arXiv subjects

Adán Cabello

Publications and source records attributed to Adán Cabello.

At least 55 records · Page 3Linked to original sources

arXiv2022

Self-Testing of a Single Quantum System: Theory and Experiment

Certifying individual quantum devices with minimal assumptions is crucial for the development of quantum technologies. Here, we investigate how to leverage single-system contextuality to realize self-testing. We develop a robust self-testing protocol based on the simplest contextuality witness for the simplest contextual quantum system, the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements (to an ideal configuration) as a function of the value of the witness under a pragmatic assumption on the measurements we call the KCBS orthogonality condition. We apply the method in an experiment with randomly chosen measurements on a single trapped $^{40}{\rm Ca}^+$ and near-perfect detection efficiency. The observed statistics allow us to self-test the system and provide the first experimental demonstration of quantum self-testing of a single system. Further, we quantify and report that deviations from our assumptions are minimal, an aspect previously overlooked by contextuality experiments.

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arXiv2021

Significant-loophole-free test of Kochen-Specker contextuality using two species of atomic-ions

Quantum measurements cannot be thought of as revealing preexisting results, even when they do not disturb any other measurement in the same trial. This feature is called contextuality and is crucial for the quantum advantage in computing. Here, we report the first observation of quantum contextuality simultaneously free of the detection, sharpness and compatibility loopholes. The detection and sharpness loopholes are closed by adopting a hybrid two-ion system and highly efficient fluorescence measurements offering a detection efficiency of $100\%$ and a measurement repeatability $>98\%$. The compatibility loophole is closed by targeting correlations between observables for two different ions in a Paul trap, a $^{171}\mathrm{Yb}^{+}$ ion and a $^{138}\mathrm{Ba}^{+}$ ion, chosen so measurements on each ion use different operation laser wavelengths, fluorescence wavelengths, and detectors. The experimental results show a violation of the bound for the most adversarial noncontextual models and open a new way to certify quantum systems.

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arXiv2021

Converting contextuality into nonlocality

We introduce a general method which converts, in a unified way, any form of quantum contextuality, including any form of state-dependent contextuality, into a quantum violation of a bipartite Bell inequality. As an example, we apply the method to a quantum violation of the Klyachko-Can-Binicioğlu-Shumovsky inequality.

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arXiv2021

Bell non-locality and Kochen-Specker contextuality: How are they connected?

Bell non-locality and Kochen-Specker (KS) contextuality are logically independent concepts, fuel different protocols with quantum vs classical advantage, and have distinct classical simulation costs. A natural question is what are the relations between these concepts, advantages, and costs. To address this question, it is useful to have a map that captures all the connections between Bell non-locality and KS contextuality in quantum theory. The aim of this work is to introduce such a map. After defining the theory-independent notions of Bell non-locality and KS contextuality for ideal measurements, we show that, in quantum theory, due to Neumark's dilation theorem, every matrix of quantum Bell non-local correlations can be mapped to an identical matrix of KS contextual correlations produced in a scenario with identical relations of compatibility but where measurements are ideal and no space-like separation is required. A more difficult problem is identifying connections in the opposite direction. We show that there are "one-to-one" and partial connections between KS contextual correlations and Bell non-local correlations for some KS contextuality scenarios, but not for all of them. However, there is also a method that transforms any matrix of KS contextual correlations for quantum systems of dimension $d$ into a matrix of Bell non-local correlations between two quantum subsystems each of them of dimension $d$. We collect all these connections in map and list some problems which can benefit from this map.

quant-ph↗

arXiv2021

Graph-Theoretic Framework for Self-Testing in Bell Scenarios

Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely, with minimal assumptions about the underlying quantum system. It is based on the observation that some extremal points in the set of quantum correlations can only be achieved, up to isometries, with specific states and measurements. Here, we present a new approach for quantum self-testing in Bell non-locality scenarios, motivated by the following observation: the quantum maximum of a given Bell inequality is, in general, difficult to characterize. However, it is strictly contained in an easy-to-characterize set: the \emph{theta body} of a vertex-weighted induced subgraph $(G,w)$ of the graph in which vertices represent the events and edges join mutually exclusive events. This implies that, for the cases where the quantum maximum and the maximum within the theta body (known as the Lovász theta number) of $(G,w)$ coincide, self-testing can be demonstrated by just proving self-testability with the theta body of $G$. This graph-theoretic framework allows us to (i) recover the self-testability of several quantum correlations that are known to permit self-testing (like those violating the Clauser-Horne-Shimony-Holt (CHSH) and three-party Mermin Bell inequalities for projective measurements of arbitrary rank, and chained Bell inequalities for rank-one projective measurements), (ii) prove the self-testability of quantum correlations that were not known using existing self-testing techniques (e.g., those violating the Abner Shimony Bell inequality for rank-one projective measurements). Additionally, the analysis of the chained Bell inequalities gives us a closed-form expression of the Lovász theta number for a family of well-studied graphs known as the Möbius ladders, which might be of independent interest in the community of discrete mathematics.

quant-ph↗

arXiv2021

Device-independent quantum key distribution based on Bell inequalities with more than two inputs and two outputs

Device-independent quantum key distribution (DI-QKD) offers the strongest form of security against eavesdroppers bounded by the laws of quantum mechanics. However, a practical implementation is still pending due to the requirement of combinations of visibility and detection efficiency that are beyond those possible with current technology. This mismatch motivates the search for DI-QKD protocols that can close the gap between theoretical and practical security. In this work, we present two DI-QKD protocols whose security relies on Bell inequalities with more than two inputs and two outputs. We show that, for maximally entangled states and perfect visibility, a protocol based on a Bell inequality with three inputs and four outputs requires a slightly lower detection efficiency than the protocols based on Bell inequalities with two inputs and two outputs.

quant-ph↗

arXiv2021

Bell nonlocality between sequential pairs of observers

We show that it is possible to have arbitrarily long sequences of Alices and Bobs so every (Alice, Bob) pair violates a Bell inequality. We propose an experiment to observe this effect with two Alices and two Bobs.

quant-ph↗

arXiv2021

Bosonic Indistinguishability-Dependent Contextuality

We uncover a form of quantum contextuality that connects maximal contextuality to boson indistinguihability in a similar way maximal nonlocality with respect to the Clauser-Horne-Shimony-Holt Bell inequality is connected to maximal entanglement. Unlike previous forms of photonic contextuality, this form cannot be simulated with classical light, as it relies on indistinguishability and higher-order interference. Ideal measurements on the bosonic system can be performed by means of dispersive coupling with an ancillary qubit. This allows us delaying at will the ending of each measurement and targeting high-dimensional contextual correlations, which are features which cannot be achieved with existing platforms.

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arXiv2020

Quantum randomness protected against detection loophole attacks

Device and semi-device independent quantum randomness generators (DI- and SDI-QRNGs) are crucial for applications requiring private randomness. However, they are vulnerable to detection inefficiency attacks and this limits severely their usage for practical purposes. Here, we present a method for protecting SDI-QRNGs in prepare-and-measure scenarios against detection inefficiency attacks. The key idea is the introduction of a blocking device that adds failures in the communication between the preparation and measurement devices. We prove that, for any detection efficiency, there is a blocking rate that provides protection against these attacks. We experimentally demonstrate the generation of private randomness using weak coherent states and standard avalanche photo-detectors.

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arXiv2020

Graph-theoretic approach to dimension witnessing

A fundamental problem in quantum computation and quantum information is finding the minimum quantum dimension needed for a task. For tasks involving state preparation and measurements, this problem can be addressed using only the input-output correlations. This has been applied to Bell, prepare-and-measure, and Kochen-Specker contextuality scenarios. Here, we introduce a novel approach to quantum dimension witnessing for scenarios with one preparation and several measurements, which uses the graphs of mutual exclusivity between sets of measurement events. We present the concepts and tools needed for graph-theoretic quantum dimension witnessing and illustrate their use by identifying novel quantum dimension witnesses, including a family that can certify arbitrarily high quantum dimensions with few events.

quant-ph↗

arXiv2020

General Bayesian theories and the emergence of the exclusivity principle

We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and update them when new information becomes available. Our framework includes as special cases classical and quantum probability theory, as well as other forms of probabilistic reasoning that may arise in future physical theories. Building on this framework, we develop a notion of ideal experiment, which in quantum theory coincides with the notion of projective measurement. We then prove that, in every general Bayesian theory, ideal experiments must satisfy the exclusivity principle, a property of projective measurements that plays a central role in the characterization of quantum correlations. Our result suggests that the set of quantum correlations may be completely characterized in terms of Bayesian consistency conditions.

quant-ph↗

arXiv2020

Bell nonlocality with intensity information only

We address the problem of detecting bipartite Bell nonlocality whenever the only experimental information are the intensities produced in each run of the experiment by an unknown number of particles. We point out that this scenario naturally occurs in Bell experiments with parametric down-conversion when the crystal is pumped by strong pulses, in Bell tests with distant sources and in which particles suffer different delays during their flight, in Bell experiments using living cells as photo detectors, and in Bell experiments where the pairing information is physically removed. We show that, although Bell nonlocality decreases as the number of particles increases, if the parties can distinguish arbitrarily small differences of intensities and the visibility is larger than $0.98$, then Bell nonlocality can still be experimentally detected with fluxes of up to $15$ particles. We show that this prediction can be tested with current equipment in a Bell experiment where pairing information is physically removed, but requires the assumption of fair sampling.

quant-ph↗

arXiv2020

Hidden variables simulating quantum contextuality increasingly violate the Holevo bound

In this paper from 2011 we approach some questions about quantum contextuality with tools from formal logic. In particular, we consider an experiment associated with the Peres-Mermin square. The language of all possible sequences of outcomes of the experiment is classified in the Chomsky hierarchy and seen to be a regular language. Next, we make the rather evident observation that a finite set of hidden finite valued variables can never account for indeterminism in an ideally isolated repeatable experiment. We see that, when the language of possible outcomes of the experiment is regular, as is the case with the Peres-Mermin square, the amount of binary-valued hidden variables needed to de-randomize the model for all sequences of experiments up to length n grows as bad as it could be: linearly in n. We introduce a very abstract model of machine that simulates nature in a particular sense. A lower-bound on the number of memory states of such machines is proved if they were to simulate the experiment that corresponds to the Peres-Mermin square. Moreover, the proof of this lower bound is seen to scale to a certain generalization of the Peres- Mermin square. For this scaled experiment it is seen that the Holevo bound is violated and that the degree of violation increases uniformly.

cs.LO↗

arXiv2020

Experimental Certification of Sustained Entanglement and Nonlocality after Sequential Measurements

Entanglement is a fundamental resource for quantum information science. However, bipartite entanglement is destroyed when one particle is observed via projective (sharp) measurements, as it is typically the case in most experiments. Here we experimentally show that, if instead of sharp measurements, one performs many sequential unsharp measurements on one particle which are suitably chosen depending on the previous outcomes, then entanglement is preserved and it is possible to reveal quantum correlations through measurements on the second particle at any step of the sequence. Specifically, we observe that pairs of photons entangled in polarization maintain their entanglement when one particle undergoes three sequential measurements, and each of these can be used to violate a CHSH inequality. This proof-of-principle experiment demonstrates the possibility of repeatedly harnessing two crucial resources, entanglement and Bell nonlocality, that, in most quantum protocols, are destroyed after a single measurement. The protocol we use, which in principle works for an unbounded sequence of measurements, can be useful for randomness extraction.

quant-ph↗

arXiv2020

Experimental certification of an informationally complete quantum measurement in a device-independent protocol

Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their $d^2$-outcomes are enough to reconstruct any $d$-dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information. Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first time, a MIC-POVM for qubits following a device-independent protocol (i.e., modeling the state preparation and the measurement devices as black boxes, and using only the statistics of the inputs and outputs). Our certification is achieved under the assumption of freedom of choice, no communication, and fair sampling.

quant-ph↗

arXiv2019

Local certification of programmable quantum devices of arbitrary high dimensionality

The onset of the era of fully-programmable error-corrected quantum computers will be marked by major breakthroughs in all areas of science and engineering. These devices promise to have significant technological and societal impact, notable examples being the analysis of big data through better machine learning algorithms and the design of new materials. Nevertheless, the capacity of quantum computers to faithfully implement quantum algorithms relies crucially on their ability to prepare specific high-dimensional and high-purity quantum states, together with suitable quantum measurements. Thus, the unambiguous certification of these requirements without assumptions on the inner workings of the quantum computer is critical to the development of trusted quantum processors. One of the most important approaches for benchmarking quantum devices is through the mechanism of self-testing that requires a pair of entangled non-communicating quantum devices. Nevertheless, although computation typically happens in a localized fashion, no local self-testing scheme is known to benchmark high dimensional states and measurements. Here, we show that the quantum self-testing paradigm can be employed to an individual quantum computer that is modelled as a programmable black box by introducing a noise-tolerant certification scheme. We substantiate the applicability of our scheme by providing a family of outcome statistics whose observation certifies that the computer is producing specific high-dimensional quantum states and implementing specific measurements.

quant-ph↗

arXiv2019

The problem of quantum correlations and the totalitarian principle

The totalitarian principle establishes that `anything not forbidden is compulsory'. The problem of quantum correlations is explaining what selects the set of quantum correlations for a Bell and Kochen-Specker (KS) contextuality scenario. Here, we show that two assumptions and a version of the totalitarian principle lead to the quantum correlations. The assumptions are that there is a non-empty set of correlations for any KS contextuality scenario and a statistically independent realisation of any two KS experiments. The version of the totalitarian principle says that any correlation not forbidden by these assumptions can be produced. This paper contains a short version of the proof [presented in {\em Phys. Rev. A} \textbf{100}, 032120 (2019)] and explores some implications of the result. This article is part of the theme issue `Contextuality and probability in quantum mechanics and beyond'.

quant-ph↗

arXiv2019

Quantum correlations from simple assumptions

We address the problem of deriving the set of quantum correlations for every Bell and Kochen-Specker (KS) contextuality scenario from simple assumptions. We show that the correlations that are possible according to quantum theory are equal to those possible under the assumptions that there is a nonempty set of correlations for every KS scenario and a statistically independent realization of any two KS experiments. The proof uses tools of the graph-theoretic approach to correlations and deals with Bell nonlocality and KS contextuality in a unified way.

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