Recent advances in quantum technologies enabled us to make large quantum states \nand pushed towards examining quantum theory at the macroscopic level. However observation \nof quantum e ects at a macroscopic level still remains a demanding task. In this \nthesis we try to address one of the challenges and propose and explore some new solutions. \nOne of the obstacles for observation of macroscopic quantum e ects is the sensitivity \nto the measurement resolution. For many di erent cases, it has been observed that the \nprecision requirement for measuring quantum e ects increases with the system size. We \nformalize this as a conjecture that for observation of macroscopic quantum e ects, either \nthe outcome precision or the control precision of the measurements has to increase with \nsystem size. This indicates that the complexity of macroscopic quantum measurement \nincreases with the system size and sheds some lights on the quantum-to-classical transition \nat the macroscopic level. \nWe also introduce a technique to go around the sensitivity problem for observation \nof micro-macro entanglement. We propose that using a unitary deampli cation process, \none can bring the system back to the microscopic level where the measurements are less \ndemanding and quantum e ects are easier to verify. As the unitary processes do not change \nthe entanglement, this serves as a veri cation tool for micro-macro entanglement. \nWe also explored the connection between quantum e ects and thermodynamics of \nmacroscopic quantum systems for two speci c cases. For one, we investigated the e ect of \nentanglement in composite bosons and Bose-Einstein condensation. We showed that as the \nstate of the composite boson approaches a maximally entangled state, the condensation \nrate also approaches one. \nThe other case we considered was heat-bath algorithmic cooling. We found the cooling \nlimit of this class of thermodynamic transformations and showed that it decreases \nexponentially with the number of qubits. \nWe also developed an entropic version of Mermin's inequality. Here the idea is to \ndevelop a tool to reveal the entanglement in many-body quantum systems based on the \nentropy of the measurement outcomes. We introduce a new inequality that holds for locally \nrealistic models, yet can be violated with quantum measurements. One of the nice features \nof this inequality is that it can be violated maximally with quantum measurements. This \nresembles the GHZ paradox but for entropies of the measurement outcomes.
Recent advances in quantum technologies enabled us to make large quantum states \nand pushed towards examining quantum theory at the macroscopic level. However observation \nof quantum e ects at a macroscopic level still remains a demanding task. In this \nthesis we try to address one of the challenges and propose and explore some new solutions. \nOne of the obstacles for observation of macroscopic quantum e ects is the sensitivity \nto the measurement resolution. For many di erent cases, it has been observed that the \nprecision requirement for measuring quantum e ects increases with the system size. We \nformalize this as a conjecture that for observation of macroscopic quantum e ects, either \nthe outcome precision or the control precision of the measurements has to increase with \nsystem size. This indicates that the complexity of macroscopic quantum measurement \nincreases with the system size and sheds some lights on the quantum-to-classical transition \nat the macroscopic level. \nWe also introduce a technique to go around the sensitivity problem for observation \nof micro-macro entanglement. We propose that using a unitary deampli cation process, \none can bring the system back to the microscopic level where the measurements are less \ndemanding and quantum e ects are easier to verify. As the unitary processes do not change \nthe entanglement, this serves as a veri cation tool for micro-macro entanglement. \nWe also explored the connection between quantum e ects and thermodynamics of \nmacroscopic quantum systems for two speci c cases. For one, we investigated the e ect of \nentanglement in composite bosons and Bose-Einstein condensation. We showed that as the \nstate of the composite boson approaches a maximally entangled state, the condensation \nrate also approaches one. \nThe other case we considered was heat-bath algorithmic cooling. We found the cooling \nlimit of this class of thermodynamic transformations and showed that it decreases \nexponentially with the number of qubits. \nWe also developed an entropic version of Mermin's inequality. Here the idea is to \ndevelop a tool to reveal the entanglement in many-body quantum systems based on the \nentropy of the measurement outcomes. We introduce a new inequality that holds for locally \nrealistic models, yet can be violated with quantum measurements. One of the nice features \nof this inequality is that it can be violated maximally with quantum measurements. This \nresembles the GHZ paradox but for entropies of the measurement outcomes.
Glorious victories have been achieved when quantum theory (QT) is applied to microscopic systems. However, although there might be good reasons for us to believe that QT applies at the macroscopic level as well, to give a definite answer ”yes” there is still a long journey. If it does apply, a direct result is that it predicts highly counter-intuitive macroscopic quantum superpositions and entanglements, which we never experience in our daily lives. In this thesis we assume that QT applies to the macroscopic level, and try to find out why we never really observe macroscopic quantum effects. The thesis contains two projects, aiming at two reasons for the above problem. In the first project (Chapter 3 and 4), we show that the required resolution to observe macroscopic quantum effects increases with the size of the system, when both outcome precision and control precision are taken into account. This means that for really large quantum effects we need a very good measuring resolution to observe them, while what we usually do are coarse-grained measurements, whose resolutions are much lower. In the second project (Chapter 5), we try to deal with decoherence, another obstacle preventing us from observing macroscopic quantum effects. We propose to create and detect strong entanglement of micro-macro and macro-macro beams of photons with very weak cross Kerr nonlinearities that are obtainable by current technology. We analyze the entanglement under environmental decoherence with various methods, and show that strong entanglement can still be created and detected under decoherence. We hope that the above results will help to push the boundary of the realm of QT towards the macroscopic level.
Macroscopic quantum phenomena refer to quantum features in objects of 'large' sizes, systems with many components or degrees of freedom, organized in some ways where they can be identified as macroscopic objects. This emerging field is ushered in by several categories of definitive experiments in superconductivity, electromechanical systems, Bose-Einstein condensates and others. Yet this new field which is rich in open issues at the foundation of quantum and statistical physics remains little explored theoretically (with the important exception of the work of A J Leggett [1], while touched upon or implied by several groups of authors represented in this conference. Our attitude differs in that we believe in the full validity of quantum mechanics stretching from the testable micro to meso scales, with no need for the introduction of new laws of physics.) This talk summarizes our thoughts in attempting a systematic investigation into some key foundational issues of quantum macroscopic phenomena, with the goal of ultimately revealing or building a viable theoretical framework. Three major themes discussed in three intended essays are the large N expansion [2], the correlation hierarchy [3] and quantum entanglement [4]. We give a sketch of the first two themes and then discuss several key issues in the consideration of macro and quantum, namely, a) recognition that there exist many levels of structure in a composite body and only by judicious choice of an appropriate set of collective variables can one give the best description of the dynamics of a specific level of structure. Capturing the quantum features of a macroscopic object is greatly facilitated by the existence and functioning of these collective variables; b) quantum entanglement, an exclusively quantum feature [5], is known to persist to high temperatures [6] and large scales [7] under certain conditions, and may actually decrease with increased connectivity in a quantum network [8]. We use entanglement as a measure of quantumness here and pick out these somewhat counter-intuitive examples to show that there are blind spots worthy of our attention and issues which we need to analyze closer. Our purpose is to try to remove the stigma that quantum only pertains to micro, in order to make way for deeper probes into the conditions whereby quantum features of macroscopic systems manifest.
The possibility to observe quantum features at the macroscopic level stands out as one of the most challenging yet fascinating open questions in modern quantum physics. The difficulties inherent in such a quest are manifold. First, the unavoidable interaction with the surrounding environment lies deeply at the roots of the loss of coherence and corruption of quantum correlations in a quantum state, being more severe as the size of the system being studied grows. Second, one faces the debated problem of achieving a measurement-precision that is sufficient to observe quantum effects at such macro-scales. Recent studies have shown that, depending on the Hamiltonian models, classicality may emerge from the coarse-graininess of measurements performed over a quantum system.
One of the main unsolved question in Quantum Mechanics (QM) is its compatibility with classical mechanics. The laws of QM, which describe the microscopic world, must merge into the classical ones for large enough physical systems, but it is still unknown at which point, if any, the transition occurs and if the transition is smooth or sudden as the size increases. Furthermore, a strict extension of QM to the macroscopic world leads to well known 'paradoxes', which is not straightforward to solve. This question is tightly connected with the measurement problem, since any measurement apparatus must give a response which can be described at classical level. Many experiments have been performed to answer to this question. They mainly try to find to which extent the number of particles can be increased in order to observe clear evidence of violation of standard QM. In this paper we argue that the macroscopicity parameter is not the number of particles but the number of independent degrees of freedom, as proposed in a recent model for the completion of QM. This introduces a sort of change of paradigm. To support this claim a representative set of well known experiments are analyzed from this point of view. This brings to a new interpretation of the experiments. A general scheme for the quantum-classical transition is discussed in some details.
Theory and experiment both demonstrate that an entangled quantum state of two subsystems is neither a superposition of states of its subsystems nor a superposition of composite states but rather a coherent superposition of nonlocal correlations between incoherently mixed local states of the two subsystems. Thus, even if one subsystem happens to be macroscopic as in the entangled "Schrodinger's cat" state resulting from an ideal measurement, this state is not the paradoxical macroscopic superposition it is generally presumed to be. It is, instead, a "macroscopic correlation," a coherent quantum correlation in which one of the two correlated sub-systems happens to be macroscopic. This clarifies the physical meaning of entanglement: When a superposed quantum system A is unitarily entangled with a second quantum system B, the coherence of the original superposition of different states of A is transferred to different correlations between states of A and B, so the entangled state becomes a superposition of correlations rather than a superposition of states. This transfer preserves unitary evolution while permitting B to be macroscopic without entailing a macroscopic superposition. This resolves the "problem of outcomes" but is not a complete resolution of the measurement problem because the entangled state is still reversible.
Theory and experiment have not fully resolved the apparent dichotomy , which has agonized physics for the past eighty years: on the one hand, the description of microsystems by quantum mechanics and, on the other, the description of macrosystems by classical dynamics or statistical mechanics. Derivations of the time-irreversible Liouville equation for an open quantum system, based on projecting out its environment, have narrowed the gap between the quantum and classical descriptions. Yet our `classical' intuition continues to be confronted by quantum-mechanical results like the Einstein--Podolsky--Rosen paradox that challenges the classical notion of locality, or the quantum Zeno effect which suggests that the isolation of a system is not the only way to preserve its quantum state. There are two key concepts in any discussion of such issues. The first, which is responsible for the most salient nonclassical properties, is entanglement , that is partial or complete correlation or, more generally, inseparability of the elements comprising a quantum ensemble . Even after their interaction has ceased, this inseparability, originating from their past interaction, can affect the state of one element when another element is subject to a nonunitary action, such as its measurement, tracing- out, or thermalization. The second key concept is decoherence of open quantum systems, which is the consequence of their entanglement with their environment, a `meter' or a thermal `reservoir', followed by the tracing-out of the latter. Despite new insights into entanglement and decoherence, there are still no complete, unequivocal answers to the fundamental questions of the transition from quantal to classical behaviour: how do irreversibility and classicality emerge from unitarity as systems and their environments become increasingly complex ? At what stage does system--meter entanglement give rise to a classical readout of the meter? Is there an upper limit on the size or complexity of systems displaying entanglement? Major developments have opened new vistas into controlled entanglement , which is the resource of quantum information processing. However, these developments have mainly focused on ensembles of simple two- and three-level systems that are thoroughly isolated from their environments. Treatments of coherence in quantum computing have mostly assumed that only a single or a few the elements of the quantum ensemble may simultaneously undergo an uncontrolled intervention---a quantum error. Decoherence-control protocols for more general types of errors are still incomplete. In order to resolve the outstanding issues of the quantum--classical transition, and study the control of entanglement and decoherence without the foregoing restrictions, we must venture into the domain of Quantum Complex Systems (QUACS), either consisting of a large number of inseparable elements or having many coupled degrees of freedom. Our conviction is that fundamental understanding and manipulation of entanglement within QUACS or their entanglement with the environment or a meter, call for the creation of a new conceptual framework or paradigm, that would encompass phenomena common to cold atoms in laser fields, large molecules, Josephson junctions, quantum gases and solids, with the view of employing these systems for quantum information processing and computing. Progress within this paradigm should allow us to answer the questions: does entanglement play an essential role in the evolution of large collections of complex systems? What are the size and complexity limits of systems and ensembles still controllable by an external intervention? What are the most appropriate decoherence protection schemes and control algorithms? This special issue addresses the challenge of understanding in depth and manipulating the basic quantum properties of optical, atomic, molecular and condensed-matter QUACS, and large ensembles thereof. In view of the interdisciplinary character of this issue, we find it expedient to look at the presented articles not only according to the physical objects they describe, but also from a unifying standpoint. Several unifying themes may be discerned: memory effects in dephasing and relaxation; protection of quantum information by its distribution throughout the ensemble; control of decoherence and entanglement by time-dependent interventions or measurements; manifestations of entanglement in scattering off statistical ensembles; measurment-induced dynamics. The concerted discussion of the topics outlined above should help us advance the new paradigm that addresses our abilities to diagnose and manipulate the entangled states of complex quantum objects and their robustness against decoherence. These abilities are required for quantum information (QI) applications in matter--wave interferometry in molecular, semiconducting or superconducting systems. On the fundamental level, this book may help establish the notion of dynamical information exchange between quantum systems and chart in detail the route from unitarity to classicality. Further developments within the outlined paradigm should yield novel, advantageous QI processing schemes and high-sensitivity interferometers, owing to decoherence suppression and effective control of many degrees of freedom. In the long run, these strategies may prove to be the first step towards the (hitherto unattempted) use of entanglement in nanotechnology, metrology and chemistry, with potentially remarkable novel applications.