6/04/15 and 13/04/15 15:30H Minicourse@UFRJ – Leandro Aolita – IF-UFRJPosted: March 31, 2015
Title: Mini-course on quantum state certification
A major roadblock for large-scale quantum technologies is the lack of practical reliable certification tools. In the first lecture of this mini-course, I will make a brief general review of basic tools available for quantum validation — ranging from brute-force quantum state tomography, via compressed-sensing, to quantum interactive proofs and direct fidelity-estimation techniques. I will then formally define the notion of quantum-state certification tests. The level of this first part will be introductory and thus ideal for students or non-specialists. In the second lecture, I will focus on recent results on reliable quantum certification for photonic quantum technologies. Here, I will try to provide some degree of technicality. I will introduce an experimentally friendly (efficient) certification test for experimental preparations of arbitrary $m$-mode pure Gaussian states, pure non-Gaussian states generated by linear-optical circuits with $n$-boson Fock-basis states as inputs, and pure states generated from the latter class by subsequently post-selecting with Fock-basis measurements on ancillary modes. We will follow the mindset of an untrusted prover, who prepares the state, and a skeptic certifier, with classical computing and single-mode homodyne-detection capabilities only. This test exploits an extremality-based fidelity bound that is interesting in its own right. The estimation of this bound relies, in turn, on non-Gaussian state nullifiers, which I will introduce on the way. With this technique, the certification of many-mode photonic networks, as those used for photonic quantum simulations, boson samplers, and quantum metrology, seems now within reach.
UFRJ- Centro de Tecnologia do Fundão, Bloco A, sala 312