The Greenberger–Horne–Zeilinger (GHZ) puzzle has been used to study quantum nonlocality and provide an all-or-nothing, no-go theorem for local hidden-variable models. Recent experiments using coincident-detected entangled photons prepared in a three-particle GHZ state have been used to test quantum nonlocality, but fail to rule out local realism due to a reliance on the fair-sampling hypothesis and insufficient detection efficiency. This paper describes a physically motivated local hidden-variable model based on amplitude-threshold detection that is capable of producing similar results. Detection efficiencies for the model are within the bounds permitted for local realism and, interestingly, exhibit statistical correlations between detectors, even when the detection events are spacelike separated. Increasing the detection threshold improves agreement with the ideal quantum predictions at the cost of decreased detection efficiency. A curious emergent feature of the model is that detection efficiencies may depend upon which observables are chosen for measurement.
The Greenberger–Horne–Zeilinger (GHZ) puzzle has been used to study quantum nonlocality and provide an all-or-nothing, no-go theorem for local hidden-variable models. Recent experiments using coincident-detected entangled photons prepared in a three-particle GHZ state have been used to test quantum nonlocality, but fail to rule out local realism due to a reliance on the fair-sampling hypothesis and insufficient detection efficiency. This paper describes a physically motivated local hidden-variable model based on amplitude-threshold detection that is capable of producing similar results. Detection efficiencies for the model are within the bounds permitted for local realism and, interestingly, exhibit statistical correlations between detectors, even when the detection events are spacelike separated. Increasing the detection threshold improves agreement with the ideal quantum predictions at the cost of decreased detection efficiency. A curious emergent feature of the model is that detection efficiencies may depend upon which observables are chosen for measurement.
An experiment has recently been performed to demonstrate quantum nonlocality by establishing contextuality in one of a pair of photons encoding four qubits; however, low detection efficiencies and use of the fair-sampling hypothesis leave these results open to possible criticism due to the detection loophole. In this Letter, a physically motivated local hidden-variable model is considered as a possible mechanism for explaining the experimentally observed results. The model, though not intrinsically contextual, acquires this quality upon post-selection of coincident detections. • A local hidden-variable model is applied to a recent quantum optics experiment. • The experiment was designed to demonstrate quantum nonlocality via local contextuality. • Using a single fitting parameter, the model accurately predicts the observed results.
The Greenberger-Horne-Zeilinger (GHZ) version of the Einstein-Podolsky-Rosen (EPR) paradox is widely regarded as a conclusive logical argument that rules out the possibility of describing quantum phenomena within the framework of any model of local hidden variables in which the observers are free to choose their own experimental settings. In this paper, we show, however, that the GHZ argument implicitly relies on a subtle, though crucial, assumption that is not required by fundamental physical principles, and which had gone unnoticed. Namely, we note that the argument implicitly assumes the existence of an absolute angular frame of reference with respect to which the polarization properties of the hypothetical hidden configurations of the entangled particles, as well as the orientations of the measurement devices that test them, can be defined. We further note that such an absolute frame of reference may not exist if the hidden configurations of the entangled particles spontaneously break the gauge rotational symmetry. Indeed, by skipping the disputed requirement we are able to build a model of local hidden variables for the GHZ state, which complies with the 'free-will' hypothesis and reproduces the quantum mechanical predictions. Our model, thus, completes-in the EPR sense-the quantum description of the GHZ state.
The Greenberger-Horne-Zeilinger~(GHZ) version of the Einstein-Podolsky-Rosen~(EPR) paradox is widely regarded as a conclusive logical argument that rules out the possibility of describing quantum phenomena within the framework of a local and realistic model of hidden variables in which the observers are free to choose their own experimental settings. In this paper we show, however, that the GHZ argument implicitly relies on an additional crucial assumption, which is not required by fundamental physical principles and had gone unnoticed. Namely, we note that the argument implicitly assumes the existence of an absolute angular frame of reference with respect to which the polarization properties of the hypothetical hidden configurations of the entangled particles as well as the orientation of the measurement apparatus that test the system can be defined. We further note that such an absolute frame of reference would not exist if the hidden configurations of the entangled particles spontaneously break the gauge rotational symmetry. Indeed, by skipping this unnecessary additional assumption we are able to build an explicitly local and realistic model of hidden variables for the GHZ state, which complies with the 'free-will' hypothesis and reproduces the quantum mechanical predictions, and thus completes the description of the system in the EPR sense.
The Greenberger-Horne-Zeilinger (GHZ) paradox, involving quantum systems with three or more subsystems, offers an 'all-vs-nothing' test of quantum nonlocality. Unlike Bell tests for bipartite systems, which reveal statistical contradictions, the GHZ paradox demonstrates a definitive (i.e. 100%) conflict between local hidden variable theories and quantum mechanics. Given this, how can the claim made in the title be justified? The key lies in recognising that GHZ games are typically played under a predefined promise condition for input distribution. By altering this promise, different GHZ games can be constructed. Here, we introduce a randomized variant of GHZ game, where the promise condition is randomly selected from multiple possibilities and revealed to only one of the parties chosen randomly. We demonstrate that this randomized GHZ paradox can also be perfectly resolved using a GHZ state, revealing a potentially stronger form of nonlocality than the original paradox. The claim of enhanced nonlocality is supported by its operational implications: correlations yielding perfect success in the randomized game offer a greater communication advantage than traditional GHZ correlations in a distributed multi-party communication complexity task.
A local hidden-variable model for tripartite GHZ states is constructed, in which a single threshold on the local signal magnitude governs detection and violates the fair-sampling assumption. The detection probability depends on the hidden variables, so the detected sample is unrepresentative, while the single-detector efficiency is independent of the polarizer settings. On the postselected sample the model violates the Mermin and Svetlichny inequalities, reaching M3=3.85 and S3=5.66, at a single-detector efficiency of 72.49%, below the threshold eta_crit=3/4 of Cabello et al.; the full ensemble satisfies both inequalities. A necessary upper bound eta <= 74.64% for the exact reproduction of the GHZ correlations by any model in this class is derived.
Introduction Since its inception, fifty years ago, Bell's theorem has had a long history not only of experimental tests but also of theoretical developments. Studying pairs of correlated quantummechanical particles separated in space, in a composite “entangled” state, Bell [1] showed that the joint ascription of hidden variables and locality to the system led to an inequality that is violated by the predictions of quantum mechanics. Fifteen years later, experiments confirmed the predictions of quantum mechanics, ruling out a large class of local realist theories. One of the most meaningful theoretical developments that followed Bell's work was the Greenberger–Horne–Zeilinger (GHZ) theorem, also known as Bell's theorem without inequalities. In 1989, the American physicists Daniel Greenberger and Michael Horne, who had been working on Bell's theorem since the late 1960s, together with the Austrian physicist Anton Zeilinger, introduced a novelty into the testing of entanglement, extending Bell's theorem in a different and interesting direction. According to Franck Laloë [2], For many years, everyone thought that Bell had basically exhausted the subject by considering all really interesting situations, and that two-spin systems provided the most spectacular quantum violations of local realism. It therefore came as a surprise to many when in 1989 Greenberger, Horne, and Zeilinger (GHZ) showed that systems containing more than two correlated particles may actually exhibit even more dramatic violations of local realism. The trio analyzed the Einstein, Podolsky, and Rosen 1935 argument once again and were able to write what are now called Greenberger–Horne–Zeilinger (GHZ) entangled states, involving three or four correlated spin-1/2 particles, leading to conflicts between local realist theories and quantum mechanics. However, unlike Bell's theorem, the conflict now was not of a statistical nature, as was the case with Bell's theorem, insofar as measurements on a single GHZ state could lead to conflicting predictions with local realistic models [3–5]. In this paper we present the history of the creation of this theorem and analyze its scope.