While measuring the orbital angular momentum state of bright light beams can be performed using imaging techniques, a full characterization at the single-photon level is challenging. For applications to quantum optics and quantum information science, such characterization is an essential capability. Here, we present a setup to perform the quantum state tomography of photonic qubits encoded in this degree of freedom. The method is based on a projective technique using spatial mode projection via fork holograms and single-mode fibers inserted into an interferometer. The alignment and calibration of the device is detailed as well as the measurement sequence to reconstruct the associated density matrix. Possible extensions to higher-dimensional spaces are discussed.
While measuring the orbital angular momentum state of bright light beams can be performed using imaging techniques, a full characterization at the single-photon level is challenging. For applications to quantum optics and quantum information science, such characterization is an essential capability. Here, we present a setup to perform the quantum state tomography of photonic qubits encoded in this degree of freedom. The method is based on a projective technique using spatial mode projection via fork holograms and single-mode fibers inserted into an interferometer. The alignment and calibration of the device is detailed as well as the measurement sequence to reconstruct the associated density matrix. Possible extensions to higher-dimensional spaces are discussed.
Orbital angular momentum (OAM) of light is a promising degree of freedom for quantum communication and quantum computation. However, efficient methods to transform and measure OAM modes are still not available readily. Here, we propose a method for full quantum state tomography for arbitrary OAM states of light. The key component in our scheme is the helicity sorter, a device that can sort OAM modes of a light beam based on their Helicity. We present two setups to implement the Helicity sorted, one requires O(N) number of optical elements for 2N OAM modes, and the other uses spatial light modulators and is independent of the number of OAM modes. Ours is the first method to provide the efficient and scalable full quantum state tomography of the OAM modes and can be extremely important for quantum communication and quantum computation.
In the context of quantum information theory, the use of certain photonic degrees of freedom allows the creation of high-dimensional quantum states, called qudits, which offer advantages over qubits in applications such as communication, cryptography, and fundamental tests of quantum mechanics. In many of these applications, it is necessary to reconstruct the quantum state to be used, since it contains all the measurable properties of a physical system. Recently, a simple method for reconstructing pure quantum states, called quantum ptychography, has been proposed. It is based on projections of the input state into various partial overlapping subspaces, each one followed by a projective measurement in the Fourier basis, which is generated by the quantum Fourier transform (QFT) of the computational basis. At the end, an iterative algorithm estimates the state from the collected data. In this work, we propose to apply this method to pure states of qudits encoded in angular position and orbital angular momentum (OAM) of single photons. For this purpose, we define these qudits based on the discretization of the spatial profile of a photon in cylindrical coordinates, through an arrangement of D angular slits, and describe their representation in the OAM basis. To apply ptychography to these qudits, we show that the intermediate projections will be implemented by simple binary spatial filters, while the measurement in the Fourier basis of the post-projection states will be performed by measuring in a basis defined by D OAM modes. Finally, we demonstrate the applicability of the ptychographic method by simulating the reconstruction of angular qudits for D = 5 and D = 12, and evaluate its experimental feasibility.
Orbital angular momentum (OAM) of light has acquired the interest of scientists due to its novel properties. The high-dimensional Hilbert space and entanglement that OAM offers make it a valuable DOF for many quantum optical protocols. However, conventional measurement of OAM state, which exploits coincidence count-based quantum state tomography (QST), suffers from low-brightness and subsequent need for data accumulation times. Such problems are a serious obstacle, especially for high-dimensional OAM qudits. In this work, we suggest stimulated emission tomography (SET) as a solution for bright and efficient measurement of OAM entangled photons. We show that SET can successfully extract information of SPDC photons by measuring the spiral bandwidth and reconstructing the density matrix of SPDC photons. The fidelity and linear entropy of the reconstructed density matrix are [Formula: see text] and [Formula: see text], respectively, while the time required for each projective measurement is 1 s. Our results show the potential of SET as an efficient alternative to conventional QST.
Photonic quantum technologies utilize various degrees of freedom (DOFs) of light, such as polarization, frequency, and spatial modes, to encode quantum information. In the effort of further improving channel capacity of quantum communication, and for increasing the complexity of available quantum operations, high-dimensional and hyperentangled states are now gaining interest. However, efficiently measuring these high dimensional states is challenging due to the large number of measurements required for reconstructing the full density matrix via quantum state tomography (QST), and the fact that each measurement requires some modification in the experimental setup. Here, we propose a framework for reconstructing the density matrix of a single-photon hyperentangled across multiple DOFs using a single intensity-measurement obtainable from traditional cameras, and discuss extensions for multiphoton hyperentangled states. Our method hinges on the spatial DOF of the photon and uses it to encode the quantum information from the other DOFs. We numerically demonstrate this method for single-photon OAM-spin and OAM-frequency entangled states using an ideal coupler and a multimode fiber, to perform the information mixing and transfer the encoding to spatial information, where it is detected using a simple camera. This technique simplifies the experimental setup and reduces acquisition time compared to traditional QST-based methods. Moreover, it allows the recovery of DOFs that conventional cameras cannot detect, such as polarization, thus eliminating the need for projection measurements.
Twisted photons can in principle carry a discrete unbounded amount of orbital angular momentum (OAM), which are of great significance for quantum communication and fundamental tests of quantum theory. However, the methods for characterization of the OAM quantum states present a fundamental limit for miniaturization. Metasurfaces can exploit new degrees of freedom to manipulate optical fields beyond the capabilities of bulk optics, opening a broad range of novel and superior applications in quantum photonics. Here we present a scheme to reconstruct the density matrix of the OAM quantum states of single photons with all-dielectric metasurfaces composed of birefringent meta-atoms. We have also measured the Schmidt number of the OAM entanglement by the multiplexing of multiple degrees of freedom. Our work represents a step toward the practical application of quantum metadevices for the measurement of OAM quantum states in free-space quantum imaging and communications.
High-dimensional (HD) entanglement enables an encoding of more bits than in the two-dimensional case and promises to increase communication capacity over quantum channels and to improve robustness to noise. In practice, however, one of the central challenges is to devise efficient methods to quantify the HD entanglement explicitly. Full quantum state tomography is a standard technology to obtain all the information about the quantum state, but it becomes impractical because the required measurements increase exponentially with the dimension in HD systems. Hence, it is highly anticipated that a new method will be found for characterizing the HD entanglement with as few measurements as possible and without introducing unwarranted assumptions. Here, we present and demonstrate a scan-free tomography method independent of dimension, which only requires two measurements for the characterization of two-photon HD orbital angular momentum (OAM) entanglement. Taking Laguerre-Gaussian modes of photons as an example, the density matrices of OAM entangled states are experimentally reconstructed with very high fidelity. Our method is also generalized to the mixed HD OAM entanglement. Our results provide realistic approaches for quantifying more complex OAM entanglement in many scientific and engineering fields such as multiphoton HD quantum systems and quantum process tomography.