In mesoscopic quantum regime (mean photon number 10000) and non-orthogonal coherent state(number of non-orthogonal coherent state 2000), why probability of detection by performing quantum unambiguous measurement is less than random guess(1/2000). My question is that, if probability of detection is less than random guess following any particular quantum measurement process, then it will be better to follow random-guess(no-measurement).
Answer
The title of the paper is "Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States".
Random guessing is an ambiguous discrimination procedure. It can return the wrong answer without telling you that it failed.
More generally, unambiguous discrimination procedures are less likely to succeed because removing any chance of accidental failure also sacrifices any chance of accidental success. You don't get the free $+1/n$ boost that ambiguous procedures get from falling back to random guessing when all else fails. They start from zero, and when the states are really close and have trace distance $<< 1/n$ that makes quite a big difference.
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