Abstract:

For a tripartite quantum state ρABC, the conditional mutual information is an entropic value which quantifies the correlations between subsystems A and C, conditioned on B. When this value is zero, the state can be considered aquantum Markov chain, and there exists a map which can precisely recover ρABC from ρAB alone. A related map exists for states with small, but nonzero, conditional mutual information, which approximately recovers ρABC, with the recovery fidelity approaching unity as the conditional mutual information approaches zero. Motivated by the potential of universal state recovery in the context of qubit loss and noisy circuits, this project examined the evolution of conditional mutual information through a few standard circuits: the quantum Fourier transform, phase estimation, and Grover's search. I first present the general findings, which suggest that recoverable settings can arise naturally in quantum circuits. Lastly, I discuss both the potential application of the recovery map as a new approach to circuit optimization, as well as the next steps required to determine its viability.