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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Lower bounds for decoherence

Lawrence S. Schulman

Published Jul 1, 1997• 0 citations
Publisher

Abstract

Both quantum computing and tests of certain theories of quantum measurement require tight control over entanglement of the degrees of freedom of the system with those of the environment. In particular, one wishes to avoid entanglement-induced decoherence due to the confining of the system by the macroscopic apparatus. Nonetheless, when the system interacts with its walls (treated quantum mechanically), there is an inevitable intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. It will generally lead to error. The wave function optimization required to avoid decoherence is also examined.

DOI
10.1117/12.277663

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Both quantum computing and tests of certain theories of quantum measurement require tight control over entanglement of the degrees of freedom of the system with those of the environment. In particular, one wishes to avoid entanglement-induced decoherence due to the confining of the system by the macroscopic apparatus. Nonetheless, when the system interacts with its walls (treated quantum mechanically), there is an inevitable intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. It will generally lead to error. The wave function optimization required to avoid decoherence is also examined.
Quantum decoherence refers to the phenomenon when the interaction of a quantum system with its environment results in the degradation of quantum coherence. Decoherence is considered to be the most popular mechanism responsible for the emergence of classicality from quantum mechanics. The issue of formulating a measure of decoherence is addressed here. The approach taken here is that decoherence results from the entanglement of a quantum system with certain environment degrees of freedom, and quantifying this entanglement should yield the most natural measure of decoherence. A simple measure of decoherence is presented based on this notion, and it is examined for various example systems. The measure proves to be effective and is relatively straightforward to compute. In addition, a method has been proposed to measure decoherence in a Mach-Zehnder interferometer which may be useful in neutron interferometry.
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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.
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 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.
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.