Henry attempts to sneak into Eve’s residence undetected by taking advantage of his quantum coherence, but his quantum entanglement with Schred puts him in peril: Henry can no longer interfere with himself, he decoheres, since his two versions are differently tagged by correlations with different versions of Schred. Entanglement in composite systems is not only the hallmark of quantumness but also the key to its demise, alias decoherence. Decoherence, by transforming quantum information into classical information, is the biggest obstacle towards controlling complex quantum systems, particularly quantum computers. Information is collected and processed by “observers”: all life forms and their artificial (computerized) extensions. The question that reflects the millennia-long controversy on free will is: do observers have the freedom to choose the mode of their observation? The appendix to this chapechapter investigates the interference of two quantum systems as a function of their entanglement.
Henry attempts to sneak into Eve’s residence undetected by taking advantage of his quantum coherence, but his quantum entanglement with Schred puts him in peril: Henry can no longer interfere with himself, he decoheres, since his two versions are differently tagged by correlations with different versions of Schred. Entanglement in composite systems is not only the hallmark of quantumness but also the key to its demise, alias decoherence. Decoherence, by transforming quantum information into classical information, is the biggest obstacle towards controlling complex quantum systems, particularly quantum computers. Information is collected and processed by “observers”: all life forms and their artificial (computerized) extensions. The question that reflects the millennia-long controversy on free will is: do observers have the freedom to choose the mode of their observation? The appendix to this chapechapter investigates the interference of two quantum systems as a function of their entanglement.
Henry and Eve try to outrace each other, so as to get first to the unique quantum crystals deposited in an underground mine. In his descent into the mine, Henry resorts to coherent transfer. When he tries to return the same way, he gets stuck halfway up, because his entanglement to Eve’s sensors decoheres him. This scenario represents any environment where the interaction of each constituent with the quantum system is weak. Yet, together these many constituents and the system become completely entangled, causing environment-induced decoherence. This consensual narrative on decoherence conceals conceptual hurdles. Where does one draw the line between the system and the environment? How can the unitarity of QM be reconciled, whereby our past and future are interchangeable, with the irreversible evolution of quantum systems under decoherence, culminating in death? The appendix to this chapter describes coherent oscillations in a quantum system and their decay by decoherence.
In this adventure, two quantum characters interact, because Henry has constructed a quantum suit for his cat, Schred. Henry and Schred end up in a quantum-entangled state. Remarkably, by measuring one of two entangled systems, the state of the other system is immediately collapsed, even if they are far apart. This bizarre feature of entanglement implies non-locality—synchronization or “collusion” between quantum objects, regardless of their distance. Cosmology provides an explanation: the universe emerged from a unified state describable as a quantum-entangled “hologram”. This notion resonates with the ancient Hindu view that the common essence of all things, the Brahman, can be revealed at every level of the natural hierarchy. The appendix to this chapter discusses operators that create entanglement.
Henry seeks to to evade his foe, Eve, by controlling the phase of his superposition state. With this control, Henry can choose where to be or not to be, by having his two waves interfere with the same phase, thereby reinforcing each other, or with opposite phases, resulting in his two waves extinguishing each other. The historical debate on quantum interference and its competing interpretations is reviewed. The spin, an internal rotation of a quantum particle, which constitutes a two-state quantum system, is beneficial for understanding quantum interference and underlies a variety of applications, from magnetic resonance imaging (MRI) to quantum information (QI). Quantum interference allows an object to coexist in states of “being” and “non-being” at a given time. Such coexistence and QI logic contradict the basic dichotomy between being and nothingness postulated 2,500 years ago by Parmenides, yet they resonate with the teachings of the Buddhist thinker Nagarjuna.
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.
Eve attempts to eavesdrop on Henry, who discovers that her eavesdropping strategy is susceptible to hindrances imposed by the QM uncertainty principle. Eve can detect Henry’s whereabouts to any precision she chooses. However, a precise position measurement induces a large spread of Henry’s velocities and renders his position extremely uncertain, defeating Eve’s attempt to further track him. Such restriction on the maximal accuracy of measuring “complementary” observables was viewed by Bohr as a fundamental limitation on human perception of the world. A deeper explanation of complementarity may assume that the observer’s cognition and the observed object are inseparable, in the spirit of Spinoza, who considered nature as one substance with both mental and physical modalities. By studying these modalities, human knowledge may some day be freed from complementarity constraints. The appendix to this chapter introduces operators and their commutation relation and clarifies the position–momentum uncertainty relation.
Henry is in peril after bailing out from a burning airplane, because his quantum suit has uncontrollably split him into four quantum versions, only one of which can get hold of the parachute. In order to survive, all his versions must recombine via interference exactly where the parachute is. To this end, the phases of all his versions must be fully in control. Alas, Henry’s ejection has scrambled (randomized) his phases by decoherence (dephasing), which is common in quantum systems. A tip from Eve in mid-air concerning phase reversal proves to be a life saver! This decoherence control, which is indispensable in MRI, is termed sin echo, as the dynamics after the phase reversal echoes the dynamics before this operation. The much further-reaching potential goal of decoherence control may be to influence metabolism and even the process of dying. The appendix to this chapter explains dephasing and its control by the spin-echo method.