The Hilbert Schmidt inner product, quantum illumination, and beyond

Abstract

Quantum Illumination (QI)1 is a proposed remote targeting protocol using entangled states in which the experimenter sends a signal towards an expected target in a noisy environment that has a probability of reflecting off the surface or, in the case of no surface, being lost. Upon return, the noisy signal is jointly measured with the idler, which has been held in local memory, to determine if the surface has been detected. The idler effectively increases the brightness of the noisy signal to help distinguish it from the surrounding noise. Even though the returned mixed state is in the un-entangled regime, it has been shown that QI outperforms a conventional protocol that only sends separable states as the signal. We analyzed QI as a quantum channel discrimination protocol and circumvented computational issues that rely on diagonalization of the quantum states by using the normalized Hilbert-Schmidt (NH-S) inner product as a measure of state distinguishability.2 Because the NH-S inner product is simple to compute, for a choice of entangled pure state and bipartition, we were able to rank the performance of QI entirely in terms of the dimension of the composite Hilbert space and the purity of the idler subsystem. We also showed that the greatest advantage gained by quantum illumination over conventional illumination occurs when one uses a Bell state, and for a fixed dimension d, the optimal performance of QI is achieved when the purity of the idler subsystem is minimal. In this talk, we review the results of,2 and present our progress on extending this analysis to a broader class of quantum information protocols beyond QI.