<title>Generalized measurement of process and states</title>

Abstract

ABSTRACT The simultaneous inseparable reconstruction of quantum process and states is presented. The method is basedon constrained extremization of the likelihood functional. This statistical approach is ingenuous in quantummechanical frame and ensures physically correct results. Adopted scheme predicts the input density operatorsand the operator of quantum process all at once with help of noisy measured data only. Attention is paid to thecomparison of posed method with sequential measurement of the states and the process. Method is illustratedby numerical simulations.Keywords: quantum measurement, quantum state reconstruction, quantum process reconstruction, maximumlikelihood, completely positive maps 1. INTRODUCTION Measuring of quantum state of physical systems has attracted increased attention recently.15 Topical exper- iments often include extracting of quantum state from measured data as it's native part and many methods were developed for this purpose during recent years. Nevertheless most of them yield reconstructed objectswhich are not bona fide physical states. Only constrained statistical methods can simply integrate various ex-perimental data and guarantee the non-negativity of estimated density matrix. Physically the most importantis maximum likelihood principle61' representing genuine quantum measurement. Maximum likelihood methodensures existence of path in state space along which the likelihood of state monotonically increases.12Discussions of experimental results and understanding quantum nature behind them require however recog-nition of quantum processes, not only input or output quantum states. Examination of quantum communicationchannels and evaluation of performance of quantum gates are examples of practical applicability of quantumprocess reconstruction.1320 And again, maximum likelihood appears as the efficient and exceptional