A quantum system is always in interaction with its environment. This interaction inevitably alters the state of the quantum system, which causes loss of information encoded in the system. The system under consideration is not a closed system any more when interaction with the outside world is in action. We formulate the theory of an open quantum system in this chapter by regarding the combined system of the quantum system and its environment as a closed system and subsequently trace out the environmental degrees of freedom. Let ρS and ρE be the density matrices of the system and the environment, respectively. Even when the initial state is an uncorrelated state ρS ⊗ ρE , the system-environment interaction entangles the total system so that the total state develops to an inseparable entangled state in general. Decoherence is a process in which environment causes various changes in the quantum system, which manifests itself as undesirable noise.
A quantum system is always in interaction with its environment. This interaction inevitably alters the state of the quantum system, which causes loss of information encoded in the system. The system under consideration is not a closed system any more when interaction with the outside world is in action. We formulate the theory of an open quantum system in this chapter by regarding the combined system of the quantum system and its environment as a closed system and subsequently trace out the environmental degrees of freedom. Let ρS and ρE be the density matrices of the system and the environment, respectively. Even when the initial state is an uncorrelated state ρS ⊗ ρE , the system-environment interaction entangles the total system so that the total state develops to an inseparable entangled state in general. Decoherence is a process in which environment causes various changes in the quantum system, which manifests itself as undesirable noise.
In this chapter we shall deal with the quantum dynamics of an open system. By open quantum system we mean here a system which interacts with an environment (see Sec. 9.4): since we are not interested in the dynamics of the environment, we shall have to describe the evolution of the system in some “effective” way. In particular, if we consider only the evolution of the system, it will be non-unitary, and this will represent the subject of this chapter. As we know, Hamiltonian quantum dynamics is unitary and changes pure states into pure states. On the other hand, non-unitary dynamics changes an initially pure state into a mixture, which must be described by a density matrix (see Ch. 5). In the case of macroscopic systems, the coupling with the environment may be arbitrarily reduced and therefore its influence can be made correspondingly small (see Sec. 1.1). Microscopic systems, however, always couple to the environment and this coupling cannot be considered negligible. This is the reason why the quantum theory of open systems is one of the most important and fundamental chapters of quantum mechanics that, though born in quantum optics, has many implications in almost all fields of physics. The present chapter can be seen as a further development of the measurement theory (see Ch. 9), as open systems manifest a decoherent dynamics (see in particular Sec. 9.4).
Abstract This chapter describes the basic features of open quantum systems, i.e. quantum systems that are affected by noise due to uncontrollable degrees of freedom of an environment or bath. This noise is responsible for effects such as dissipation,decoherence and irreversibility. We study the equilibrium states of open quantum systems and review tools from quantum measurement theory, which describe how to theory, that describe how to extract information from an (open) quantum system. We generalize these tools to multimulti-time statistics and define the notion of a quantum stochastic process and a quan tum Markov process. Finally, we study in which cases a quantum stochastic process looks classical.
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.
Abstract This chapter deals with the important field of environment-induced decoherence and the transition to the classical behaviour of open quantum systems. A number of techniques is developed that allows the determination of decoherence time scales. The decoherence behaviour in several Markovian models is investigated in detail, such as vacuum and thermal decoherence, decoherence in quantum Brownian motion, and the destruction of coherence through internal degrees of freedom and through the scattering of environmental particles. Moreover, experiments on the decoherence of Schrödinger cat states of the electromagnetic field are discussed, as well as the non-Markovian destruction of quantum coherence in the Caldeira–Leggett model, and the environment-induced selection of a pointer basis in the quantum theory of measurement.
Quantum systems are rarely isolated, and often interact with a large number of degrees of freedom that we generically call the environment. As the system becomes entangled with the environment, it effectively loses the interference within the system because it transforms from a product state superposition to an entangled state superposition. Thus, when the system is measured, the interference effects within the system are reduced because we do not measure the entangled environment degrees of freedom. The details for how we describe the behavior of this so-called decoherence is complicated. In this chapter, we investigate how to formulate descriptions of decoherence, we apply this formalism to real systems such as nuclear magnetic resonance and the damped quantum harmonic oscillator, and then we examine the interplay between squeezing and decoherence in trapped ions and the implications for precision measurements.
This work presents Version 2.0 of Quantum Decoherence and Conditional Recoherence as Loss and Restoration of Shared Phase Influence, a clarification and extension of standard decoherence theory within orthodox quantum mechanics.The paper reframes quantum decoherence as the physical loss of shared phase influence between components of a quantum system due to unavoidable entanglement with environmental degrees of freedom. Using standard density-matrix and system–environment coupling formalisms, decoherence is shown to correspond to dispersal of phase information into the environment rather than destruction of quantum states or invocation of fundamental wavefunction collapse.Conditional recoherence is treated within the same framework, demonstrating that restoration of coherence is possible only under constrained physical conditions where phase information has not irreversibly propagated into uncontrolled environmental modes. Known mechanisms such as spin-echo refocusing, dynamical decoupling, and quantum error correction are shown to be consistent with this interpretation.This Version 2.0 manuscript emphasizes structural clarity over speculative interpretation. It preserves unitary quantum dynamics, avoids observer-dependent or consciousness-based claims, and remains fully compatible with open-quantum-system formalisms including Lindblad-type master equations. The work provides a clearer physical account of measurement, irreversibility, and classical emergence without introducing new forces or modifying established quantum theory.The manuscript is intended for researchers and educators working in quantum foundations, open quantum systems, and quantum information theory, and is suitable for citation and pedagogical use.