Entanglement is characterized, to the best knowledge of these days, from bipartite pure states to multipartite mixed states, and including the problems of di erent tensor product structures determination for a given quantum system and identical particles' entanglement. The manipulation of entanglement for impinging which way information on interferometers, as well as its later erasure (the so called \quantum erasure"), is presented, with emphasis on an experiment made by UFMG optics group and on a discussion about what is really quantum in such eraser. A quick introduction to the concepts of quantum state teleportation and quantum cryptography is given. Open quantum systems are put in perspective and, from this perspective, the environment e ects on an experiment made to explore the quantum-classical frontier are discussed. This analisys allows the proposal of modi cations for better exploring this frontier. The di erent time scales for dissipation, thermalization, and decoherence are obtained for the problem of one harmonic oscillator interacting with a huge set of other harmonic oscillators, in a situation which mimics the Schröodinger's cat. From the quantum information protection perspective, decoherence free subspaces and noiseless subsystems are discussed. Speci c models are studied and their experimental implementation discussed. An experiment realized to show the principles of decoherence free subspaces is also studied. In the considerações nais, the questions raised by these works are pointed.
Entanglement is characterized, to the best knowledge of these days, from bipartite pure states to multipartite mixed states, and including the problems of di erent tensor product structures determination for a given quantum system and identical particles' entanglement. The manipulation of entanglement for impinging which way information on interferometers, as well as its later erasure (the so called \quantum erasure"), is presented, with emphasis on an experiment made by UFMG optics group and on a discussion about what is really quantum in such eraser. A quick introduction to the concepts of quantum state teleportation and quantum cryptography is given. Open quantum systems are put in perspective and, from this perspective, the environment e ects on an experiment made to explore the quantum-classical frontier are discussed. This analisys allows the proposal of modi cations for better exploring this frontier. The di erent time scales for dissipation, thermalization, and decoherence are obtained for the problem of one harmonic oscillator interacting with a huge set of other harmonic oscillators, in a situation which mimics the Schröodinger's cat. From the quantum information protection perspective, decoherence free subspaces and noiseless subsystems are discussed. Speci c models are studied and their experimental implementation discussed. An experiment realized to show the principles of decoherence free subspaces is also studied. In the considerações nais, the questions raised by these works are pointed.
A great effort has been devoted to understand Quantum InformationTheory. This interest comes from the fact that this field has given us advanced methods to process and store information. Among these proposals we can cite the teleportation, the quantum cryptography, and the quantum computation. Interestingly, entanglement is the main resource that puts the quantum approach in a higher level than the classical counterpart. On the other hand, the theory of entanglement allows also a better understanding of physical phenomena already treated by the fields of condensed matter, statistical physics, and quantum optics among others. In this dissertation we aim to review the main topics concerning the Theory of Entanglement and propose new results on this theme as well. Firstly, we will discuss how the notion of entanglement raises naturally, how to determine whether a state is entangled, and how to quantify it. Moving on to the three qubit context,we will show a tomographic process able to determine the quantum stateof a system using only two detectors. It will be shown the connection between multipartite entanglement and the exceptions to our process. In the multipartite scenario we will obtain novel results in the formalism of the theory.Specifically, we study the question: are all maximally entangled statespure? While for bipartite systems almost all entanglement quantifiers agree in a positive answer, in a more general context this is not the case. Indeed, we will show a multipartite entanglement quantifier for which all maximally entangled states are pure. Finally, we address some questions on identical particle entanglement, i.e.: the entanglement coming just from the indistinguishabilityof quantum particles.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
Entanglement and decoherence arguably define the central issues of concern in present day quantum information theory. Decoherence occurs when a system interacts with its environment in an irreversible way; this prevents the quantum superposition of the system + environment's wavefunction from interfering with each other. A better understanding of environment-induced destruction of coherent superposition states is needed, as well as a clear description of the degree of entanglement between the quantum system and its environment. We quantitatively establish a correspondence between entanglement, decoherence, and spin dynamics for a two-state system coupled to a bath of harmonic oscillators, resulting in the celebrated spin-boson model. Applications to solid-state and cold atomic systems are also discussed.
For a long time the conceptually challenging predictions of quantum physics for individual experiments have been the issue of such bizarre discussions as Schrodinger's cat gedanken experiment. There, quantum superposition would imply the co-existence of the states of a live cat and a dead cat, quantum randomness would imply the fundamental unpredictability of the results of an observation of the cat's real and factual properties, and entanglement means that the state of the cat, dead or alive, is entangled with the state of an radioactive atom. Interestingly these same concepts, randomness, superposition, and entanglement, have become cornerstone concepts in a new quantum information technology. The most important applications are quantum cryptography, quantum computation, and quantum teleportation. Quantum cryptography permits the encoding of confidential information in a way that its security against eavesdropping is guaranteed by the laws of physics. A quantum computer would be able to operate in a quantum superposition of many different states thus enabling exponential speedup for some problems. Quantum teleportation allows transferring directly the quantum state of an individual system onto a distant one thus providing an ideal way for quantum computers to communicate with each other.
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.