Unambiguous comparison of ensembles of quantum states

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We present a solution of the problem of the optimal unambiguous comparison of two ensembles of unknown quantum states ${|{\ensuremath{\psi}}_{1}⟩}^{\ensuremath{\bigotimes}k}$ and ${|{\ensuremath{\psi}}_{2}⟩}^{\ensuremath{\bigotimes}l}$. We consider two cases: (1) The two unknown states $|{\ensuremath{\psi}}_{1}⟩$ and $|{\ensuremath{\psi}}_{2}⟩$ are arbitrary states of qudits. (2) Alternatively, they are coherent states of a harmonic oscillator. For the case of coherent states we propose a simple experimental realization of the optimal ``comparison'' machine composed of a finite number of beam splitters and a single photodetector.