Device-Independent Tests of Classical and Quantum Dimensions

Gallego, Rodrigo; Brunner, Nicolás; Hadley, Christopher; Acín, Antonio

doi:10.1103/physrevlett.105.230501

Cited by 283 publications

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“…Obviously, also the condition of projective measurement must be verified. Notice that our dimension witnesses involve always the same Leggett-Garg inequality and measurement scheme, in contrast to other proposal based on Bell [24] or noncontextuality [30] inequalities, and the prepare-and-measure scenario [31], where specific inequalities violated only by high-dimensional systems and involving more complex measurement schemes must be found.A further interesting application is the discrimination between Lüders' and von Neumann's state-update rules [25], i.e., which one, if any, correctly represents the measurement scenario. A violation of the bound corresponding to M = 2 shows a contradiction with Lüders rule.…”

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Temporal Quantum Correlations and Leggett-Garg Inequalities in Multilevel Systems

2014

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We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels N that can be accessed by the measurement apparatus via projective measurements. We provide exact bounds for small N , that exceed the known bound for the Leggett-Garg inequality, and show that in the limit N → ∞ the Leggett-Garg inequality can be violated up to its algebraic maximum.PACS numbers: 03.65. Ud, 03.65.Ta Introduction.-Bell inequalities place fundamental bounds on the nature of correlations between spatiallyseparated entities within a local hidden variable framework [1]. Leggett and Garg showed that temporal correlations obey similar inequalities based on assumptions of macroscopic realism and non-invasive measureability [2]. Quantum particles are bound neither by local hidden variables nor macroscopic realism and so can violate both Bell and Leggett-Garg inequalities (LGIs).The maximum degree to which a quantum system can violate a Bell inequality is known as the Tsirelson bound [3], significantly less than the largest-conceivable value, the algebraic bound [4]. Violations of a Bell inequality beyond the Tsirelson bound would be evidence of a new physics beyond quantum theory [6].With interest in the LGIs growing (see Ref.[7] for a review), we ask here whether there is such a thing as a temporal Tsirelson bound for the LGIs. In the light of some recent results [8,9] and given the formal symmetry between the two types of inequality [10,11] and the general trend towards unification between temporal and spatial correlations [12][13][14][15], one would expect that the Tsirelson bound for the LGIs holds analogously to the spatial case. Surprisingly, and as we show here, this is not the case. By considering a broader class of projective measurements than hitherto considered, we show that the maximum quantum violation of the LGIs can exceed the Tsirelson value, and increases with increasing system size, even up to the algebraic bound in the asymptotic limit.Let us now be more concrete and consider the simplest LGI which, for dichotomous observable Q = ±1, readswhere C βα = Q(t β )Q(t α ) is the correlation function of variable Q at the two times t β ≥ t α . For a two-level system, the maximum quantum value of K 3 is K max 3 = 3 2 [2], which we shall refer to as the Lüders bound, K Lüders 3 = 3 2 , for reasons to become clear shortly. It has been proven rigorously that for measurements given by just two projectors, Π + and Π − , onto eigenspaces associated with results Q = +1 and Q = −1, the maximum quantum value of K 3 is the same as for the qubit, irrespective of system size [9]. This has been reflected in several studies: the experiment of Ref.[16] on a three-level system obtained a maximum value less than 3 2 ; on the theory side, multi-level quantum systems such as a large spin [17], optoelectromechanical systems [18] and photosynthetic complexes [19] have also been observed to obey. From this, one might co...

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Temporal Quantum Correlations and Leggett-Garg Inequalities in Multilevel Systems

2014

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“…First, it is a resource for several Quantum Information Processing (QIP) tasks [Bar+05]. Examples of them are Device-Independent Quantum Key Distribution (DIQKD) [Pir+13], Certified Quantum Random Number Generation (CQRNG) [Pir+10], Randomness Amplification (RA) [CR12], Dimensionality Witnessing (DW) [Gal+10], and many other tasks that fall into the Device-Independent (DI) paradigm (see Section 2.2.1). Hence, being able to reveal the nonlocality of a composite quantum system is a central problem in QIP, and it is going to be one of the crucial problems of future quantum technologies.…”

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confidence: 99%

Characterizing Entanglement and Quantum Correlations Constrained by Symmetry

Brugués¹

2017

Springer Theses

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EnglishEntanglement and nonlocal correlations constitute two fundamental resources for quantum information processing, as they allow for novel tasks that are otherwise impossible in a classical scenario. However, their elusive characterization is still a central problem in Quantum Information Theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space, as well as the space of nonlocal correlations. Physical systems of interest, on the other hand, display symmetries that can be exploited to reduce this complexity, opening the possibility that, for such systems, some of these questions become tractable.This PhD Thesis is dedicated to the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It contains original results in these four threads of research: PPT entanglement in the symmetric states, nonlocality detection in many-body systems, the non-equivalence between entanglement and nonlocality and elemental monogamies of correlations.First, we study PPT entanglement in fully symmetric n-qubit states. We solve the open question on the existence of four-qubit PPT entangled states of these kind, providing constructive examples and methods. Furthermore, we develop criteria for separability, edgeness and the Schmidt number of PPT entangled symmetric states. Geometrically, we focus on the characterization of extremal states of this family and we provide an algorithm to find states with such properties.Second, we study nonlocality in many-body systems. We consider permutationally and translationally invariant Bell inequalities consisting of two-body correlators. These constitute the first tools to detect nonlocality in many-body systems in an experimentally-friendly way with our current technology. Furthermore, we show how these Bell inequalities detect nonloi cality in physically relevant systems such as ground states of Hamiltonians that naturally arise e.g., in nuclear physics. We provide analytical classes of Bell inequalities and we analytically characterize which states and measurements are best suited for them. We show that the method we introduce can be fully generalized to correlators of any order in any Bell scenario. Finally, we provide some feedback from a more experimental point of view.Third, we demonstrate that entanglement and nonlocality are inequivalent concepts in general; a question that remained open in the multipartite case. We show that the strongest form of entanglement, genuinely multipartite entanglement, does not imply the strongest form of nonlocality, genuinely multipartite nonlocality, in any case. We give a constructive method that, starting from a multipartite genuinely multipartite state admitting a K-local model, extends it to a genuinely multipartite entangled state of any number of parties while preserving the degree of locality.Finally, we show that nonlocal correlations are monogamous in a much stronger sense than the typical one, in which th...

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“…However, sometimes we still want to draw nontrivial conclusions on the quantum properties of the involved system. This sounds like a challenging, or even impossible task, but it has been shown to be possible in many cases [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. These kinds of tasks are called device-independent as their application assumes only the correctness of quantum mechanics as a valid description of nature, and is independent of the internal workings of the devices used.…”

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Device-independent characterizations of a shared quantum state independent of any Bell inequalities

Wei

Sikora

2017

Phys. Rev. A

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In a Bell experiment two parties share a quantum state and perform local measurements on their subsystems separately, and the statistics of the measurement outcomes are recorded as a Bell correlation. For any Bell correlation, it turns out that a quantum state with minimal size that is able to produce this correlation can always be pure. In this work, we first exhibit two deviceindependent characterizations for the pure state that Alice and Bob share using only the correlation data. Specifically, we give two conditions that the Schmidt coefficients must satisfy, which can be tight, and have various applications in quantum tasks. First, one of the characterizations allows us to bound the entanglement between Alice and Bob using Renyi entropies and also to bound the underlying Hilbert space dimension. Second, when the Hilbert space dimension bound is tight, the shared pure quantum state has to be maximally entangled. Third, the second characterization gives a sufficient condition that a Bell correlation cannot be generated by particular quantum states. We also show that our results can be generalized to the case of shared mixed states.Introduction.-In the study of quantum physics, frequently the internal workings of a quantum device are not exactly known. For example, it is often the case that we do not have sufficient knowledge of the internal physical structure, or the precision of the quantum controls is very limited, or even the devices we are using cannot be trusted. In these cases, it could be that the only reliable information available is the measurement statistics from observing the quantum system. However, sometimes we still want to draw nontrivial conclusions on the quantum properties of the involved system. This sounds like a challenging, or even impossible task, but it has been shown to be possible in many cases [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. These kinds of tasks are called device-independent as their application assumes only the correctness of quantum mechanics as a valid description of nature, and is independent of the internal workings of the devices used. Device-independence is a very valuable property in physical implementations of various quantum schemes. Typical examples of its usefulness include the transmission of information safely using untrusted devices, and easy monitoring of the overall performance of vulnerable quantum devices [11][12][13][14].We consider in this paper the setting of a Bell experiment, i.e., two spatially separated parties sharing a quantum state and performing local measurements on their subsystems. The corresponding statistics of the measurement outcomes is called a Bell correlation. It has been shown that the dimension and the entanglement of the underlying quantum state can be quantified in a device-independent way using only the Bell correlation data [5,[8][9][10]. In fact, some quantum states can even be pinned down completely by their violations of particular Bell inequalities, but this is only known to be possible for some special cases [1][2][...

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Device-Independent Tests of Classical and Quantum Dimensions

Cited by 283 publications

References 12 publications

Temporal Quantum Correlations and Leggett-Garg Inequalities in Multilevel Systems

Temporal Quantum Correlations and Leggett-Garg Inequalities in Multilevel Systems

Characterizing Entanglement and Quantum Correlations Constrained by Symmetry

Device-independent characterizations of a shared quantum state independent of any Bell inequalities

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