δ -Quench Measurement of a Pure Quantum-State Wave Function

Abstract

Measurement of quantum state wavefunction not only acts as a fundamental part in quantum physics but also plays an important role in developing practical quantum technologies. Conventional quantum state tomography has been widely used to estimate quantum wavefunctions, which, however, requires huge measurement resources exponentially growing with the dimension of state. The recent weak-value-based quantum measurement circumvents this resources issue but relies on an extra pointer space. Here, we propose and demonstrate a simple and direct measurement strategy based on δ-quench probe: By quenching its complex probability amplitude one by one (δ-quench) in the given bases, we can directly obtain the quantum wavefunction by projecting the quenched state onto a post-selection state. As compared to the conventional approaches, it needs only one projection basis. We confirm its power by experimentally measuring photonic complex temporal wavefunctions. This new method is versatile and can find applications in quantum information science and engineering.

On the experiment-friendly formulation of quantum backflow

“…While more ingenious strategies may exist, an experimental measurement of the wave function itself (using, e.g., techniques developed in Refs. [41][42][43][44]) can in principle be used to reconstruct the Husimi distribution.…”

Direct measurement of ultrafast temporal wavefunctions

“…Next, we remark on previous studies related to direct measurement of the temporal wavefunction. A recently reported experiment on δ-quench measurement [37] has demonstrated measurement of the temporal mode of light by applying instantaneous phase modulation followed by projection onto a specific frequency. Although this method differs from direct measurement using weak measurement [24] and our direct measurement method, it satisfies the definition of direct measurement of the temporal wavefunction.…”

Increase the Efficiency of Post-selection in Direct Measurement of Quantum Wave Function

“…The method has also been generalized from the weak measurement to the strong measurement [20][21][22][23][24]. An alternative direct measurement strategy based on a δ-quench probe was developed: by quenching its complex probability amplitude one by one (δ quench) in the given basis, one can directly obtain the quantum wave function of a pure ensemble by projecting the quenched state onto a post-selection state [25]. However, the efficiency of these direct measurement methods is limited by the success probability of the post-selection, which is usually pretty low in a practical experiment, and thus increasing the efficiency of the post-selection is in demand.…”