We consider a state of N correlated particles, each with spin j, in which the quantum expectation value of an operator A^ is evaluated. This is found to exceed a bound on A^ obtained from considerations of classical realism. It is indicated from numerical results that this contradiction between quantum mechanics and classical realism persists in the ``strong'' macroscopic limit, i.e., when the values of both N and j are arbitrarily increased. In this argument, the notion of classical realism embodies the twin assumptions of locality (no action at a distance) and noncontextuality (a measurement simply reveals the preexisting value of an observed quantity).
We consider a state of N correlated particles, each with spin j, in which the quantum expectation value of an operator A^ is evaluated. This is found to exceed a bound on A^ obtained from considerations of classical realism. It is indicated from numerical results that this contradiction between quantum mechanics and classical realism persists in the ``strong'' macroscopic limit, i.e., when the values of both N and j are arbitrarily increased. In this argument, the notion of classical realism embodies the twin assumptions of locality (no action at a distance) and noncontextuality (a measurement simply reveals the preexisting value of an observed quantity).
An ensemble consisting on systems of two entangled spin 1/2 particles, all of them in the same global quantum state, are considered. The two spins are measured, each of them, on a fixed direction, at two randomly selected measurement times. Realism, plus locality and freedom of choice referred to these chosen times, are assumed. Then, from the sole correlation function related to the two measurements, without considering any Bell inequalities, a contradiction between these assumptions and quantum mechanics is found.
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.
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 violation of a Leggett–Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states—or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell’s locality premise. We follow recent work and propose the validity of a subset of Einstein–Podolsky–Rosen (EPR) and Leggett–Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett–Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the “element of reality” defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett–Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory.
The quantitative quantum-mechanical analysis of the Einstein-Podolsky-Rosen experiment for correlated particles of arbitrary spin s is shown to contradict a generalized form of Bell's inequality, for suitable orientations of the detectors. As the classical ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) limit is approached, the range of angles for which the contradiction arises vanishes as s1.