Quantum state tomography is an important tool for quantum communication, computation, metrology, and simulation. Efficient quantum state tomography on a high dimensional quantum system is still a challenging problem. Here, we propose a novel quantum state tomography method, auxiliary Hilbert space tomography, to avoid pre-rotations before measurement in a quantum state tomography experiment. Our method requires projective measurements in a higher dimensional space that contains the subspace that includes the prepared states. We experimentally demonstrate this method with orbital angular momentum states of photons. In our experiment, the quantum state tomography measurements are as simple as taking a photograph with a camera. We experimentally verify our method with near-pure- and mixed-states of orbital angular momentum with dimension up to
d=13, and achieve greater than 95 % state fidelities for all states tested. This method dramatically reduces the complexity of measurements for full quantum state tomography, and shows potential application in various high dimensional quantum information tasks.
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.
The tomography of photonic quantum states is key in quantum optics, impacting quantum sensing, computing, and communication. Conventional detectors are limited in their temporal and spatial resolution, hampering high-rate quantum communication and local addressing of photonic circuits. Here, we propose to utilize free electron-photon interactions for quantum state tomography, introducing electron homodyne detection with potential for femtosecond-temporal and nanometer-spatial resolutions. The detectable quantum information level depends on the electron-photon interaction strength. Our Letter opens avenues for free-electron-based photodetection utilizing the ultrafast, subwavelength, nondestructive nature of free electrons.