Randomized Compressive State Tomography with No A-priori Information Using a Quantum Pulse Gate in Time and Frequency

Abstract

High-dimensional optical modes usually require a large number of measurements to be characterized— typically of the order O ( d 2 ) where d is the dimension of the underlying Hilbert space. Recently developed compressive tomography techniques can reconstruct low-rank signals with minimum measurements and no a priori assumptions [1] , [2] , [3] , [4] . We discuss results of randomized compressive tomography (RCT) implemented with a quantum pulse gate (QPG), a device that performs flexible optical measurements in the time-frequency domain [5] , [6] . In our experiments, we perform different random von Neumann basis measurements with a QPG that exploits dispersion-engineered sum-frequency generation in lithium niobate waveguides to implement projections onto arbitrary user-specified temporal mode superpositions. Based solely on the measurement data and nothing else, one can deterministically compute a positive number s cvx that monotonically estimates the size of the convex set of signal states consistent with the measurement data. For a sufficient number of informationally complete (IC) QPG projections, the convex set converges to a single point ( s cvx = 0), where the signal is uniquely reconstructed.