Quantum correlations in prepare-and-measure scenarios and their semi-device-independent applications

Abstract

A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum correlations in prepare-and-measure scenarios. Inspired by the developments in Bell nonlocality and device-independent information processing, this line of research aims to characterize the possibilities and limits of quantum systems for communication, in particular to precisely capture the advantage they offer over classical systems. In addition to fundamental insights, these ideas also underpin the concept of semi-device-independent quantum information processing. Exploring trade-offs between security, performance and ease-of-implementation, this approach opens promising directions for novel quantum information processing technologies and devices. A number of protocols and proof-of-principle demonstrations have been reported in recent years, in particular for quantum randomness certification and key distribution. Here, we provide a comprehensive introduction to quantum prepare-and-measure correlations and semi-device independent applications.

Figures (3)

• Figure 1: Prepare-and-measure scenario. A preparation device (Alice) receives an input $x$ and prepares a quantum state $\rho_x$ that is sent to a measurement device (Bob) which, based on input $y$, measures the state and obtains an outcome $b$. Either the preparation or measurement (or both) may be partially characterised. In addition, the devices may have access to a shared resource which could be classical (shared randomness) or quantum (shared entangled states). The behaviour of the setup is characterised by the conditional probability distribution $p(b|x,y)$.
• Figure 2: Optimal quantum RAC strategy. Alice encodes her bits into qubit states forming a square rotated by $45^\circ$ in the $XZ$ plane of the Bloch sphere. If Bob measures $Z$ for $y=1$ and $X$ for $y=2$, each term in \ref{['RAC']} equals $(1 + \frac{1}{\sqrt{2}})/2$.
• Figure 3: Elements of a prepare-and-measure SDI-QRNG protocol. Data is first collected from a physical setup. The entropy in the raw data block is lower bounded based on SDI assumptions about the setup and potentially tests on the data. Finally, randomness extraction is performed, compressing the raw data to a shorter output bit string $\epsilon$-close to uniform. The data collection consumes seed randomness for choosing the preparations and measurement settings. Commonly used extractors, e.g. based on two-universal hashing, also require seeds.