Southwest Quantum Information and Technology

Shadow tomography of continuous-variable quantum systems

Presenting Author: Srilekha Gandhari, Joint Center for Quantum Information and Computer Science, NIST/University of Maryland
Contributing Author(s): Victor Albert, Jacob Taylor, Michael Gullans

Shadow tomography is a framework for constructing classical descriptions of quantum states, called classical shadows, with powerful methods to bound the estimators used. Classical shadows are well-studied in the discrete-variable case such as for qubits. Here, we extend the framework of shadow tomography to continuous-variable quantum systems, such as optical modes and harmonic oscillators. These are important quantum resources with continuous variable descriptions. We show how to adapt homodyne and heterodyne experimental methods from optical tomography to efficiently construct classical shadows for finite-dimensional estimations of the infinite dimensional unknown state. We provide rigorous bounds on the variance of estimating density matrices from homodyne and heterodyne measurements. We show that to reach a desired precision of the classical shadow of an N-photon density matrix with high probability, homodyne tomography requires on the order of N^5 measurements whereas heterodyne tomography requires only on the order of N^4 measurements. We discuss extensions to multimode classical shadows and consider practical conditions required to realize our protocols.

(Session 5 : Thursday from 12:00pm-2:00 pm)