We describe a simple experimental setting where joint measurements performed on a single (classical or quantum) entity can violate both the Bell-CHSH inequality and the marginal laws (also called no-signaling conditions). Once emitted by a source, the entity propagates within the space of Alice’s and Bob’s detection screens, with the measurements’ outcomes corresponding to the entity being absorbed or not absorbed in a given time interval. The violation of the marginal laws results from the fact that the choice of the screen on the side of Alice affects the detection probability on the side of Bob, and vice versa, and we show that for certain screen choices, the Bell-CHSH inequality can be violated up to its mathematical maximum. Our analysis provides a clarification of the mechanisms that could be at play when the Bell-CHSH inequality and marginal laws are violated in entangled bipartite systems, which would not primarily depend on the presence of a bipartite structure but on the fact that the latter can manifest as an undivided whole.
We describe a simple experimental setting where joint measurements performed on a single (classical or quantum) entity can violate both the Bell-CHSH inequality and the marginal laws (also called no-signaling conditions). Once emitted by a source, the entity propagates within the space of Alice’s and Bob’s detection screens, with the measurements’ outcomes corresponding to the entity being absorbed or not absorbed in a given time interval. The violation of the marginal laws results from the fact that the choice of the screen on the side of Alice affects the detection probability on the side of Bob, and vice versa, and we show that for certain screen choices, the Bell-CHSH inequality can be violated up to its mathematical maximum. Our analysis provides a clarification of the mechanisms that could be at play when the Bell-CHSH inequality and marginal laws are violated in entangled bipartite systems, which would not primarily depend on the presence of a bipartite structure but on the fact that the latter can manifest as an undivided whole.
It is already known that one can always find a set of measurements on any two-qubit entangled state that will lead to a violation of the CHSH inequality. We provide an explicit state in terms of the angle between Alice's choice of measurements and the angle between Bob's choice of measurements, such that the CHSH inequality is always violated provided Alice's or Bob's choice of inputs are not collinear. We prove that inequalities with a corresponding Bell operator written as a linear combination of tensor products of Pauli matrices, excluding the identity, will generate the most nonlocal correlations using maximally entangled states in our experiment. From this result and a proposition from Horodecki et. al., we are able to construct the state that generates these optimal correlations. To achieve this state in a lab, one party must rotate their qubit using the orthogonal operation we provide and also rotate their Bloch sphere such that all their measurements lie in the same plane. We provide a comprehensive study of how Bell inequalities change when experiments introduce error via imperfect detection efficiency. The original cases of perfect efficiency are covered first and then a more realistic approach, when inefficient detectors are used, will follow. It is shown that less entanglement is needed to demonstrate more nonlocality in some Clasure-Horne-Shimony-Holt (CHSH) experiments when detector inefficiency is introduced. An example of this is shown for any given specific set of measurements in the CHSH Bell experiment. This occurs when one party has a detector of efficiency for each choice of input and the other party makes projective measurements. The efficiency can be pushed down to fifty percent while still violating the CHSH inequality, and for the experimental set-up illustrated, there is more nonlocality with less entanglement. Furthermore, it is shown that if the first party has an imperfect detector for only one choice of inputs rather than two, the efficiency can be brought down arbitrarily close to zero percent while still violating the CHSH inequality. Historically, nonlocality and entanglement were viewed as two equivalent resources, but recently this equality has come under question; these results further support this fundamental difference. Further more, we introduce Mermin's game in the case of relaxed conditions. The original constraints were that when the detectors in separate labs of a two-qubit experiment are in the same setting, then the results should be the same. We require that the outcomes are the same at least part of the time, given by some epsilon variable. Initially, one could find a maximum violation of one-fourth by allowing to parties to share the singlet state and have measurement settings one-hundred and twenty degrees apart from one another. By allowing some epsilon error in the perfect correlations regime, one can find a maximum violation of minus one plus the square root of two using the singlet state and measurement inputs that achieve Tsirelson's bound for the CHSH experiment. The reason is that we show Mermin's inequality is technically the CHSH inequality "in disguise", but with using constraints the CHSH experiment does not use. We derive Mermin's inequality under new conditions and give the projective measurements needed to violate maximally.
Abstract We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence measurements are considered, the violation of the ‘marginal laws’, in addition to the Bell-CHSH inequality, is also to be expected. The situation can be described in the quantum formalism by considering the presence of entanglement not only at the level of the states, but also at the level of the measurements. However, at the “local” level of a specific joint measurement, a description where entanglement is only incorporated in the state remains always possible, by adopting a fine-tuned tensor product representation. But contextual tensor product representations should only be considered when there are good reasons to describe the outcome-states as (non-entangled) product states. This will not in general be true, hence, the entanglement resource will have to generally be allocated both in the states and in the measurements. In view of the numerous violations of the marginal laws observed in physics’ laboratories, it remains unclear to date if entanglement in micro-physical systems is to be understood only as an ‘entanglement of the states’, or also as an ‘entanglement of the measurements’. But even if measurements would also be entangled, the corresponding violation of the marginal laws (also called ‘no-signaling conditions’) would not for this imply that a superluminal communication would be possible.
Alice and Bob each have half of a pair of entangled qubits. Bob measures his half and then passes his qubit to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with the single Alice. This scenario was introduced in [R. Silva et al., Phys. Rev. Lett. 114, 250401 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.250401] where the authors mentioned evidence that when the Bobs act independently and with unbiased inputs then at most two of them can expect to violate the CHSH inequality with Alice. Here we show that, contrary to this evidence, arbitrarily many independent Bobs can have an expected CHSH violation with the single Alice. Our proof is constructive and our measurement strategies can be generalized to work with a larger class of two-qubit states that includes all pure entangled two-qubit states. Since violation of a Bell inequality is necessary for device-independent tasks, our work represents a step towards an eventual understanding of the limitations on how much device-independent randomness can be robustly generated from a single pair of qubits.
Bell inequalities are usually derived by assuming locality and realism, and therefore experimental violations of Bell inequalities are usually taken to imply violations of either locality or realism, or both.But, after reviewing an oversight by Bell, here we derive the Bell-CHSH inequality by assuming only that Bob can measure along the directions b and b ′ simultaneously while Alice measures along either a or a ′ , and likewise Alice can measure along the directions a and a ′ simultaneously while Bob measures along either b or b ′ , without assuming locality.The observed violations of the Bell-CHSH inequality therefore simply verify the manifest impossibility of measuring along the directions b and b ′ (or along the directions a and a ′ ) simultaneously, in any realizable EPR-Bohm type experiment.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation. In particular, within the framework of a standard Bell experiment, i.e., a Bell inequality test that is directly performed on a single copy of a quantum state r, we have derived two algorithms to determine, respectively, a lower bound and an upper bound on the strength of correlations that r can offer for any given Bell inequality. Both of these algorithms make use convex optimization techniques in the form of a semidefinite program. By examples, we show that these algorithms can often be used in tandem, in conjunction with convexity arguments, to determine if a quantum state can offer nonclassical correlations and hence violates a given Bell inequality. On the other hand, since a standard Bell experiment typically involves measurements over many copies of the quantum systems, we have also investigated the possibility of enhancing the strength of nonclassical correlation by, instead, performing collective measurements on multiple copies of the quantum systems. Our findings show that even without postselection, such joint measurements may also lead to stronger nonclassical correlations, and hence a better Bell inequality violation. Meanwhile, previous studies have indicated that entangled state admitting locally causal models may still lead to observable nonclassical correlations if, prior to a standard Bell experiment, the state is subjected to some appropriate local preprocessing. This phenomenon of hidden nonlocality was discovered more than a decade ago, but to date, it is still not known if all entangled states can demonstrate nonclassical correlations through these more sophisticated Bell experiments. A key result in this thesis then consists of showing that for all bipartite entangled states, observable nonclassical correlations, in the form of a Bell-CHSH inequality violation, can indeed be derived if we allow both local preprocessing and the usage of shared ancillary state which by itself does not violate the Bell-CHSH inequality. This establishes a kind of equivalence between bipartite entanglement and states that cannot be simulated by classical correlations. In summary, for a standard Bell experiment where no local preprocessing on a quantum state r is allowed, we have provided two algorithms that can be used in tandem to determine if r can be simulated by a locally causal theory, whereas in the scenario where local preprocessing is allowed, we have demonstrated that bipartite entangled states are precisely those which cannot always be simulated classically.
Summary form only given. In a Bell experiment, one prepares pairs of entangled particles and sends them to two observers, Alice and Bob, for measurement and detection [1]. For some choices of their measurement settings, Alice and Bob may observe strong correlations between their results in accordance with the predictions of quantum mechanical theory. Conversely, any physical theory that assumes no physical influence can be faster than the speed of light and that properties of physical systems are elements of reality [2] - a local realistic theory - can predict only a limited amount of correlation between Alice's and Bob's measurement outcomes. Upon observing correlations sufficient to violate Bell's inequality, Alice and Bob must abandon local realism.It is common that in an experiment, some particles emitted by the source will not be detected. Then the subset of detected particles might display correlations that violate the Bell inequality although the entire ensemble can be described by a local realistic theory [3]. To achieve a conclusive Bell violation without assuming that the detected particles are a “fair” sample, a highly efficient setup is necessary. Due to experimental limitations, fair sampling has been assumed in most Bell experiments performed to date, and it has never been possible to avoid this assumption with photons due to the absence of efficient sources and detectors. Here we report the first Bell experiment with photons that does not rely on any fair-sampling assumption. In our experiment we employ the Eberhard inequality, a Bell inequality that by construction does not rely on the fair-sampling assumption [4]. Our source of entangled photon pairs utilizes bulk-crystal spontaneous parametric downconversion in a Sagnac configuration, which has shown to be very efficient [5, 6]. For photon detection, we employ superconducting transition-edge sensors, which not only offer high efficiency but also are intrinsically free of dark counts [7]. This combination of features is imperative for an experiment in which no correction of count rates can be tolerated. We achieve uncorrected coupling efficiencies over 73% in each arm of our source, facilitating a violation of the inequality by nearly 70 standard deviations after five minutes of measurement. Since the first experimental Bell test, a satisfactory laboratory realization of the motivating gedankenexperiment has remained an outstanding challenge. The two other main assumptions include “locality” [8, 9] and “freedom of choice” [10]. Invoking any of these renders an experiment vulnerable to explanation by a local realistic theory. The realization of an experiment that is free of all three assumptions-a so-called loopholefree Bell test-remains an important outstanding goal for the physics community with strong implications for quantum technologies. We note that with our experiment, photons are the first physical system for which each of these three assumptions has been successfully addressed, albeit in different experiments. This represents promise for practical applications like one-sided device-independent quantum key distribution [11], and in an additional test, we also demonstrate that our experimental apparatus is capable of implementing this protocol on both sides.