On the postselected sample the model violates the CHSH inequality for |Phi_r>, reaching 2*sqrt(2) at |r|=1, with single-detector efficiency ≈ 85%, outside the assumptions of both the CHSH inequality and Mermin's 82.8% efficiency bound. The CH--Eberhard parameter, which does not assume fair sampling, satisfies J<0 over the full entanglement range.