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