Errors in the control of quantum systems may be classified as unitary, decoherent and incoherent. Unitary errors are systematic, and result in a density matrix that differs from the desired one by a unitary operation. Decoherent errors correspond to general completely positive superoperators, and can only be corrected using methods such as quantum error correction. Incoherent errors can also be described, on average, by completely positive superoperators, but can nevertheless be corrected by the application of a locally unitary operation that "refocuses" them. They are due to reproducible spatial or temporal variations in the system's Hamiltonian, so that information on the variations is encoded in the system's spatiotemporal state and can be used to correct them. In this paper liquid-state nuclear magnetic resonance (NMR) is used to demonstrate that such refocusing effects can be built directly into the control fields, where the incoherence arises from spatial inhomogeneities in the quantizing static magnetic field as well as the radio-frequency control fields themselves. Using perturbation theory, it is further shown that the eigenvalue spectrum of the completely positive superoperator exhibits a characteristic spread that contains information on the Hamiltonians' underlying distribution.

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In recent years, many design approaches have been developed for automated manufacturing systems in the fields of reconfigurable manufacturing systems (RMSs), holonic manufacturing systems (HMSs), and multi-agent systems (MASs). One of the principle reasons for these developments has been to enhance the reconfigurability of a manufacturing system, allowing it to adapt readily to changes over time. However, to date, reconfigurability assessment has been limited. Hence, the efficacy of these design approaches remains inconclusive. This paper is the first of two in this issue to address reconfigurability measurement. Specifically, it seeks to address 'reconfiguration potential' by analogy. Mechanical degrees of freedom have been used in the field of mechanics as a means of determining the independent directions of motion of a mechanical system. By analogy, manufacturing degrees of freedom can be used to determine independent ways of production. Furthermore, manufacturing degrees of freedom can be classified into their production and product varieties. This paper specifically focuses on the former to measure the product-independent aspects of manufacturing system 'reconfiguration potential'. This approach will be added to complementary work on the measurement of 'reconfiguration ease' so as to form an integrated reconfigurability measurement process described elsewhere [1][2][3][4][5].

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Abstract-In recent years, the fields of reconfigurable manufacturing systems, holonic manufacturing systems, and multi-agent systems have made technological advances to support the ready reconfiguration of automated manufacturing systems. While these technological advances have demonstrated robust operation and been qualitatively successful in achieving reconfigurability, their ultimate industrial adoption remains limited. Amongst the barriers to adoption has been the relative absence of formal and quantitative multi-agent system design methodologies based upon reconfigurability measurement. Hence, it is not clear 1.) the degree to which these designs have achieved their intended level of reconfigurability 2.) which systems are indeed quantitatively more reconfigurable and 3.) how these designs may overcome their design limitations to achieve greater reconfigurability in subsequent design iterations. To our knowledge, this paper is the first multi-agent system reference architecture for reconfigurable manufacturing systems driven by a quantitative and formal design approach. It is rooted in an established engineering design methodology called axiomatic design for large flexible engineering systems and draws upon design principles distilled from prior works on reconfigurability measurement. The resulting architecture is written in terms of the mathematical description used in reconfigurability measurement which straightforwardly allows instantiation for system-specific application.