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arXiv:2101.07830 · Physical Review Letters

Semi-Device-Independent Framework Based on Restricted Distrust in Prepare-and-Measure Experiments

Armin Tavakoli

Published May 25, 2021• 28 citations
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Abstract

A semi-device-independent framework for prepare-and-measure experiments is introduced in which an experimenter can tune the degree of distrust in the performance of the quantum devices. In this framework, a receiver operates an uncharacterized measurement device and a sender operates a preparation device that emits states with a bounded fidelity with respect to a set of target states. No assumption on Hilbert space dimension is required. The set of quantum correlations is investigated and bounded from both the interior and the exterior. Furthermore, the optimal performance of quantum state discrimination with bounded distrust is derived and applied to certification of detection efficiency. Quantum-over-classical advantages are demonstrated and the magnitude of distrust compatible with such advantages is explored. Finally, efficient schemes for semi-device-independent random number generation are developed.

DOI
10.1103/physrevlett.126.210503

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A semi-device-independent framework for prepare-and-measure experiments is introduced in which an experimenter can tune the degree of distrust in the performance of the quantum devices. In this framework, a receiver operates an uncharacterized measurement device and a sender operates a preparation device that emits states with a bounded fidelity with respect to a set of target states. No assumption on Hilbert space dimension is required. The set of quantum correlations is investigated and bounded from both the interior and the exterior. Furthermore, the optimal performance of quantum state discrimination with bounded distrust is derived and applied to certification of detection efficiency. Quantum-over-classical advantages are demonstrated and the magnitude of distrust compatible with such advantages is explored. Finally, efficient schemes for semi-device-independent random number generation are developed.
Semi-device-independent (SDI) methods provide a convenient way to characterize quantum systems under additional physical assumptions, and these methods have wide applications in quantum information processing, such as quantum key distribution, quantum random number generation and quantum certification. Recently, Tavakoli proposed an SDI scheme to investigate quantum correlations based on the assumption of restricted distrust. Here, we experimentally investigate quantum correlations in an SDI framework with restricted distrust, where the preparer emits states with a bounded fidelity with respect to a set of target states and the measurer operates an uncharacterized measurement device. In our work, we experimentally realize quantum state discrimination with bounded distrust and apply it to the certification of detection efficiency. Moreover, we demonstrate the advantages of quantum systems over classical counterparts even at substantial degrees of distrust. Finally, we investigate SDI random number generation with restricted distrust and show that high rates of randomness can also be generated at experimentally realistic levels of distrust. Our work opens new avenues for SDI quantum information processing.
The semi-device-independent approach provides a framework for prepare-and-measure quantum protocols using devices whose behavior must not be characterized nor trusted, except for a single assumption on the dimension of the Hilbert space characterizing the quantum carriers. Here, we propose instead to constrain the quantum carriers through a bound on the mean value of a well-chosen observable. This modified assumption is physically better motivated than a dimension bound and closer to the description of actual experiments. In particular, we consider quantum optical schemes where the source emits quantum states described in an infinite-dimensional Fock space and model our assumption as an upper bound on the average photon number in the emitted states. We characterize the set of correlations that may be exhibited in the simplest possible scenario compatible with our new framework, based on two energy-constrained state preparations and a two-outcome measurement. Interestingly, we uncover the existence of quantum correlations exceeding the set of classical correlations that can be produced by devices behaving in a purely pre-determined fashion (possibly including shared randomness). This feature suggests immediate applications to certified randomness generation. Along this line, we analyze the achievable correlations in several prepare-and-measure optical schemes with a mean photon number constraint and demonstrate that they allow for the generation of certified randomness. Our simplest optical scheme works by the on-off keying of an attenuated laser source followed by photocounting. It opens the path to more sophisticated energy-constrained semi-device-independent quantum cryptography protocols, such as quantum key distribution.
Certifying that quantum devices behave as intended is crucial for quantum information science. Here, methods are developed for certification of both state preparation devices and measurement devices based on prepare-and-measure experiments with independent devices. The experimenter assumes the independence of the devices and knowledge of the Hilbert space dimension. Thus no precise characterization of any part of the experiment is required. The certification is based on a randomized version of unambiguous state discrimination and targets the class of state ensembles corresponding to quantum t designs of any size and any dimension. These quantum designs are sets of states over which the average of any t-degree polynomial equals its average over all pure states, and they accommodate many of the most useful discrete structures in quantum information processing. Furthermore, it is shown that the same experiments also certify the detection efficiency of the measurement devices, as well as their nonprojective nature. The presented methods can readily be implemented in experiments.
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.
Prepare-and-measure scenarios are among the simplest and most widely used settings for quantum communication. A sender prepares a physical system in one of several possible states, which a receiver then measures. Despite this simple structure, these scenarios offer a rich framework for exploring the differences between classical and quantum communication, revealing quantum advantages, and developing protocols for quantum cryptography and device certification. In this tutorial, we give a ground-up introduction to prepare-and-measure scenarios and the methods used to study them. We introduce different frameworks for constraining and characterising communication, with an emphasis on semi-device-independent approaches to quantum information. We also cover modern convex-optimisation techniques for characterising the correlations achievable in these scenarios and illustrate how these tools can be applied in practice. Our aim is to give newcomers the conceptual and technical foundations needed to approach the current literature and apply prepare-and-measure methods in their own research. We conclude with a discussion of open problems and directions for future work.
Quantum information tasks are often analyzed under varying trust assumptions about the devices involved. The semi-device-independent (SDI) framework offers a balance between needed assumptions and experimental feasibility. In this work, we study the energy-constrained SDI scenario, where the only assumption in a prepare-and-measure setup is an upper bound on the energy of the prepared quantum states. In contrast to previous studies that restricted the preparation and measurement devices to be classically correlated, we show that allowing entanglement strictly enlarges the set of achievable correlations. We identify two operational consequences of this result. The first concerns randomness certification, where we show that allowing the adversary to employ entangled strategies may significantly reduce the amount of certifiable randomness. This includes situations where the amount of randomness drops to zero in the presence of entanglement, while it remains positive when entanglement is excluded. Second, for the task of distinguishing an arbitrary quantum channel from the identity, we show that the known dimension-independent bound on the advantage conferred by entanglement is violated under an energy constraint.