Naresh Kumar Sharma

Multipartite entanglement of three trapped ions in a cavity and W-state generation

A scheme to generate three qubit maximally entangled W-states, using three trapped ions interacting with the red sideband tuned single-mode field of a high finesse cavity, is proposed. For the cavity field initially prepared in a number state, the probability of generating the three-ion W-state is calculated. By using the ion-cavity coupling strengths achieved in experimental realizations, the interaction time needed for W-state generation is found to be of the order of 10 µs. It is found that for a fixed number of photons in the cavity the nature of entanglement of ionic internal states can be manipulated by an appropriate choice of the initial-state phonon number. The ionic qubits in the W-like state are found to be entangled to cavity photons. Analytical expressions for global negativity and partial K-way negativities (K = 2 to 4) are obtained to study the evolution of entanglement distribution as a function of the interaction parameter. Reversible entanglement exchange between different entanglement modes is observed. For specific values of the interaction parameter, the three ions and photon–phonon system are found to have 4-partite entanglement, generated by 2-way and 3-way correlations.

Integration of dynamic multi-response systems using the product of normalised squared-bias and variance

The quality loss function developed by Taguchi for smaller-the-better and nominal-the-best characteristics can be decomposed into two components: variance and bias. For the larger-the-better characteristics with an infinite target, a decomposition of this nature is not straightforward. However, the decomposition for the larger-the-better characteristic is possible when a finite target is considered. This research proposes decomposing all three types of characteristics in the same way for similarity and equality among characteristics for multi-response cases. The two components of quality loss are utilised to formulate a metric called the product of normalised squared-bias and variance. This metric can in turn be employed to simultaneously improve both the dynamic and the static multiple responses of a system. An example is also provided to demonstrate the proposed methodology in a dynamic multi-response system.

Quality loss function for bivariate response - unified methodology

Various methods have been proposed for multi-response quality loss functions as an extension of the quality loss function for a single characteristic given by Taguchi. Multivariate responses are assumed to follow a multivariate normal distribution. When one of the characteristics is transformed using a reciprocal transformation the characteristic itself and the multivariate response do not remain normally distributed. In these circumstances, the basic assumption of a multivariate normal distribution does not hold. Moreover, the reciprocal transformation has several issues such as inconsistency in the methodologies among the three characteristics, incomparable results, and inappropriate change of parameter unit. The multi-response quality loss function also requires the reciprocal transformation for larger-the-better characteristics. This paper proposes a simple linear transformation for a bivariate response which combines the larger-the-better characteristic with any of the characteristics. This enables a...

Signal-to-Noise Ratio for Operating Window Using Unified Methodology

Operating window is a particular case of multi-variate system in which the objective is to make the system robust with respect to one particular factor in the presence of others. The signal-to-noise ratio of an operating window is the addition of the signal-to-noise ratios at the lower and upper thresholds of the window. Linear transformation on the lower threshold and reciprocal transformation on the upper threshold tend to render different weights at these thresholds, which results in an imbalanced optimization of a nondynamic operating window. In this article, a new signal-to-noise ratio for an operating window based on the unified methodology is proposed to reduce or eliminate this bias. Advantages of this methodology are discussed and an example is used to demonstrate the proposed methodology and compare with an existing methodology.

Application and limitation of axiomatic design complexity in quality engineering

Purpose – Complexity is an important element in axiomatic design theory. The current method for calculating complexity for a system following normal distribution is unbounded and approximate. The purpose of this paper is to present a detailed bounded solution for complexity using design and system ranges on a single function requirement. Design/methodology/approach – This paper discusses the complexity measure for a system following a uniform distribution. The complexities of two types of systems, a system performing with a uniform distribution and a system performing on target according to a normal distribution are then considered and compared. The research proposes a complexity measure for a system performing within specification limits with a uniform distribution. In addition, a new concept of relative complexity is proposed. Findings – A bounded solution for complexity for a normal distribution based on the existing assumptions was given which includes bias in addition to variance. The bounded solution was then compared to the existing approximate solution from the variance as well as bias standpoint. It was found that bias has an inappropriately reverse relationship with the bounded solution of complexity. Therefore, complexity cannot be used to approximate the system improvement when the improvement is based on a reduction in bias. Originality/value – The current method for calculating complexity for a system following normal distribution is unbounded and approximate. This paper proposed a complexity measure for a system performing within specification limits with a uniform distribution.

Dynamics of Entanglement Transfer from Squeezed Field to Remote Atomic Qubits

Dynamics of entanglement transfer from two-mode squeezed field and initially entangled atomic qubit pair to atomic qubits located in remote cavities is examined. Remote qubits become entangled through interaction with two mode squeezed light.

Dynamics of Four-tangle and Pairwise Entanglement of Two Atoms Coupled to Cavity Field

We examine analytically and numerically the dynamics of negativity, four-tangle, and pairwise entanglement invariants of two atoms coupled to cavity field. The amount of entanglement lost due to state reduction is obtained.

Customer Expectation and Warranty Cost — Nominal-the-Best Case

A fixed target, be it at zero or infinity, is assumed in Taguchis method for formulating the quality loss function (QLF). The QLF only accounts for immediate issues within manufacturing facilities whereas warranty cost occurs during customer use. Variable customer expectation has not been considered in the Taguchi methodology. This article presents a methodology to predict warranty probability, the probability of customer complaint, on the basis of two independent variables; product performance and consumer expectation. It is expected that the formulation presented will serve as a basic model for predicting warranty loss using warranty probability due to a single characteristic under certain assumptions. The nominal-the-best case is considered in this article and warranty cost is estimated for an automotive example to demonstrate the methodology.