One of the fundamental problems with the interpretation of Quantum Mechanics, according to Bohr, is the fact that "our usual description of physical phenomena is based entirely on the idea that the phenomena concerned may be observed without disturbing them appreciably". Furthermore in his articles discussing the subject Bohr argues that the action of the probe will be affected by the system and inasmuch the system will be affected by the probe. Specifically in Gedanken experiments he tests the wave-particle duality of the system and implicitly assumes that the probe is also a quantum system. A universal character can only be attributed to Quantum Mechanics provided a complementarity relation is also valid for the probe. As a consequence the state system-probe becomes entangled. In the past fourty years complementarity tests have been proposed. However, much less attention has been paid to the study of an arbitrary probe system. In the present contribution, we fill in this gap and show that the key ingredient for the quantum-classical transition is not necessarily the information generated by the system-probe interaction but rather by its accessibility. Our results have been successfully tested in the interferometric experiment. Our results also allow for a simple physical interpretation of the physics of Ramsey Zones where one photon (average) interacts with a two level atom in a classical manner, i.e., no entanglement is generated.
One of the fundamental problems with the interpretation of Quantum Mechanics, according to Bohr, is the fact that "our usual description of physical phenomena is based entirely on the idea that the phenomena concerned may be observed without disturbing them appreciably". Furthermore in his articles discussing the subject Bohr argues that the action of the probe will be affected by the system and inasmuch the system will be affected by the probe. Specifically in Gedanken experiments he tests the wave-particle duality of the system and implicitly assumes that the probe is also a quantum system. A universal character can only be attributed to Quantum Mechanics provided a complementarity relation is also valid for the probe. As a consequence the state system-probe becomes entangled. In the past fourty years complementarity tests have been proposed. However, much less attention has been paid to the study of an arbitrary probe system. In the present contribution, we fill in this gap and show that the key ingredient for the quantum-classical transition is not necessarily the information generated by the system-probe interaction but rather by its accessibility. Our results have been successfully tested in the interferometric experiment. Our results also allow for a simple physical interpretation of the physics of Ramsey Zones where one photon (average) interacts with a two level atom in a classical manner, i.e., no entanglement is generated.
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.
Bohr's complementarity principle is of fundamental historic and conceptual importance for quantum mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like character of a quantum system, but not both. However, it was eventually realized that these dual behaviors can both manifest partially in the same experimental setup, and, using ad hoc proposed measures for the wave and particle aspects of the quanton, complementarity relations were proposed limiting how strong these manifestations can be. Recently, a formalism was developed and quantifiers for the particleness and waveness of a quantum system were derived from the mathematical structure of QM entailed in the density matrix's basic properties ($\ensuremath{\rho}\ensuremath{\ge}0, \mathrm{Tr}\ensuremath{\rho}=1$). In this article, using IBM Quantum Experience quantum computers, we perform experimental tests of these complementarity relations applied to a particular class of one-qubit quantum states and also for random quantum states of one, two, and three qubits.
Complementarity and Deconstruction: Plotnitsky's Analysis and Beyond Makoto Katsumori Akita University The philosophical thought of the modern physicist Niels Bohr (1885–1962), which revolves around the concept of complementarity, has long been a major subject of historical and philosophical inquiry. Many prior studies of Bohr's complementarity, however, seem to be limited by the fact that they largely proceed within the conceptual frames of the "mainstream" philosophy of science. This being the case, his radical questioning of traditional scientific and philosophical notions—such as the unambiguity of concepts and words—has not been adequately addressed, insofar as these notions are uncritically presupposed by the commentators themselves. In other words, Bohr's thought has often been interpreted under certain tacit premises of scientific rationality that are precisely of the kind targeted by his epistemological critique. In recent years, however, there have emerged new approaches to Bohr's idea of complementarity that place it in different, less conventional, philosophical contexts. Among the most notable of these is Arkady Plotnitsky's endeavor to connect Bohr's complementarity with Jacques Derrida's project of deconstruction. In the present article, based on my recent doctoral dissertation,1 I take up this contribution by Plotnitsky as a suitable point of reference from which to [End Page 435] explore anew Bohr's thought with its radical philosophical implications. After outlining Bohr's complementarity argument and Plotnitsky's reading thereof (in the first and second sections, respectively), I will examine a series of problems that seem to face, or to be left unsolved by, Plotnitsky's account (in the third section). This critical appraisal will finally lead me to sketch a new interpretive approach of my own (in the fourth section), which both extends and delimits the intersections between complementarity and deconstruction. As regards the historical development of Bohr's complementarity, I will largely restrict myself to the period between 1927 and 1950, in which the most crucial of his innovative ideas seem to have been presented. I. Bohr's Idea of Complementarity In his 1927 lecture delivered in Como, Italy, entitled "The Quantum Postulate and the Recent Development of Atomic Theory," Niels Bohr introduced the concept and framework of complementarity as a pivotal idea in his interpretation of quantum theory. From then on, he continually developed the idea of complementarity with regard not only to quantum theory but to other fields of knowledge as well. In what follows, I will first outline his complementarity argument in its "early" period, stretching from 1927 to the mid-thirties,—or, more precisely, until just before his 1935 debate with EPR.2 Bohr starts by noting that "our usual description of physical phenomena is based entirely on the idea that the phenomena concerned may be observed without disturbing them appreciably."3 This notion of physical phenomena as undisturbed by observation underlies all of classical physics and is still maintained in the theory of relativity. However, Bohr continues, a new situation has arisen with the development of quantum theory, specifically with "the so-called quantum postulate, which attributes to any atomic process an essential discontinuity, or rather individuality, completely foreign to the classical theories"; this "individuality" implies that "any observation of atomic phenomena will involve an interaction with the [End Page 436] agency of observation not to be neglected" (PWNB, 1: 53–54.). In more specific terms, any observation aimed at space-time coordination brings about an exchange of momentum and energy with the measuring rods and clocks. It is crucial here that this interaction between the object and the instrument of observation is not simply unavoidable, but "uncontrollable," which represents a "feature of irrationality" brought into the description of nature (PWNB, 1: 68, 91). For insofar as the measuring instruments are to fulfill their purpose, the interaction itself cannot be taken into account, and thus the magnitude of the disturbance always remains unknown. It follows, in Bohr's view, that "an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation...
The dispersion of the initial state of a probe system, be it a quantum object or a macroscopic system in a classical interference experiment, is in general an essential element in the analysis of quantum interference phenomena. The general situation is discussed briefly with particular reference to generic cases in two-colour atomic-physics experiments. The effect of dispersion is, at first sight, somewhat counter-intuitive: if the probe is dispersion-free there is no interference except in special cases, while quantum interference gains full weight in the classical limit , where the dispersion is large. We propose experiments in which a continuous transition between the two regimes may be observed.
Updating the wave-particle duality Maria C. Bosca e-mail: bosca@ugr.es Departamento de Fisica Atomica, Molecular y Nuclear Universidad de Granada E-18071. Granada Spain The wave-particle-duality, the fundamental component of the new quantum formalism in Bohr’s opinion, must be reformulated by incorporating the results of some experiments accomplished in the last decades of twentieth century. The Bohr´s complementarity principle stated the mutual exclusiveness and joint full completeness of the two (classical) descriptions of quantum systems; after Einstein-Podolsky-Rosen’paper, the wave-particle duality, or wave-particle complementarity, could be expressed by stating that it is impossible to build up an experimental arrangement in which we observe at the same time both corpuscular and wave aspects. In a two-slit experiment, they would correspond, respectively, to the which-way knowledge and the observation of interference pattern. Bohr showed this mutual exclusivity in numerous examples , and linked it to the unavoidable disturbance inherent in any measurement event. In quantum mechanical formalism, the complementarity principle has a clear mathematical expression: two observables are complementary if precise knowledge of one of them implies that all possible outcomes of the other are equally probable; their extension to classical concepts (as wave and particle) is not concerned. In 1991 Scully et al published a variant of the two-slit experiment that incorporates two micromasers cavities and a laser beam to provide which-path information without net momentum transferred during the interaction ; the impossibility of know which slit an atom went through and still observe the interference fringes is preserved by the establishing of quantum correlations between the measuring apparatus and the system being observed. They claimed that complementarity, of which wave-particle duality would be to them a manifestation, is more fundamental than the uncertainty principle . In 1996 B-G. Englert, following an approach originally due to Wooters and Zurek , derived , without making use of Heisenberg’s uncertainty relation, an inequality that quantifies the mutual compatibility relation between fringe visibility and which-way information. The inequality, that they denominated as “interferometric duality”, has the expression D^2 + V^2 ≤ 1, where D stands for the distinguishability of the ways and V for the fringe visibility; both of them are mathematical expressions that can be measured to check experimentally the inequality . Today, it is clear that intermediate particle-wave behaviours exist and, in addition to that, there are single experiments in which both classical wave-like and particle-like behaviours are showed total and simultaneously on an individual system. For instance, in the Bose’s double-prism experiment , tunnelling and perfect anticoincidence were observed in single photon states. Consequently, the meaning of the wave-particle duality must incorporate the simultaneous use of the two classical descriptions in the interpretation of experiments, loosing their original mutual exclusivity , which is incorporated as an extreme case in the new interferometric duality, a continuous quantum concept . The wave-particle duality, therefore, must be formulated as an interpretative addition to quantum mechanics, to which is possible to renounce if any pretension of visualize quantum phenomena in terms of classical concepts and intuitions is abandoned.
Abstract Since the beginning of quantum physics, the relation between the properties of the microscopic quantum and the macroscopic classical world has been an important source for the development of the theory, and has led to new insights on the role of the environment in the transition from quantum to classical physics. Decoherence affects both coherence and entanglement of open systems. Quantum optics and cavity quantum electrodynamics have allowed detailed investigations of this phenomenon, within the framework of microwaves and light waves. In this paper, I present a personal account of theoretical and experimental developments that have led to the probing of the subtle frontier between quantum and classical phenomena.