# Quantum theory of unambiguous measurements - Quantum Physics

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Abstract: In the present paper I formulate a framework that accommodates manyunambiguous discrimination problems. I show that the prior information aboutany type of constituent state, channel, or observable allows us toreformulate the discrimination among finite number of alternatives as thediscrimination among finite number of average constituents. Using thisframework I solve several unambiguous tasks. I present a solution to optimalunambiguous comparison of two ensembles of unknown quantum states. I considertwo cases: 1 The two unknown states are arbitrary pure states of qudits. 2Alternatively, they are coherent states of single-mode optical fields. For thiscase I propose simple and optimal experimental setup composed of beam-splittersand a photodetector. As a second tasks I consider an unambiguous identificationUI of coherent states. In this task identical quantum systems are prepared incoherent states and labeled as unknown and reference states, respectively. Thepromise is that one reference state is the same as the unknown state and thetask is to find out unambiguously which one it is. The particular choice of thereference states is unknown to us, and only the probability distributiondescribing this choice is known. In a general case when multiple copies ofunknown and reference states are available I propose a scheme consisting ofbeamsplitters and photodetectors that is optimal within linear optics. UI canbe considered as a search in a quantum database, whose elements are thereference states and the query is represented by the unknown state. Thisperspective motivated me to show that reference states can be recovered afterthe measurement and might be used with reduced success rate in subsequent UI.Moreover, I analyze the influence of noise in preparation of coherent states onthe performance of the proposed setup. Another problem I address is theunambiguous comparison of a pair of unknown qudit unitary channels. Icharacterize all solutions and identify the optimal ones. I prove that inoptimal experiments for comparison of unitary channels the entanglement isnecessary. The last task I studied is the unambiguous comparison of unknownnon-degenerate projective measurements. I distinguish between measurementdevices with apriori labeled and unlabeled outcomes. In both cases only thedifference of the measurements can be concluded unambiguously. For the labeledcase I derive the optimal strategy if each unknown measurement is used onlyonce. However, if the apparatuses are not labeled, then each measurement devicemust be used at least twice. In particular, for qubit measurement apparatuseswith unlabeled outcomes I derive the optimal test state in the two-shotsscenario.

Author: ** Michal Sedlák**

Source: https://arxiv.org/