Quantum entanglement is known to give rise to nonlocal correlations that are not possible in a classical theory. Even though quantum correlations are stronger than classical correlations, they are still limited by the mathematical structure of quantum mechanics. Since physical limits usually emerge from physical principles, multiple principles were suggested in order to give a more physical explanation of the quantum limit on nonlocal correlations. None of these principles were able to completely rule out all super-quantum correlations. In this work, we study the principle of non-trivial communication complexity (NTCC), that sets a limit on what can be done in a particular information processing setting. Nonlocal correlations that violate this principle are believed to be impossible in nature. In this work, we expand the set of super-quantum correlations that are known to be ruled out by the NTCC principle, thus providing an explanation for their impossibility in quantum mechanics. We achieve this result by studying the consequences of more general super-quantum correlations in a protocol from Brassard, Buhrman, Linden, M ethot, Tapp and Unger. Additionally, we give a new proof of NTCC violation by a certain type of super-quantum correlations studied by Brunner and Skrzypczyk by describing and analyzing a simple and elegant protocol. Our work provides a framework for further studies of the consequences of super-quantum correlations on the NTCC principle.

Bell's theory of nonlocality in quantum mechanics allows for interesting correlations between separated parties. In this scenario, both parties share a quantum state and measure it to obtain a classical value. Through entanglement, the results of the measurement from one party can affect the results of the other party's measurement. Quantum correlations reflect this idea as a probability distribution p(ab|xy) based on the measurements used (x for Alice and y for Bob) and the respective results obtained (a and b). In this thesis, we introduce an expression that limits what quantum states could be used to generate a given quantum correlation. This, in turn, yields a lower bound on the dimension needed for this quantum state. For a quantum correlation p(ab|xy), the dimension of the quantum state acts as a resource needed to generate it. Thus, having a bound on the dimension helps one to quantify the resources needed to generate a given correlation. In addition to quantum correlations, we adjust the bound to work with classical correlations as well, which are correlations generated using a shared probability distribution instead of a quantum state. We apply our quantum and classical bounds to well-studied correlations to test them based on known results and also generate randomly generated correlations to better understand their behavior. Finally, we report on our numerical findings. / Master of Science / In quantum theory, the state of a quantum object, the simplest known as a qubit, can be manipulated from two or more different physical locations, even when they are not connected through any type of network. This is known as Bell's theory, and it allows for interesting behavior involving two or more separated locations that would not be possible otherwise. However, the minimum amount of resources needed for certain behaviors may be unknown. In this thesis, we present a lower bound on the quantum resources needed in such a scenario. We also apply it to the classical case and test our bounds on well-studied and randomized examples and report on our findings.

Non-local forces exist in nature for two reasons. First that the recent experiments on locality are supposed to be accurate enough. Second that there is no local theory that can reproduce all the predictions of orthodox quantum theory which, almost for about a century, have been proved to be correct experimentally again and again. This thesis concerns both of these. A brief discussion of the measurement in quantum theory is followed by two comments which show that the quantum description is frame dependent and that the collapse of the wave-function of a system may occur without the relevant measurement being performed. After this the Bohm model and a modified version of the Bohm model are described. Next we introduce a new method for obtaining the Bell-type inequalities which can be used for testing locality. We derive more inequalities by this method than obtained by other existing procedures. Using Projection Valued(PV) and Positive Operator Valued Measures(POVM) measurements we have designed experiments which violates one of the Bell inequalities by a larger factor than existing violations which in turn could increase the accuracy of experiments to test for non-locality. This is our first result. After discussing the non-locality and non-Lorentz invariant features of the Bohm model, its retarded version, namely Squires' model - which is local and Lorentz invariant - is introduced. A problem with this model, that is the ambiguity in the cases where the wave-function depends on time, is removed by using the multiple-time wave-function. Finally, we apply the model to one of the experiments of locality and prove that it is in good agreement with the orthodox quantum theory.

This report provides a new theoretical measure for the nonlocality of an arbitrary three-qubit pure state system similar to the method used to describe tripartite entanglement, resulting in a concept referred to as residual nonlocality, η. This report also investigates the special cases that can be encountered when using η. This method assigns a numerical value between 0 and 1 in order to indicate the degree of nonlocality between three-qubits. It was discovered that η has the characteristic of being consistently larger or equal to the value found for the residual entanglement which can provide further insights regarding the relation between nonlocality and entanglement. / I rapporten föreslås och analyseras ett nytt teoretisk mått för ickelokalitet hos tre-kvantbitsystem på ett liknande sätt till metoden som används för tredelad sammanflätningar. Detta ger en koncept som vi har valt att benämna residual ickelokalitet η. Rapporten undersöker också specialfall som kan påträffas när man använder η. Metoden som läggs fram i rapporten ger ett numeriskt värde mellan 0 och 1 för att visa graden av ickelokalitet mellan kvantbitarna. Vår undersökning visar att η kommer under alla sammanhang vara större eller lika med den graden av tredelad sammanflätning i samma system vilket kan ge en bättre förståelse av relationen mellan sammanflätning och ickelokalitet.

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.

Structures that demonstrate nonclassicality are of foundational interest in quantum mechanics, and can also be seen as resources for numerous applications in quantum information processing - particularly in the Hilbert space of N qubits. The theory of entanglement, quantum contextuality, and quantum nonlocality within the N-qubit Pauli group is further developed in this thesis. The Strong Kochen-Specker theorem and the structures that prove it are introduced and explored in detail. The pattern of connections between structures that show entanglement, contextuality, and nonlocality is explained. Computational search algorithms and related tools were developed and used to perform complete searches for minimal nonclassical structures within the N-qubit Pauli group up to values of N limited by our computational resources. Our results are surveyed and prescriptions are given for using the elementary nonclassical structures we have found to construct more complex types of such structures. Families of nonclassical structures are presented for all values of N, including the most compact family of projector-based parity proofs of the Kochen-Specker theorem yet discovered in all dimensions of the form 2N, where N>=2. The applications of our results and their connection with other work is also discussed.

Two chlorophylls of the FMO complex, the light-harvesting complex of the green sulfur bacteria, are modeled as two coupled qubits, each surrounded by one spin-bath simulating the environment. The dynamics of the system at a non-zero temperature provide exact analytical expressions for the transition probability and the coherence. It is shown that the decoherence-inducing interaction with the environment enhances the electronic energy transfer. Also the correlations in terms of entanglement and nonlocality are quantitatively studied, sensitively differing when introducing a decay term to resemble both chlorophylls being in their ground states. It is proved that nonlocality is a stronger form of correlation than entanglement.

In this paper, we introduce the motivation for Bell inequalities and give some background on two different types: CHSH and Mermin's inequalities. We present a proof for each and then show that certain quantum states can violate both of these inequalities. We introduce a new result stating that for four given measurement directions of spin, two respectively from Alice and two from Bob, which are able to produce a violation of the Bell inequality for an arbitrary shared quantum state will also violate the Bell inequality for a maximally entangled state. Then we provide another new result that characterizes all of the two-qubit states that violate Mermin's inequality.

<div>The widely accepted Non-equilibrium Greens functions (NEGF) method and the Self-Consistent Born Approximation, to include scattering, is employed. Due to the large matrix sizes typically needed when solving Greens functions, an efficient recursive algorithm is typically utilized. However, the current state of the art of this so-called recursive Greens function algorithm only allows the inclusion of local scattering or non-locality within a limited range. Most scattering mechanisms are Coulombic and are therefore non-local. Recently, we have developed an addition to the recursive Greens function algorithm that can handle arbitrary non-locality. Validation and performance will be assessed for nanowires.</div><div><br></div><div>The second half of this work discusses the modeling of an active ingredient in a liquid environment. The state of the art is outlined with options for different modeling approaches - mainly the implicit and the explicit solvation model. Extensions of the explicit model to include an open, quantum environment is the main work of the second half. First results for an extension of the commonly used molecular dynamics with thermodynamic integration are also presented.</div>

no / The finite set of subsystems of a finite quantum system with variables in Z(n), is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more general concept than superposition. Consequently, the quantum probabilities related to commuting projectors in the subsystems, are incompatible with associativity of the join in the Heyting algebra, unless if the variables belong to the same chain. This leads to contextuality, which in the present formalism has as contexts, the chains in the Heyting algebra. Logical Bell inequalities, which contain "Heyting factors," are discussed. The formalism is also applied to the infinite set of all finite quantum systems, which is appropriately enlarged in order to become a complete Heyting algebra.