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Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed…
Recent empirical work in the field of 'weak measurements' has yielded novel ways of more directly accessing and exploring the quantum wavefunction. Measuring either position or momentum for a photon in a 'weak' manner yields a wide range of…
Wavefunction is the foundation of quantum theory, which is assumed to give a complete description of a quantum system. For a long time, wavefunction is introduced as an abstract element of the theory and there lacks effective ways to…
Central to quantum theory, the wavefunction is the complex distribution used to completely describe a quantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition.…
It was recently pointed out (and demonstrated experimentally) by Lundeen et al. that the wave function of a particle (more precisely, the wave function possessed by each member of an ensemble of identically-prepared particles) can be…
Weak measurement is a standard measuring procedure with two changes: it is performed on pre- and post-selected quantum systems and the coupling to the measuring device is weakened. The outcomes of weak measurements, ``weak values'' are very…
The time-symmetric formalism endows the weak measurement and its outcome, the weak value,many unique features. In particular, it allows a direct tomography of quantum states without resort to complicated reconstruction algorithms and…
The physical interpretation of weak measurements has been the subject of much debate. It is known that anomalous phenomena and results that appear in weak measurements are essentially related to the phase of the quantum system being…
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…
The standard method of "measuring" quantum wavefunction is the technique of {\it indirect} quantum state tomography. Owing to conceptual novelty and possible advantages, an alternative {\it direct} scheme was proposed and demonstrated…
New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only $O(d)$…
Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed…
The direct measurement of a complex wavefunction has been recently realized by using weak-values. In this paper, we introduce a method that exploits sparsity for compressive measurement of the transverse spatial wavefunction of photons. The…
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
Entanglement and wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using Weak Values, was demonstrated by Lundeen et al., Nature…
A novel method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently Vallone and Dequal…
A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to…
Historically, weak values have been associated with weak measurements performed on quantum systems. Over the past two decades, a series of works have shown that weak values can be determined via measurements of arbitrary strength. One such…
In contrast to the standard quantum state tomography, the direct tomography seeks the direct access to the complex values of the wave function at particular positions (i.e., the expansion coefficient in a fixed basis). Originally put…