Device-independent tests of quantum channels

Toward the Device-Independent Certification of a Quantum Memory

Quantum memories represent one of the main ingredients of future quantum communication networks. Their certification is therefore a key challenge. Here we develop efficient certification methods for quantum memories. Considering a device-independent approach, where no a priori characterization of sources or measurement devices is required, we develop a robust self-testing method for quantum memories. We then illustrate the practical relevance of our technique in a relaxed scenario by certifying a fidelity of 0.87 in a recent solid-state ensemble quantum memory experiment. More generally, our methods apply for the characterization of any device implementing a qubit identity quantum channel.

What is entropy? A perspective from games of chance

The crucial role of channels in physics and information theory motivates the task of characterizing the entropy, or uncertainty, of a channel. Games of chance become a natural candidate for this task, as a system's performance in a gambling game depends solely on the uncertainty of its output. In this work, we construct families of games that induce preorders corresponding to majorization, conditional majorization, and channel majorization. Finally, we provide operational interpretations for all preorders, show the relevance of these results to dynamical resource theories, and find the only asymptotically continuous classical channel entropy.

Experimental Self-Characterization of Quantum Measurements

The accurate and reliable description of measurement devices is a central problem in both observing uniquely nonclassical behaviors and realizing quantum technologies from powerful computing to precision metrology. To date quantum tomography is the prevalent tool to characterize quantum detectors. However, such a characterization relies on accurately characterized probe states, rendering reliability of the characterization lost in circular argument. Here we report a self-characterization method of quantum measurements based on reconstructing the response range-the entirety of attainable measurement outcomes, eliminating the reliance on known states. We characterize two representative measurements implemented with photonic setups and obtain fidelities above 99.99% with the conventional tomographic reconstructions. This initiates range-based techniques in characterizing quantum systems and foreshadows novel device-independent protocols of quantum information applications.

Contextuality, memory cost and non-classicality for sequential measurements

The Kochen-Specker theorem, and the associated notion of quantum contextuality, can be considered as the starting point for the development of a notion of non-classical correlations for single systems. The subsequent debate around the possibility of an experimental test of Kochen-Specker-type contradiction stimulated the development of different theoretical frameworks to interpret experimental results. Starting from the approach based on sequential measurements, we will discuss a generalization of the notion of non-classical temporal correlations that goes beyond the contextuality approach and related ones based on Leggett and Garg's notion of macrorealism, and it is based on the notion of memory cost of generating correlations. Finally, we will review recent results on the memory cost for generating temporal correlations in classical and quantum systems. The present work is based on the talk given at the Purdue Winer Memorial Lectures 2018: probability and contextuality. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.

Certifying the Building Blocks of Quantum Computers from Bell's Theorem

Bell's theorem has been proposed to certify, in a device-independent and robust way, blocks either producing or measuring quantum states. In this Letter, we provide a method based on Bell's theorem to certify coherent operations for the storage, processing, and transfer of quantum information. This completes the set of tools needed to certify all building blocks of a quantum computer. Our method distinguishes itself by its robustness to experimental imperfections, and so could be used to certify that today's quantum devices are qualified for usage in future quantum computers.

Device-Independent Tests of Quantum Measurements

We consider the problem of characterizing the set of input-output correlations that can be generated by an arbitrarily given quantum measurement. Our main result is to provide a closed-form, full characterization of such a set for any qubit measurement, and to discuss its geometrical interpretation. As applications, we further specify our results to the cases of real and complex symmetric, informationally complete measurements and mutually unbiased bases of a qubit, in the presence of isotropic noise. Our results provide the optimal device-independent tests of quantum measurements.