The measurement of a quantum state wave function 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 wave functions, which usually requires complicated measurement techniques. The recent weak-value-based quantum measurement circumvents this resource issue but relies on an extra pointer space. Here, we theoretically propose and then experimentally demonstrate a direct and efficient measurement strategy based on a δ-quench probe: by quenching its complex probability amplitude one by one (δ quench) in the given basis, we can directly obtain the quantum wave function of a pure ensemble by projecting the quenched state onto a postselection state. We confirm its power by experimentally measuring photonic complex temporal wave functions. This new method is versatile and can find applications in quantum information science and engineering.
The measurement of a quantum state wave function 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 wave functions, which usually requires complicated measurement techniques. The recent weak-value-based quantum measurement circumvents this resource issue but relies on an extra pointer space. Here, we theoretically propose and then experimentally demonstrate a direct and efficient measurement strategy based on a δ-quench probe: by quenching its complex probability amplitude one by one (δ quench) in the given basis, we can directly obtain the quantum wave function of a pure ensemble by projecting the quenched state onto a postselection state. We confirm its power by experimentally measuring photonic complex temporal wave functions. This new method is versatile and can find applications in quantum information science and engineering.
Density matrix, which characterizes a quantum state, plays an important role in quantum mechanics. Recently, a method which can directly measure the elements of a density matrix was proposed. Compared with the conventional quantum state tomography which is widely used to reconstruct the density matrix, this measurement method has the advantages of directness and simplicity. However, this direct measurement method relies on an extra pointer space. The addition of this extra pointer can increase the complexity of an experiment. In this paper, we first review previous work on direct measurement, then we propose a scheme to directly measure the density matrix based on δ-quench, which is also a direct measurement method but needs no additional pointer. This proposal reduces the complexity of the measuring system and further simplifies the measurement. We propose two schemes to realize this δ-quench measurement, then analyse their superiorities in different situations of measurement. An experiment to measure photon's density matrix is also designed.
The direct measurement of a complex wave function has been recently realized by using weak values. In this Letter, we introduce a method that exploits sparsity for the compressive measurement of the transverse spatial wave function of photons. The procedure involves weak measurements of random projection operators in the spatial domain followed by postselection in the momentum basis. Using this method, we experimentally measure a 192-dimensional state with a fidelity of 90% using only 25 percent of the total required measurements. Furthermore, we demonstrate the measurement of a 19,200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique.
Weak values, emerging from weak measurements in pre- and postselection, exhibit complex-valued properties, enabling the direct characterization of quantum systems. However, conventional weak values do not account for system evolution, restricting their capability to capture quantum dynamical information. To overcome this limitation, we introduce the process weak value (PWV), which incorporates quantum evolution between observables during pre- and postselection. By establishing a connection between PWVs and the matrix elements of unitary operators, we develop a theoretical framework for the direct characterization of quantum processes. Our experimental validation encompasses single-photon and two-photon unitary processes, as well as non-Hermitian parity-time symmetric quantum processes. Compared to standard quantum process tomography, our method reduces the required bases for state preparation and measurements while circumventing complex reconstruction algorithms, enhancing efficiency and scalability. Our PWV formalism opens avenues for broader foundational investigations of weak measurements and enables efficient applications in characterizing sophisticated quantum processes.
The ability to manipulate light has allowed scientists to verify fundamental theories of physics and to develop a new generation of technologies that use photons as a primary resource. Recent developments in quantum measurement theory have offered new alternatives to approach some of the most remarkable problems in quantum physics. Consequently, the principles of quantum mechanics have been exploited in the development of quantum technologies such as optical metrology, quantum communication, and quantum information. In recent years, weak measurements and two of its most remarkable variants: weak value amplification and direct measurement, have been developed and are considered important resources for quantum applications. In this paper, we discuss weak measurements and some significant applications of weak values. We elaborate on how distinct forms of weak values are used to observe and amplify small effects or to directly measure the quantum wave function of photons, a crucial task for schemes for quantum communication and quantum information. We also review some of the most recent methods for weak value amplification and direct measurement that our group has developed.
Abstract In contrast to the standard quantum state tomography, the direct tomography seeks a direct access to the complex values of the wave function at particular positions. Originally put forward as a special case of weak measurement, it has been extended to arbitrary measurement setup. We generalize the idea of “quantum metrology,” where a real-valued phase is estimated, to the estimation of complex-valued phase. We show that it enables to identify the optimal measurements and investigate the fundamental precision limit of the direct tomography. We propose a few experimentally feasible examples of direct tomography schemes and, based on the complex phase estimation formalism, demonstrate that direct tomography can reach the Heisenberg limit.
Efficient acquiring information from a quantum state is important for research in fundamental quantum physics and quantum information applications. Instead of using standard quantum state tomography method with reconstruction algorithm, weak values were proposed to directly measure density matrix elements of quantum state. Recently, similar to the concept of weak value, modular values were introduced to extend the direct measurement scheme to nonlocal quantum wavefunction. However, this method still involves approximations, which leads to inherent low precision. Here, we propose a new scheme which enables direct measurement for ideal value of the nonlocal density matrix element without taking approximations. Our scheme allows more accurate characterization of nonlocal quantum states, and therefore has greater advantages in practical measurement scenarios.