Abstract
This article presents an overview for the theory of sequential products of quantum effects. We first summarize some of the highlights of this relatively recent field of investigation and then provide some new results. We begin by discussing sequential effect algebras which are effect algebras endowed with a sequential product satisfying certain basic conditions. We then consider sequential products of (discrete) quantum measurements. We next treat transition effect matrices (TEMs) and their associated sequential product. A TEM is a matrix whose entries are effects and whose rows form quantum measurements. We show that TEMs can be employed for the study of quantum Markov chains. Finally, we prove some new results concerning TEMs and vector densities.
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