arXiv:1207.2574 · Physical Review A

Robustness of device-independent dimension witnesses

Michele Dall’Arno, Elsa Passaro, Rodrigo Gallego, Antonio Acín

Published Oct 11, 2012• 38 citations

Abstract

Device-independent dimension witnesses provide a lower bound on the dimensionality of classical and quantum systems in a ``black box''scenario where only correlations between preparations, measurements, and outcomes are considered. We address the problem of the robustness of dimension witnesses, namely that to witness the dimension of a system or to discriminate between its quantum or classical nature, even in the presence of loss. We consider the case when shared randomness is allowed between preparations and measurements and provide a threshold in the detection efficiency such that dimension witnessing can still be performed.

DOI: 10.1103/physreva.86.042312

Related papers

Device-Independent Tests of Classical and Quantum Dimensions

Rodrigo Gallego, Nicolas Brunner, Christopher Hadley +1 more

We address the problem of testing the dimensionality of classical and quantum systems in a "black-box" scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension necessary to reproduce given measurement data. Furthermore, we generalize the concept of quantum dimension witnesses to arbitrary quantum systems, allowing one to place a lower bound on the Hilbert space dimension necessary to reproduce certain data. Illustrating these ideas, we provide simple examples of classical and quantum dimension witnesses.

arXiv:1010.5064Physical Review LettersNov 30, 2010287 citations

Device-independent dimension tests in the prepare-and-measure scenario

Jamie Sikora, Antonios Varvitsiotis, Zhaohui Wei

Analyzing the dimension of an unknown quantum system in a device-independent manner, i.e., using only the measurement statistics, is a fundamental task in quantum physics and quantum information theory. In this paper, we consider this problem in the prepare-and-measure scenario. Specifically, we provide a lower bound on the dimension of the prepared quantum systems, which is a function that only depends on the measurement statistics. Furthermore, we show that our bound performs well in several examples. In particular, we show that our bound provides insights into the notion of dimension witness, and we also use it to show that the sets of restricted-dimensional prepare-and-measure correlations are not always convex.

arXiv:1606.03878Physical Review AOct 25, 201615 citations

Shared randomness and device-independent dimension witnessing

Julio I. de Vicente

It has been shown that the conditional probability distributions obtained by performing measurements on an uncharacterized physical system can be used to infer its underlying dimension in a device-independent way both in the classical and the quantum setting. We analyze several aspects of the structure of the sets of probability distributions corresponding to a certain dimension, taking into account whether shared randomness is available as a resource. We first consider the so-called prepare-and-measure scenario. We show that quantumness and shared randomness are not comparable resources. That is, on the one hand there exist behaviors that require a quantum system of arbitrarily large dimension in order to be observed while they can be reproduced with a classical physical system of minimal dimension together with shared randomness. On the other hand, there exist behaviors that require exponentially larger dimensions classically than quantumly even if the former is supplemented with shared randomness. We also show that in the absence of shared randomness, the sets corresponding to a sufficiently small dimension are negligible (zero measure and nowhere dense) both classically and quantumly. This is in sharp contrast to the situation in which this resource is available, and it explains the exceptional robustness of dimension witnesses in the setting in which devices can be taken to be uncorrelated. We finally consider the Bell scenario in the absence of shared randomness, and we prove some nonconvexity and negligibility properties of these sets for sufficiently small dimensions. This shows again the enormous difference induced by the availability (or lack thereof) of this resource.

arXiv:1611.01105Physical Review AJan 30, 201718 citations

Certifying the Dimension of Classical and Quantum Systems in a Prepare-and-Measure Scenario with Independent Devices

Joseph Bowles, Marco Túlio Quintino, Nicolas Brunner

We consider the problem of testing the dimension of uncharacterized classical and quantum systems in a prepare-and-measure setup. Here we assume the preparation and measurement devices to be independent, thereby making the problem nonconvex. We present a simple method for generating nonlinear dimension witnesses for systems of arbitrary dimension. The simplest of our witnesses is highly robust to technical imperfections, and can certify the use of qubits in the presence of arbitrary noise and arbitrarily low detection efficiency. Finally, we show that this witness can be used to certify the presence of randomness, suggesting applications in quantum information processing.

arXiv:1311.1525Physical Review LettersApr 11, 2014116 citations

A general bound for the dimension of quantum behaviours in the prepare-and-measure scenario

Julio I. de Vicente

Abstract The prepare-and-measure scenario offers the possibility to infer the dimension of an unknown physical system in a device-independent way, i.e. using only raw measurement data with apparatuses regarded as black boxes. We provide here a general lower bound on the dimension necessary to observe arbitrary quantum behaviours in this scenario based on simple matrix analysis. This bound holds even if the preparer and measurer share randomness. This is relevant in scenarios where the parties are free to access this resource or it is not safe to assume that the devices are not correlated. We further use this result to bound the success probability of random access codes in general as a function of the dimension of the quantum systems sent from one party to another and we provide constructions of dimension witnesses.

arXiv:1809.02414Journal of Physics A Mathematical and TheoreticalJan 11, 20198 citations

Robust genuine high-dimensional steering with many measurements

Sébastien Designolle

Quantum systems of high dimensions are attracting a lot of attention because they feature interesting properties when it comes to observing entanglement or other forms of correlations. In particular, their improved resistance to noise is favorable for experiments in quantum communication or quantum cryptography. However, witnessing this high-dimensional nature remains challenging, especially when the assumptions on the parties involved are weak, typically when one of them is considered as a black box. In this context, the concept of genuine high-dimensional steering has been recently introduced and experimentally demonstrated [Phys. Rev. Lett. 126, 200404 (2021)]; it allows for a one-sided device-independent certification of the dimension of a bipartite shared state by only using two measurements. Here I overcome this limitation by developing, for more than two measurements, universal bounds on the incompatibility robustness, turned into meaningful dimension certificates. Interestingly, even though the resulting bounds are quite loose, they still often offer an increased resistance to noise and could then be advantageously employed in experiments.

arXiv:2110.14435Physical Review AMar 15, 202213 citations