The free will theorem states that if experimenters have free will in the sense that their choices are not a function of the past, so must some elementary particles. The theorem goes beyond Bell's theorem as it connects the two fundamental resources behind quantum technologies: single-particle contextuality, which supplies the power for quantum computation, and two-particle non-locality, which allows for quantum secure communication. The theorem relies on three axioms: (i) There is a maximum speed for propagation of information, (ii) single particles can exhibit contextuality, (iii) two separated particles can exhibit Einstein-Podolsky-Rosen (EPR) correlations. Here we report the first experimental test of the free will theorem. We used pairs of hyper-entangled photons entangled in path and polarization and enforced the conditions for invoking axiom (i) by measuring each photon in a different laboratory. We certified axiom (ii) by testing the violation of the Peres-Mermin non-contextuality inequality and axiom (iii) by showing EPR correlations between the two laboratories. The three axioms imply an upper bound on the sum of the correlations among the outcomes of sequential measurements in the same laboratory and the correlations between the outcomes in both laboratories. We observed a violation of this bound by more than 66 standard deviations. This reveals that quantum non-locality can be produced when single-particle contextuality is combined with correlations which are not non-local by themselves. Our results demonstrate the resources needed for quantum computation and quantum secure communication simultaneously in the same experiment and open the door to quantum machines that efficiently achieve both tasks.
The free will theorem states that if experimenters have free will in the sense that their choices are not a function of the past, so must some elementary particles. The theorem goes beyond Bell's theorem as it connects the two fundamental resources behind quantum technologies: single-particle contextuality, which supplies the power for quantum computation, and two-particle non-locality, which allows for quantum secure communication. The theorem relies on three axioms: (i) There is a maximum speed for propagation of information, (ii) single particles can exhibit contextuality, (iii) two separated particles can exhibit Einstein-Podolsky-Rosen (EPR) correlations. Here we report the first experimental test of the free will theorem. We used pairs of hyper-entangled photons entangled in path and polarization and enforced the conditions for invoking axiom (i) by measuring each photon in a different laboratory. We certified axiom (ii) by testing the violation of the Peres-Mermin non-contextuality inequality and axiom (iii) by showing EPR correlations between the two laboratories. The three axioms imply an upper bound on the sum of the correlations among the outcomes of sequential measurements in the same laboratory and the correlations between the outcomes in both laboratories. We observed a violation of this bound by more than 66 standard deviations. This reveals that quantum non-locality can be produced when single-particle contextuality is combined with correlations which are not non-local by themselves. Our results demonstrate the resources needed for quantum computation and quantum secure communication simultaneously in the same experiment and open the door to quantum machines that efficiently achieve both tasks.
Here we present an experiment which, firstly, demonstrates single-particle contextuality on the particles in one laboratory. Then, since our particles have been previously entangled with other particles in a distant laboratory, we can also reveal the EPR correlations between both laboratories. Interestingly, even though the correlations in the first laboratory can be explained by LHV theories, and the EPR correlations between the two laboratories can be explained by LHV theories, we show that there is no LHV theory explaining both of them. Our experiment is a test of the free will theorem since it implements the conditions under which axiom (i) applies, then checks axioms (ii) and (iii), and finally reveals an extreme violation of the predictions of theories in which elementary particles have no free will.
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an a priori different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure communication.
There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive strategy proposed by Cabello [Phys. Rev. Lett. 127, 070401 (2021)], Bell inequalities can be violated by state-independent contextuality sets. However, the experimental realization of such ideas is challenging as it requires high-dimensional entanglement. Orbital angular momentum provides an unlimited state space and the number of effective dimensions can be readily tailored as required. We performed an experimental test of non-locality based on Bell inequalities from contextuality, using orbital angular momentum entanglement in a bipartite photonic system. Our experiment not only shows a new way to produce non-locality but also connects contextuality and non-locality, two fundamental quantum resources that are critical for quantum computation and secure communication tasks.
The rapidly developing interdisciplinary field of quantum information, which merges quantum and information science, studies non-classical aspects of quantum systems. These studies are motivated by the promise that the non-classicality can be used to solve tasks more efficiently than classical methods would allow. In many quantum informational studies, non-classical behaviour is attributed to the notion of entanglement. In this thesis we use photons to experimentally investigate fundamental questions such as: What happens to the entanglement in a system when it is affected by noise? In our study of noisy entanglement we pursue the challenging task of creating bound entanglement. Bound entangled states are created through an irreversible process that requires entanglement. Once in the bound regime, entanglement cannot be distilled out through local operations assisted by classical communication. We show that it is possible to experimentally produce four-photon bound entangled states and that a violation of a Bell inequality can be achieved. Moreover, we demonstrate an entanglement-unlocking protocol by relaxing the condition of local operations. We also explore the non-classical nature of quantum mechanics in several single-photon experiments. In these experiments, we show the violation of various inequalities that were derived under the assumption of non-contextuality. Using qutrits we construct and demonstrate the simplest possible test that offers a discrepancy between classical and quantum theory. Furthermore, we perform an experiment in the spirit of the Kochen-Specker theorem to illustrate the state-independence of this theorem. Here, we investigate whether or not measurement outcomes exhibit fully contextual correlations. That is, no part of the correlations can be attributed to the non-contextual theory. Our results show that only a small part of the experimental generated correlations are amenable to a non-contextual interpretation.
In 1935, Einstein, Podolsky, and Rosen (EPR) argued that (then new) quantum mechanics was incomplete. At the heart of EPR’s paradox was the strange non-local nature of an entangled state which allowed EPR to simultaneously assign local values for position and momentum of a particle. In 1964, John Bell proposed an inequality (Bell’s inequality) that must be satisfied by any local realistic theory. The experimental confirmation of quantum physics, i.e., the experimental test of Bell’s inequality, required a pair of particles in an entangled state. The experiments first performed in the early 1970s, followed by a series of experiments until now, have confirmed the violation of Bell’s inequality, strongly implying that local realistic descriptions of nature are not consistent with experimental observations. The early simplistic view of entanglement has now been significantly expanded to include mixed states and multiple particles. Moreover, theoretical and experimental studies on the nature of entanglement have led to quantum information science where entanglement is an essential resource. In this article, we briefly review the early experiments on Bell’s inequality and experimental attempts to close “loopholes” as well as some key experiments on quantum information.
Quantum physics violates the basic assumptions of local realism. Particles can be entangled with each other in ways that allow correlations stronger than possible in classical physics. This was first realized by Einstein, Podolsky and Rosen (EPR) in 1935 and led them to conclude that quantum theory was incomplete. It took about 30 years before J. S. Bell found observable consequences of this phenomenon by showing how entangled states violate inequalities for two-particle correlations derived purely from the assumption that the world obeys local realism. Violations of Bell inequalities were first observed experimentally in the Aspect experiment, which will be discussed below. Such experiments are technically challenging and care is needed to avoid any loopholes in the experimental setup that would still permit the description of the experiments by a local realistic theory. Bell inequalities describe violations of local realism on average, meaning that each individual experimental outcome could occur in a local realistic theory. It is the statistics of these outcomes that violates local realism. In contrast, another class of quantum states, so-called Greenberger–Horne–Zeilinger (GHZ) states, which contain three particles, can be shown to violate local realism in each measurement outcome. We will also discuss this class of states and experiments by Zeilinger's group, which demonstrated this type of violation of local realism for the first time. Our aim here is not to discuss the exact relations between quantum entanglement, non-locality and realism, and their physical and philosophical implications. While this is a highly interesting topic which attracts a lot of attention from researchers, such an exploration would go beyond the scope of this book.