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sdf Delayed-Choice Erasing of Which-Way Information Proposition of a New Possibility sdf Mohammad Bahrami, Afshin Shafiee Department of Chemistry, Sharif University of Technology, P.O.Box, , Tehran, Iran Abstract In a double-slit experimental arrangement, by obtaining Welcher Weg (Which Way) Information or the existence of detectable WW Information (that makes the paths to be distinguishable), the interference pattern will be destroyed. However, the distinguishing information could be erased by a suitable non-unitary change and then the interference pattern will be restored. This is the main idea of Quantum Eraser (QE). To our best knowledge, the common feature of pervious demonstrations of QE is that their erasing process (a non-unitary change) is a quantum measurement [1]. A statistical examination of these proposals suggests that whenever the Bayesian rule is taken into account for two relevant events in two successive times, the probabilistic description of them is unavoidably time-symmetric. Consequently, it seems that they cannot fulfill the implications of a so-called delayed-choice experiment. As a possible alternative, however, we suggest a new experimental arrangement in which one can change the whole state of a given system at a proper time (without measurement) to accomplish an actual delayed-choice experiment with a time- asymmetric attribute. The peculiar features of this experiment are then discussed. As a result, independent of any physical interpretation, the time sequence of our observations on A or B has no influence on calculating p(A,B|C). Thus the probabilistic description of events in QE is time-symmetric. This is a consequence of the Bayesian rule for the joint probability of two events in different occasions when there is no preferred order of time in statistical characterization of events. So it can be easily concluded that in the above mentioned situations, the delayed mode of measurement has no special importance. Accordingly, we conclude that proposed QE cannot fulfill the implications of a delayed-choice experiment in which the time sequence of events should have a direct effect on the final result [2]. Discussion of Pervious QE demonstrations In the pervious QE proposals, the interference pattern is recovered for a joint probability. In double-slit setup, we denote this joint probability as p(A,B|C) where: A : detection of atoms on the detector-plate. B : determination of the QE measurement. C : experimental arrangement (state sspreparation). p(A|C) shows no interference pattern. To obtain p(A,B|C), the observer can choose one of the below mentioned procedures: (QE1): he first observe A and then B. then he obtains p(A,B|C) as p(A,B|C)=p(A|C) p(B|A,C). (QE2):he first observe B and then A. then he obtains p(A,B|C) as p(A,B|C)=p(B|C) p(A|B,C). Our propounded possibility of erasing WW information Consider the representative work of Scully, Englert and Walther[3] in which the WW information is stored in the distinguishable states (|10> and |01>) of a composite system of cavities where |10> describes the situation in which one photon is in cavity-1 and none in cavity-2, and |01> describes the situation in which one photon is in the cavity-2 while there is none in cavity-1. These states include the accessible WW Information. Since the atoms can pass through just one of the cavities and not both, and meanwhile the |10> and |01> are distinguishable physical states of composite system of the cavities, then it is apparent that =0. Now suppose that when the atoms are still flying between the slits and the detector-plate, we remove the plate S. By removing the differentiating plate (S), the distinguishable states of cavities (which describe a composite system) are changed into one unique state |1> (which describes a simple system containing one photon). Therefore, one cannot obtain the WW Information, although the photon is not erased too. In fact, in our proposed experiment, the possibility of obtaining WW Information is erased. The WW Information Erasing process, here, depends on what the observer decides to perform before the particle’s detection. This is a delayed-choice experiment, since the time order of events has a prominent role in its quantum (probabilistic) description. Meanwhile, here, the interference pattern is recovered for the whole ensemble of data obtained on the detector-plate and not sub- ensemble of it. A References 1- M. Bahrami, A. Shafiee, On The Significance of Which-Way Expositions: Propounding a New Possibility, arXiv:quant-ph/ v2arXiv:quant-ph/ v2 2- J. A. Wheeler, Law Without Law, published in “Quantum theory and measurement”, edited by J.A.Wheeler, W.H.Zurek, (Princeton University Press, New Jersey, 1983) pp M. O. Scully, B. G. Englert, and H. Walther, Quantum optical tests of complementarity, Nature, 351, 111–116, (1991). Here, to observe the interference pattern the experimenter should erase the possibility of obtaining WW Information only during the time interval when atoms are between the slits and the detector-plate. Our Proposed Eraser Process

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