اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAnother look at the optimal Bayes cost in the binary decision problem
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تأليف
Bernhard K. Meister
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The problem of quantum state discrimination between two wave functions of a particle in a square well potential is considered. The optimal minimum-error probability for the state discrimination is known to be given by the Helstrom bound. A new strategy is introduced here whereby the square well is compressed isoenergetically, modifying the wave-functions. The new contracted chamber is then probed using the conventional optimal strategy, and the error probability is calculated. It is shown that in some cases the Helstrom bound can be violated, i.e. the state discrimination can be realized with a smaller error probability.
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The problem of quantum state discrimination between two wave functions of a particle in a square well potential is considered. The optimal minimum-error probability is known to be given by the Helstrom bound. A new strategy is introduced by inserting
an impenetrable barrier in the middle of the square well, which is either a nodal or non-nodal point of the wave function. The energy required to insert the barrier is dependent on the initial state. This enables the experimenter to gain additional information beyond the standard probing of the state envisaged by Helstrom and to improve the distinguishability of the states. It is shown that under some conditions the Helstrom bound can be violated, i.e. the state discrimination can be realized with a smaller error probability.
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State discrimination with the aim to minimize the error probability is a well studied problem. Instead, here the binary decision problem for operators with a given prior is investigated. A black box containing the unknown operator is probed by select
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