Quantum Measurement

We propose and demonstrate the δ-quench measurement of quantum wavefunctions as a new versatile measurement method to measure relative phase. By sequentially quenching the phase of the basis, the quantum wavefunction can be obtained using one fixed post-selection state. In this method, we only do the projection once, and it requires no ancillary pointer state. For the state in high dimension Hilbert space, we can see the number of projective measurements scales linearly with the dimension. We apply this novel method to measure a photonic temporal wavefunction and achieve a measurement fidelity of around 99%. This δ-quench protocol can also be used to measure wavefunctions in other Hilbert spaces, such as the spatial, polarization, and orbital angular momentum degree of freedom. In addition, in spite of that the quench operation is assumed to be unitary above, it is, nevertheless, worth notice that this strategy can also work with non-unitary quench operation, such as controllable loss, which is currently beyond a conventional quantum measurement explanation and would potentially inspire interesting discussions.