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PROBLEMS IN QUANTUM MEASUREMENT AND APPLICATIONS

Sun Chang

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

In connection with the recent experiments on quantum measurement, such as the “which-way”detection using the Bragg scattering of cold atoms and quantum interference using a small molecular C 60 quantum system, we introduce the quantum measurement problem and its relevant fundamental concepts and ideas, such as quantum coherence, quantum decoherence and quantum entanglement. In order to understand the loss of quantum coherence for a quantum system due to its interaction with another system behaving classically or macroscopically, we discuss some quantum dynamical models to describe the quantum decoherence and quantum dissipation induced by couplings to the external environment or inner motions. In the classical or macroscopic limit, it is shown that the wave function of the total system formed by the quantum system plus another system interacting with it is factorized as an entangled state with correlation between the measured quantum states and the configurations of the external large system or the inner degrees of freedom. In association with a novel viewpoint about quantum measurement, which has been directly verified by recent experiments (e.g.,S. Durr et al., Nature,1998,33:359), it is shown that quantum entanglement is indeed responsible for the quantum decoherence, and thus it can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. These arguments give us a possible solution to the “Schrdinger cat paradox” and to whether the coherent superposition of macroscopic states exists. These discussions are also applied to the quantum decoherence problems in quantum information including quantum computing and quantum communication.

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In connection with the recent experiments on quantum measurement, such as the “which-way”detection using the Bragg scattering of cold atoms and quantum interference using a small molecular C 60 quantum system, we introduce the quantum measurement problem and its relevant fundamental concepts and ideas, such as quantum coherence, quantum decoherence and quantum entanglement. In order to understand the loss of quantum coherence for a quantum system due to its interaction with another system behaving classically or macroscopically, we discuss some quantum dynamical models to describe the quantum decoherence and quantum dissipation induced by couplings to the external environment or inner motions. In the classical or macroscopic limit, it is shown that the wave function of the total system formed by the quantum system plus another system interacting with it is factorized as an entangled state with correlation between the measured quantum states and the configurations of the external large system or the inner degrees of freedom. In association with a novel viewpoint about quantum measurement, which has been directly verified by recent experiments (e.g.,S. Durr et al., Nature,1998,33:359), it is shown that quantum entanglement is indeed responsible for the quantum decoherence, and thus it can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. These arguments give us a possible solution to the “Schrdinger cat paradox” and to whether the coherent superposition of macroscopic states exists. These discussions are also applied to the quantum decoherence problems in quantum information including quantum computing and quantum communication.
Quantum measurement theory addresses several problems. All of them arise from applying a microscopically valid theory to the macroscopic domain. The most famous is the Schrödinger cat example in which the ordinary use of quantum rules suggests a superposition of macroscopically different states, something we do not seem to experience. Another problem is the Einstein-Podolsky-Rosen (EPR) paradox in which a fundamental quantum concept, entanglement, creates subtle and non-classical correlations among remote sets of measurements. Although it seems mere word play to observe that such an apparent micro-macro conflict ought to be viewed as a problem in statistical mechanics—by virtue of the way that discipline is defined—until recently the importance of this observation was seldom recognized. The founders, Bohr, Schrödinger, Heisenberg, Einstein did not emphasize this direction, but over the years the realization that measurement necessarily involves macroscopic objects—objects with potentially mischievous degrees of freedom of their own—began to be felt. For me this was brought home by the now classic fourth chapter of Gottfried's text on quantum mechanics. He takes up the following problem. The density matrix ρ 0 for a normalized pure state is ρ 0 = |ψ〉 〈ψ|. It follows that Tr ρ 0 = Tr ρ 0 2 = 1. After a non-trivial measurement, the density matrix ρ is supposed to be diagonal in the basis denned by the measured observable, with Tr ρ = 1 but Tr ρ 2 < 1.
We are in the midst of a renaissance in the study and interpretation of fundamental quantum mechanics, from quantum coherence and quantum entanglement to the quantum measurement process. This stems partly from the impressive advances in experimental techniques that are making yesterday's gedanken experiment today's reality. Another reason quantum coherence and entanglement have come to the forefront is the emerging and tantalizing field of quantum information science. The ability to store information in quantum systems may someday yield devices that process quantum superpositions of inputs in parallel or improve communication through the `wiring' implicit in quantum entanglement. Indeed, quantum computing has the remote prospect of revolutionizing the way we store and process information. This has become particularly important in the face of impending limits on the miniaturization of conventional computers due to quantum effects. Of course, all real systems face limits imposed by decoherence, or the environmentally-induced destruction of quantum coherence. Here, superpositions of quantum states suddenly become probabilistic mixtures of states when they interact with the environment or when the system parameters are fluctuating. Decoherence theory is commonly interpreted as a way to quantify the elusive boundary between quantum and classical worlds and almost always precludes the existence of complex quantum superpositions, except at extremely short time scales. In practice, it is very important to study how decoherence appears in particular quantum systems and try to fight against it. In this special issue of Journal of Optics B: Quantum and Semiclassical Optics , we highlight recent results in the exciting area of quantum coherence and entanglement, including generating interesting and complex quantum states, characterizing coherence and entanglement in these systems, and triumphing over relevant decoherence processes. We hope this issue will not only act as a bookmark in the ongoing study of fundamental quantum mechanics, but will also help guide the rapid developments in quantum information science.
Some of the quantum mechanical conceptual problems, their current status, and related theoretical developments are reviewed. The characteristics of the entangled quantum states are analyzed, and new experiments and quantum information applications involving such states are discussed. The well-known paradox of Schroedinger's cat (the impossibility of observing superpositions of macroscopically distinct states that are predicted by quantum mechanics) is discussed. It is shown that decoherence (arising when a quantum system is measured in such a way that some information about its state is recorded in its environment) prevents the distinguishing of a superposition and the corresponding mixture. This overcomes the difficulties associated with the paradoxical nature of quantum measurement provided we remain within the framework of the theory of open systems. Other conceptual difficulties, while actually lying outside physics, are now the subject of much research and have already led to new interesting interpretations of quantum mechanics. The suggestion of Wigner and others that the observer's consciousness be included in the theory of quantum measurement is discussed in this context. A hypothesis is put forward which might enable the functioning of consciousness to be described in quantum measurement terms.
Introduction WHY must I treat the measuring device classically? What will happen to me if I don't?! Eugene Wigner The quantum measurement problem – how does an apparently “classical” definite world arise out of the random world of quantum superpositions – was and continues to be one of the fundamental philosophical issues in quantum mechanics. What we mean by a classical world, for example, is one in which macroscopic objects are not in superposition states of being simultaneously in several locations at once, and cats are never in coherent superpositions of being alive and dead. This lack of coherence is actually a loss of the coherence that exists at the level of the isolated quanta, but somehow does not survive the transition to the classical level of measuring apparatus. Such incoherent states are known as mixed states. Therefore, to study the quantum–classical interface, or even to investigate whether such an interface exists at all other than in the minds of “classical sympathizers,” one should look carefully at mixed states, how they arise and how they behave. Here we describe a set of experiments, both real and gedanken , investigating the subtleties of quantum interference when mixed states are involved. We start by describing the well-known double-slit experiment, and the loss of interference when which-path information can be had.
Abstract: The quantum measurement problem has been the deepest conceptual difficulty since the birth of quantum mechanics. Standard quantum mechanics accepts wavefunction collapse as an independent postulate but never provides a physical explanation. The decoherence approach attributes collapse to the interaction between the system and its environment, but faces two fundamental limitations: the “infinite regress” problem and the “insufficiency of decoherence” problem. Within the framework of the Self-Construction Theory (SCT), this paper provides a complete resolution of the measurement problem. The core thesis is that quantum measurement is not a fundamental process independent of the laws of physical evolution, but rather a local manifestation of constructive renormalization—the scale evolution of the spacetime complex field KKK from microscopic degrees of freedom to macroscopic effective descriptions. The origins of wavefunction collapse, decoherence, and the Born rule receive a unified first‑principles interpretation in this framework. SCT’s spontaneous decoherence mechanism is the key to the resolution. Constructive renormalization inherently involves information loss—the integrated‑out microscopic degrees of freedom no longer exist in the macroscopic effective description. During a measurement, the measuring apparatus possesses a huge number (∼1023\sim10^{23}∼1023) of microscopic degrees of freedom. When the apparatus interacts with the measured system, constructive renormalization triggers information compression of these degrees of freedom—the apparatus can no longer distinguish which branch of the superposition it is in, and quantum coherence is thus spontaneously lost. No “external environment” is needed—the constructive renormalization dynamics of spacetime itself is the ultimate source of decoherence, thereby completely solving the “infinite regress” problem. Among the probability distribution given by the Born rule, the weights of non‑maximal probability branches are further suppressed by information compression under the huge number of microscopic degrees of freedom, so that macroscopic observers can perceive only a definite outcome in the effective description. The information loss caused by constructive renormalization is ontological—it does not rely on any approximation or truncation, thus fundamentally solving the “insufficiency of decoherence” problem. The Born rule—that measurement outcomes occur with probabilities given by the squared amplitudes—is directly derived from the constructive integral structure in SCT. In the constructive renormalization limit, interference terms between different configurations are naturally suppressed by off‑diagonal phase randomization, and the system automatically switches to a classical probabilistic description. In the diagonal density matrix representation, the squared amplitude is the only natural weight that is simultaneously real and non‑negative. Hence the Born rule is not an additional postulate of quantum mechanics but a necessary and unique manifestation of the relative frequencies of the constructive integral in the constructive renormalization limit. This derivation is rigorous within the mathematical framework of constructive renormalization—it does not rely on any approximations or truncations. SCT’s quantum measurement theory is deeply unified with the black hole information paradox. The “collapse” in quantum measurement and the “information loss” in black hole evaporation are different manifestations of the same core mechanism—the redistribution of information due to constructive renormalization—in two extreme physical situations. In quantum measurement, information is redistributed into the degrees of freedom of the macroscopic apparatus; in black hole evaporation, information is redistributed into the time‑point configurations on the horizon. This unification is the strongest proof of the universality of constructive renormalization as an information‑processing mechanism. Keywords: quantum measurement; spontaneous decoherence; constructive renormalization; Born rule; wavefunction collapse; information redistribution; Self-Construction Theory
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub-systems. This is not paradoxical. Standard quantum theory rigorously predicts the experimentally-observed outcomes of this state. Neither sub-system is superposed; rather, the correlations between the states of the subsystems are superposed. This resolves the problem of definite outcomes. The nonlocal properties of entanglement then ensure that only one outcome occurs while the other outcome simultaneously does not occur, resolving a problem posed by Einstein in 1927. The single outcome that occurs then triggers an irreversible process leading to macroscopic registration of the outcome. This resolves the quantum measurement problem. Collapse occurs because of entanglement and does not require a special collapse postulate. Collapse is a consequence of standard quantum physics and the irreversible nature of the macroscopic registration.