In this thesis, we experimentally test fundamental properties of quantum mechanics, namely \nnon-locality (in the form of three new families of Bell's inequalities) and the symmetry of \nenvariance. To accomplish these we use a Sagnac source of polarization entangled photon \npairs. \nIn chapters one and two we discuss the relevant background information in quantum \ninformation theory, nonlinear optics, experimental realization of polarization entangled \nphotons and a trouble-shooting and maintenance guide for a Saganc source. \nIn chapter three we experiment with a set of three newly derived families of Bell's \ninequalities. These three families are predicted to yield the largest volume of violation of \nthe local hidden variable models (LHVM). Our experimental results are in good agreement \nwith those predictions and therefore, represent the largest volume of experimental violation \nof LHVM to date. We showed a violation of up to 30 sigma from what is predicted by LHVM, \nand our results followed closely to the predictions of quantum mechanics. \nIn chapter four we experimentally test envariance, an assisted-symmetry exhibited by \nspecifi c quantum systems. Envariance is a fundamental property in the quantum world that \nhas lacked, until now, extensive experimental study. The symmetry has ramifi cations in the \nfoundations of quantum mechanics, and plays an integral role in a proof of Born's rule [1]. \nOur results serve as a benchmark the property of envariance. We show that experimental \nquantum states can be (99.66+/- 0.04)% envariant over a wide range of transformations, as \nmeasured using the average quantum fi delity [2], and (99.963 +/- 0.005)% as measured using \na modifi ed average Bhattacharya Coeffi cient [3], a measure of the overlap of two probability \ndistributions.
In this thesis, we experimentally test fundamental properties of quantum mechanics, namely \nnon-locality (in the form of three new families of Bell's inequalities) and the symmetry of \nenvariance. To accomplish these we use a Sagnac source of polarization entangled photon \npairs. \nIn chapters one and two we discuss the relevant background information in quantum \ninformation theory, nonlinear optics, experimental realization of polarization entangled \nphotons and a trouble-shooting and maintenance guide for a Saganc source. \nIn chapter three we experiment with a set of three newly derived families of Bell's \ninequalities. These three families are predicted to yield the largest volume of violation of \nthe local hidden variable models (LHVM). Our experimental results are in good agreement \nwith those predictions and therefore, represent the largest volume of experimental violation \nof LHVM to date. We showed a violation of up to 30 sigma from what is predicted by LHVM, \nand our results followed closely to the predictions of quantum mechanics. \nIn chapter four we experimentally test envariance, an assisted-symmetry exhibited by \nspecifi c quantum systems. Envariance is a fundamental property in the quantum world that \nhas lacked, until now, extensive experimental study. The symmetry has ramifi cations in the \nfoundations of quantum mechanics, and plays an integral role in a proof of Born's rule [1]. \nOur results serve as a benchmark the property of envariance. We show that experimental \nquantum states can be (99.66+/- 0.04)% envariant over a wide range of transformations, as \nmeasured using the average quantum fi delity [2], and (99.963 +/- 0.005)% as measured using \na modifi ed average Bhattacharya Coeffi cient [3], a measure of the overlap of two probability \ndistributions.
Bell's inequalities are important to our understanding of quantum foundations and critical to several quantum technologies. A recent work [E. Wolfe and S. F. Yelin, Phys. Rev. A 86, 012123 (2012)] derived three parametrized families of two-particle, two-setting Bell inequalities. These inequalities are important as they theoretically explore a larger volume of allowed quantum correlations over local hidden-variable models than previous results [A. Cabello, Phys. Rev. A 72, 012113 (2005)] by exploiting marginal, or single particle measurements. In this work we subject those predictions to experimental test using nonmaximally entangled photon pairs to optimize the expected violation. We find excellent agreement with the upper bounds predicted by quantum mechanics with violations of the limits imposed by local hidden-variable models as large as almost 30$\ensuremath{\sigma}$ for the optimal parameters and a significant violation over a wide range of parameters.
Entanglement is a key resource in many quantum information schemes and in the last years the research on multi-qubit entanglement has drawn lots of attention. In this thesis the experimental generation and characterisation of multi-qubit entanglement is presented. Specifically we have prepared entangled states of up to six qubits. The qubits were implemented in the polarisation degree of freedom of single photons. We emphasise that one type of states that we produce are rotationally invariant states, remaining unchanged under simultaneous identical unitary transformations of all their individual constituents. Such states can be applied to e.g. decoherence-free encoding, quantum communication without sharing a common reference frame, quantum telecloning, secret sharing and remote state preparation schemes. They also have properties which are interesting in studies of foundations of quantum mechanics. In the experimental implementation we use a single source of entangled photon pairs, based on parametric down-conversion, and extract the first, second and third order events. Our experimental setup is completely free from interferometric overlaps, making it robust and contributing to a high fidelity of the generated states. To our knowledge, the achieved fidelity is the highest that has been observed for six-qubit entangled states and our measurement results are in very good agreement with predictions of quantum theory. We have also performed another novel test of the foundations of quantum mechanics. It is based on an inequality that is fulfilled by any non-contextual hidden variable theory, but can be violated by quantum mechanics. This test is similar to Bell inequality tests, which rule out local hidden variable theories as possible completions of quantum mechanics. Here, however, we show that non-contextual hidden variable theories cannot explain certain experimental results, which are consistent with quantum mechanics. Hence, neither of these theories can be used to make quantum mechanics complete.
Over the past three decades or so, experiments of the type called Gedanken have become real. Recall the Schrödinger quote from Chapter 8: “… we never experiment with just one electron or atom or (small) molecule.” This is no longer true. We can do experiments involving single atoms or molecules and even on single photons, and thus it becomes possible to demonstrate that the “ridiculous consequences” alluded to by Schrödinger are, in fact, quite real. We have already discussed some examples of single-photon experiments in Chapter 6, and in Chapter 10 we shall discuss experiments performed with single atoms and single trapped ions. In the present chapter, we shall elaborate further on experimental tests of fundamentals of quantum mechanics involving a small number of photons. By fundamental tests we mean tests of quantum mechanics against the predictions of local realistic theories (i.e. hidden variable theories). Specifically, we discuss optical experiments demonstrating violations of Bell's inequalities, violations originally discussed by Bell in the context of two spin-one-half particles. Such violations, if observed experimentally, falsify local realistic hidden-variable theories. Locality refers to the notion, familiar in classical physics, that there cannot be a causal relationship between events with space-like separations. That is, the events cannot be connected by any signal moving at, or less than, the speed of light; i.e. the events are outside the light-cone. But in quantum mechanics, it appears that nonlocal effects, effects seemly violating the classical notion of locality in a certain restricted sense, are possible.
The nascent field of quantum information offers the promise of dramatic speed increases for certain types of computation and logical protocols which are classically impossible. The phenomenon of nonlocality is fundamental to this study, and polarization-entangled photons o er a clean, bright, and stable system for its experimental investigation. This thesis investigates, both experimentally and theoretically, the creation, manipulation, and measurement of polarization-entangled photon pairs. Our entangled photon pairs are created through spontaneous parametric down-conversion within a pair of adjacent, orthogonally oriented nonlinear crystals. The quality and brightness of this source is then dramatically improved through the use of birefringent crystals which compensate for an angle-dependent phase shift. The use of these compensation crystals has allowed measured count rates of two million pairs per second with 97.7% fidelity (with a maximally entangled state) or alternately, ten thousand pairs per second with 99.5% fidelity. By manipulating these entangled states, it is possible to study both how they change and how they can be used. We discuss the theory of state manipulation and the experimental implementation of extremely precise single-qubit operations. To study the operations themselves, we use quantum process tomography to characterize them and have successfully implemented the first experimental realization of ancilla-assisted process tomography. To study decoherence, we implemented the first experimental decoherence-free subspace. By using techniques developed during these investigations, we are able to transform our source of entangled photons into a source of any two-photon polarization state, mixed or pure. Developing new techniques for state creation and manipulation is possible because of simultaneous development in state measurement. In addition to detailing both a theoretical analysis and experimental instructions for state tomography, we experimentally and theoretically compared state tomography with tests of local realism (Bell inequalities) and entanglement witnesses (an entanglement detection technique). In the process, we have measured the largest violations of local realism to date, both statistical (over 2400-sigma) and absolute (S = 2:826 ± 0:005 -- within 0:2% of a maximal violation).
Quantum mechanics is undoubtedly a weird field of science, which violates many deep conceptual tenets of classical physics, requiring reconsideration of the concepts on which classical physics is based. For instance, it permits persistent correlations between classically separated systems, that are termed as entanglement. To circumvent these problems and explain entanglement, hidden variables theories--based on undiscovered parameters--have been devised. However, John S. Bell and others invented inequalities that can distinguish between the predictions of local hidden variable (LHV) theories and quantum mechanics. The CHSH-inequality (formulated by J. Clauser, M. Horne, A. Shimony and R. A. Holt), is one of the most famous among these inequalities. In the present work, we found that this inequality actually contains an even simpler logical structure, which can itself be described by an inequality and will be violated by quantum mechanics. We found 3 simpler inequalities and were able to violate them experimentally. Furthermore, the CHSH inequality can be used to devise games that can outperform classical strategies. We explore CHSH-games for biased and unbiased cases and present their experimental realizations. We also found a remarkable application of CHSH-games in real life, namely in the card game of duplicate Bridge. In this thesis, we have described this application along with its experimental realization. Moreover, non-local games with quantum inputs can be used to certify entanglement in a measurement device independent manner. We implemented this method and detected entanglement in a set of two-photon Werner states. Our results are in good agreement with theory. A peculiar form of entanglement that is not distillable through local operations and classical communication (LOCC) is known as bound entanglement (BE). In the present work, we produced and studied BE in four-partite Smolin states and present an experimental violation of a Bell inequality by such states. Moreover we produced a three-qubit BE state, which is also the first experimental realization of a tripartite BE state. We also present its activation, where we experimentally demonstrate super additivity of quantum information resources.
We describe an experimental test of local realistic and nonlocal realistic theories using polarization-entangled two-photon singlet states created using a fiber-based polarization Sagnac interferometer. We show a violation of Bell's inequality in the Clauser-Horne-Shimony-Holt form by 15 standard deviations, thus excluding local hidden-variable theories, and a violation of a Leggett-type nonlocal hidden-variable inequality by more than three standard deviations, thus excluding a class of nonlocal hidden-variable theories.