1. The unitary transformations are denoted by the map \ delta, 2. Under this convention, the Fourier transform is again a unitary transformation on. 3. In other words, it is a unitary transformation . 4. Indeed, in this case we introduce the unitary transformation 5. The relative minus sign appears because the beam splitter is a unitary transformation . 6. Each linear optical element equivalently applies a unitary transformation on a finite number of qubits. 7. The commutator of the field operators is invariant under unitary transformation ~ \ hat U ~: 8. For instance, state transformations relating observers in different frames of reference are given by unitary transformations . 9. An additional unitary transformation can be applied on the system to accelerate the convergence in some computational schemes. 10. Another approach relies on the realization of unitary transformations on temporal modes based on dispersion and pulse shaping.
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