Finding the boundary between quantum and classical domains is very much an open question that is fundamental to a great deal of research spanning across many physics communities. The division is not clear cut and a deeper understanding is necessary for the future generation and engineering of quantum devices. In this thesis we introduce and apply a variety of tests that will reveal non classicality in real physical systems. The systems that we consider in many instances can be deemed classical and so our study is well motivated by the endeavor to explain the quantum to classical transition. We investigate three main classes of nonclassicality tests: Bell non locality, Kochen-Specker quantum contextuality and violation of Leggett-Garg macrorealism. These tests are applied to specific continuous variable systems that live in infinite dimensional Hilbert spaces and represent various states of the electromagnetic field. Firstly we test non locality in multimode versions of the thermal state. We show numerous violations of relevant Bell inequalities under quite unfavorable conditions and include state generation schemes. We then demonstrate through the violation of a Kochen-Specker inequality the state-independent quantum contextuality of a range of continuous variable states. These states include variations of entangled coherent states, a two-mode squeezed state and states represented by a generalized quasi-probability function. In what follows in the thesis we study non-locality of the nonclassical state of a system consisting of a qubit and an oscillator exposed to the effects of non-Markovian evolutions. Here we show interesting features related to the various facets with which non-Markovianity manifests itself. Finally this work tests macroscopic realism of a coherent and thermal state. We successively show violation of a Leggett-Garg inequality for a range of coherent state amplitude and degree of thermal mixedness.
Finding the boundary between quantum and classical domains is very much an open question that is fundamental to a great deal of research spanning across many physics communities. The division is not clear cut and a deeper understanding is necessary for the future generation and engineering of quantum devices. In this thesis we introduce and apply a variety of tests that will reveal non classicality in real physical systems. The systems that we consider in many instances can be deemed classical and so our study is well motivated by the endeavor to explain the quantum to classical transition. We investigate three main classes of nonclassicality tests: Bell non locality, Kochen-Specker quantum contextuality and violation of Leggett-Garg macrorealism. These tests are applied to specific continuous variable systems that live in infinite dimensional Hilbert spaces and represent various states of the electromagnetic field. Firstly we test non locality in multimode versions of the thermal state. We show numerous violations of relevant Bell inequalities under quite unfavorable conditions and include state generation schemes. We then demonstrate through the violation of a Kochen-Specker inequality the state-independent quantum contextuality of a range of continuous variable states. These states include variations of entangled coherent states, a two-mode squeezed state and states represented by a generalized quasi-probability function. In what follows in the thesis we study non-locality of the nonclassical state of a system consisting of a qubit and an oscillator exposed to the effects of non-Markovian evolutions. Here we show interesting features related to the various facets with which non-Markovianity manifests itself. Finally this work tests macroscopic realism of a coherent and thermal state. We successively show violation of a Leggett-Garg inequality for a range of coherent state amplitude and degree of thermal mixedness.
We investigate the violation of noncontextuality by a class of continuous-variable states, including variations of entangled coherent states and a two-mode continuous superposition of coherent states. We generalize the Kochen-Specker (KS) inequality discussed by Cabello [A. Cabello, Phys. Rev. Lett. 101, 210401 (2008)] by using effective bidimensional observables implemented through physical operations acting on continuous-variable states, in a way similar to an approach to the falsification of Bell-Clauser-Horne-Shimony-Holt inequalities put forward recently. We test for state-independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudospin observables and a generalized quasiprobability function.
I study several aspects of tests of macrorealism (MR), which for a given data set serves to give a quantitative signal of the presence of a specific notion of non-classical behaviour. The insufficiency of classical understanding underpins both the paradoxes of quantum mechanics, its future technological promise, and so these tests are of interest both foundationally and pragmatically. I derive generalisations of the Leggett-Garg (LG) inequalities and Fine's theorem, which together establish the necessary and sufficient conditions for macrorealism. First, I extend these conditions to tests involving an arbitrary number of measurement times. Secondly, I generalise them beyond the standard dichotomic variable, to systems described by many-valued variables. I also perform a quantum mechanical analysis examining the interplay of different conditions of MR. I then develop the theoretical framework to support tests of macrorealism in continuous variable systems, where I define variables based on coarse-grainings of position. I calculate temporal correlators for general bound systems, and analyse LG violations within the quantum harmonic oscillator (QHO), in its energy eigenstates and coherent states. I analyse the precise physical mechanisms underpinning the violations in terms of probability currents, Bohm trajectories. Staying within continuous variable systems, we outline a different approach to meeting the invasiveness requirement of LG tests. Reasoning that we may approximately non-invasively measure whether a particle crosses the axis, we measure an object which is related to the standard correlators, and derive a set of macrorealistic inequalities for these modified correlators. We demonstrate violations of these modified LG inequalities for several states within the QHO.
While quantum theory has been tested to an incredible degree on microscopic scales, quantum effects are seldom observed in our everyday macroscopic world. The curious results of applying quantum mechanics to macroscopic objects are perhaps best illustrated by Erwin Schrödinger's famous thought experiment, where a cat can be put into a superposition state of being both dead and alive. Obviously, these quantum predictions are in stark contradiction to our common experience. Even with plenty of theoretical explanations put forward to explain this discrepancy, a large number of questions about the frontier between the quantum and the classical world remain unanswered. To distinguish between classical and quantum behavior, two fundamental concepts inherent to classical physics have been established over the years: The world view of local realism limits the power of classical experiments to establish correlations over space, while the world view of macroscopic realism (or macrorealism) restricts temporal correlations. Necessary conditions for both world views have been formulated in the form of Bell and Leggett-Garg inequalities, and Bell inequalities have been shown to be violated by quantum mechanics through increasingly conclusive experiments. Furthermore, many challenging steps towards convincing violations of macrorealism have been taken in a number of recent experiments. In the first part of this thesis, conditions for macrorealism are analyzed in detail. Two necessary conditions for macrorealism, the original Leggett-Garg inequality and the recently proposed no-signaling in time condition, are presented. It is then shown that a combination of no-signaling in time conditions is not only necessary but also sufficient for the existence of a macrorealistic description. Finally, an operational formulation of no-signaling in time, in terms of positive-operator valued measurements and Hamiltonians, is derived. In the next part, we argue that these results lead to a suitable definition of classical behavior. In particular, we provide a formalism to judge the classicality of measurements and time evolutions. We then proceed to apply it to a number of exemplary measurement operators and Hamiltonians. Finally, we argue for the importance of spontaneously realized Hamiltonians in our intuition of classical behavior. Next, differences between local realism and macrorealism are analyzed. For this purpose, the probability polytopes for spatially and temporally separated experiments are compared, and a fundamental difference in the power of quantum mechanics to build both types of correlations is discovered. This result shows that Fine's theorem, which states that a set of Bell inequalities is necessary and sufficient for local realism, is not transferable to macrorealism. Thus, (Leggett-Garg) inequalities are in principle not well-suited for tests of macrorealism, as they can never form a necessary and sufficient condition, and unnecessarily restrict the violating parameter space. No-signaling in time is both better suited and more strongly motivated from the underlying physical theory. In the final part of this thesis, a concrete experimental setup for implementing quantum experiments with macroscopic objects is proposed. It consists of a superconducting micro-sphere in the Meißner state, which is levitated by magnetic fields. Through its expelled magnetic field, the sphere's center-of-mass motion couples to a superconducting quantum circuit. Properly tuned, ground state cooling can be realized, since the sphere's motion is extremely well isolated from the surrounding environment. This setup therefore is a promising candidate for the observation of quantum effects in macroscopic systems.
The descriptions of the quantum realm and the macroscopic classical world di�er signi
�cantly not only in their mathematical formulations, but also in their foundational concepts
and philosophical consequences. The assumptions of local realism, non-contextuality
and macroscopic realism (macro-realism) along with the quantum mechanical violations
of these assumptions are discussed.
A complete generalization is provided of Wigner's argument inferring quantum nonlocality,
originally restricted for the EPR-Bohm entangled state, based on assuming joint
probability distributions for all the relevant dichotomic observables. Such Generalized
Wigner Inequality (GWI) turns out to be the N-partite local realist inequality which is
violated by quantum mechanics for all pure entangled states for any N.
We then exploit the non-trivial manifestation of quantum non-locality via local contextuality
on three qubit system. Here, we propose an experimental scheme to realize this
feature by deriving a new local realist inequality. The way quantum entanglement can
be used for global contextual value assigning is discussed in a quantum pseudo-telepathy
game.
In the second part of this report, we formulate Leggett-Garg inequality (LGI) in terms
of joint probability and demonstrate its quantum mechanical violation for two state oscillation,
which is initial state dependent, unlike the case of standard LGI. It has been
shown that, the newly formulated LGI reveals robustness against unsharp measurement
for testing compatibility between macro-realism and quantum mechanics. Finally we
show that, the recently proposed No-signaling in time condition, contradicts with quantum
mechanical predictions for any degree of unsharpness in measurement.
This thesis investigates three aspects of nonclassicality. The first aspect is macroscopic quantumness, a field which considers the properties of macroscopic superpositions. The various measures of macroscopicity are reviewed. An optomechanical system is described which enables us to study nonclassicality in macroscopic mechanical oscillators. We analyse the impact of different measurement settings on the macroscopicity of the mirror and the Wigner functions of the mechanical state. The same system is also considered under open system dynamics. The second nonclassical concept is the violation of macrorealism. It is shown that a two-level system can violate the Leggett-Garg inequality, thereby demonstrating that the assumptions of macrorealism do not hold. Similar dynamics are then replicated in a macroscopic mechanical system through the use of a hybrid optomechanical system in which an atom interacts with the mechanical oscillator through an optical mode. Mechanical damping is then factored into the dynamics to examine its effect on the violation of the Leggett-Garg inequality for different parameter ranges. The third is nonclassical correlations. Quantum discord and quantum entanglement are defined and several measures are explained. Entanglement distribution via separable states is introduced and then built on by adding imperfections to the operations in the protocol. It is found that the protocol is still successful in spite of the errors in the operations, both when they are unitary and non-unitary. We also develop a method of generating entanglement between two bosons through mediation with two spin systems. Through this system we demonstrate the creation of both entangled coherent states and NOON states.
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of classicality, the Bell theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS) . Tests of the Bell inequality and the BKS theorem are both of fundamental interests and of great significance . The Bell theorem has already been experimentally verified extensively on many different systems , while the quantum contextuality, which is independent of nonlocality and manifests itself even in a single object, is experimentally more demanding. Moreover, the contextuality has been shown to play a critical role to supply the `magic' for quantum computation, making more extensive experimental verifications in potential systems for quantum computing even more stringent. Here we report an experimental verification of quantum contextuality on an individual atomic nuclear spin-1 system in solids under ambient condition. Such a three-level system is indivisible and thus the compatibility loophole, which exists in the experiments performed on bipartite systems, is closed. Our experimental results confirm that the quantum contextuality cannot be explained by nonlocal entanglement, revealing the fundamental quantumness other than locality/nonlocality within the intrinsic spin freedom of a concrete natural atomic solid-state system at room temperature.