Efficient Learning of Continuous-Variable Quantum States

Abstract

The characterization of continuous-variable quantum states is crucial for applications in quantum communication, sensing, simulation and computing. However, a full characterization of multimode quantum states requires a number of experiments that grows exponentially with the number of modes. Here we propose an alternative approach where the goal is not to reconstruct the full quantum state, but rather to estimate its characteristic function at a given set of points. For multimode states with reflection symmetry, we show that the characteristic function at M points can be estimated using only O(log M ) copies of the state, independently of the number of modes. When the characteristic function is known to be positive, as in the case of squeezed vacuum states, the estimation is achieved by an experimentally friendly setup using only beamsplitters and homodyne measurements.

12 pages, 4 figures. Comments are welcome

References in corpus (6)

• Directly estimating non-classicality
• Scrambling and Complexity in Phase Space
• Continuous-Variable Instantaneous Quantum Computing is hard to sample
• Classical shadow tomography for continuous variables quantum systems
• Continuous-variable quantum state designs: theory and applications
• Quantum Similarity Testing with Convolutional Neural Networks

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• Fundamental Limits Of Quickest Change-point Detection With Continuous-Variable Quantum States