Quantum computational learning of optical states

For many optical imaging and sensing tasks, performing joint measurements across many modes or copies can sometimes be necessary to achieve optimality. Such nonlocal interactions become technologically challenging with standard optical components, especially as the system size grows. On the other hand, quantum computers inherently promise these nonlocal interaction capabilities at scale. Thus, one can imagine a metrological application of quantum computers being to coherently process the information held within multimode light fields prior to readout, in theory enabling arbitrary global measurements of light. To do this, the light needs to first be collected into the quantum computer, which can be accomplished by transducing the light field into whichever quantum computer architecture is used. We refer to this general scheme as quantum computational imaging and sensing (QCIS). In prior work, we gave a proof-of-principle example in classical communications that shows QCIS can provide a quantum enhancement over local, all-optical measurement schemes. This advantage is in terms of the error probability of discriminating coherent state codewords. More recently, we have explored the problem of learning properties of various general classes of optical states when given access to many copies of the state. Here we give an analysis of domains where QCIS may or may not provide quantum learning speedups over alternative methods.