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arXiv:quant-ph/9701031 · Physical Review A

Bounds on decoherence and error

Lawrence S. Schulman

Published Feb 1, 1998• 12 citations
arXivHTMLPDF

Abstract

When a confined system interacts with its walls (treated quantum mechanically), there is an intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. However, it will generally lead to error. The wave-function optimization required to avoid decoherence is also examined.
DOI
10.1103/physreva.57.840

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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.
We consider a movable conducting plate of finite mass, between two fixed ones, whose mechanical degrees of freedom are treated quantum-mechanically and bound to its equilibrium position by a harmonic potential. The movable wall is thus subjected to quantum fluctuations of its position. This creates a system of two subcavities separated by the movable fluctuating plate, and two massless one-dimensional scalar fields, one in each subcavity. This system is described by an appropriate generalization of the Law Hamiltonian. The presence of the movable wall yields an effective plate-fields interaction, as well as an effective interaction between the field modes. We obtain, at the second order in perturbation theory, the ground state of the interacting system and the reduced density operator of the fields in each subcavity by tracing out the wall's degrees of freedom. We calculate the entanglement between two field modes, one in each cavity, by evaluating analytically the negativity; we then evaluate numerically also the total multimode negativity. Our results show that in both cases the fields in the two subcavities are entangled, in contrast to the case in which the wall is fixed in space. We discuss the amount of the field entanglement present as a function of relevant physical parameters of the system such as the mass and oscillation frequency of the movable wall, its distance from the fixed walls and the frequencies of the field modes considered.
In the interaction between a quantum mechanical electron wave and a wall, loss of interference contrast is observed. It is of general interest to identify the mechanism and categorize its nature as dephasing or decoherence. Decoherence is of fundamental importance for the transition between the classical and quantum boundary, while dephasing is often an experimental detriment that needs to be understood and overcome. We find that the loss of contrast is attributed to a local charge distribution induced by secondary emission: a dephasing mechanism. This mechanism is expected to be present for many materials, is clearly visible for copper oxide, and can mask decoherence mechanisms. The local charge distribution on the wall causes a loss of contrast and electron beam deformation. A model based on Coulomb interaction with the surface charge gives good agreement for both features. Our model can thus be used to improve the experimental design and lead to separate out decoherence phenomena in the electron-wall system.