Certifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses

Aguilar, Edgar A.; Farkas, Máté; Martínez, Daniel; Alvarado, Matı́as; Cariñe, Jaime; Xavier, G. B.; Barra, Johanna F.; Cañas, Gustavo; Pawłowski, Marcin; Lima, G.

doi:10.1103/physrevlett.120.230503

Cited by 44 publications

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“…Experimental demonstration of high-dimensional quantum communication advantage.-We present an experimental demonstration of the advantages of single-system quantum communication in the considered CCPs for d = 6, ..., 10. In our experiment, d-dimensional quantum systems are encoded into the linear transverse momentum of single photons transmitted by programmable diffractive apertures, which nowadays is a standard technique used for high-dimensional quantum information processing [44][45][46][47][48][49][50][51][52][53][54].…”

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“…In the final part of the setup, a "pointlike" avalanche single-photon detector (APD) with a 10 µm pinhole is placed at the center of the far field plane of the SLM4. In this case, the probability of single-photon detection P (x, x 0 , y, b) is proportional to | ϕ y,b |ψ x,x0 | 2 [45][46][47][48]. However, since for each d one of the targeted protocol measurements is rank-two projective (see Append.…”

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High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

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Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the preparation, transmission and measurement of a single quantum system; in other words quantum communication. Here, we show the advantages of the latter over the former in high-dimensional Hilbert space. We focus on a family of CCPs, based on facet Bell inequalities, study the advantage of high-dimensional quantum communication, and realise such quantum communication strategies using up to ten-dimensional systems. The experiment demonstrates, for growing dimension, an increasing advantage over quantum strategies based on Bell inequality violation. For sufficiently high dimensions, quantum communication also surpasses the limitations of the post-quantum Bell correlations obeying only locality in the macroscopic limit. Surprisingly, we find that the advantages are tied to the use of measurements that are not rank-one projective. We provide an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.Introduction.-Communication complexity problems (CCPs) are tasks in which distant parties hold local data, the collection of which is needed for a computation of their interest. To make the computation possible, the parties communicate with each other. However, the amount of communication is limited and therefore not all data can be sent. The CCP consist in parties adopting an efficient communication strategy which allows them to perform the desired computation with a probability as high as possible. Efficient use of quantitatively limited communication is a broadly relevant matter [1], which provides fundamental insights on physical limitations [2,3].The ability to process information depends on the choice of the physical system into which the information is encoded [4]. Consequently, quantum entities without a classical counterpart can be regarded as tools for quantum information processing. The most famous example is entanglement. In a quantum CCP, parties may share an entangled state on which they perform local measurements, generating strongly correlated data which violates a Bell inequality. That data can then be used to assist a classical communication strategy [5]. In fact, Bell inequalities have been systematically linked to CCPs [6-8], and their violation enables better-than-classical communication efficiencies [7][8][9][10][11][12][13][14][15].Nevertheless, quantum theory presents also a second approach to CCPs: substituting classical communication with quantum communication. The justification for such a substitution relies on the Holevo theorem [16] which implies that no more information can be extracted from quantum d-level system than from a classical d-level system. Hence, in a quantum communication strategy, information is encoded in a quantum state of a specified Hilbe...

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High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

et al. 2018

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“…[46,47]). Moreover, the notion of communication cost has been investigated, not only for generating correlations [48,49], but also in relation to quantum information theoretic tasks, such as dimension witnesses, quantum memories and random access codes [50][51][52][53][54][55][56][57].…”

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Contextuality, memory cost and non-classicality for sequential measurements

Budroni

2019

Phil. Trans. R. Soc. A.

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The Kochen–Specker theorem, and the associated notion of quantum contextuality, can be considered as the starting point for the development of a notion of non-classical correlations for single systems. The subsequent debate around the possibility of an experimental test of Kochen–Specker-type contradiction stimulated the development of different theoretical frameworks to interpret experimental results. Starting from the approach based on sequential measurements, we will discuss a generalization of the notion of non-classical temporal correlations that goes beyond the contextuality approach and related ones based on Leggett and Garg's notion of macrorealism, and it is based on the notion of memory cost of generating correlations. Finally, we will review recent results on the memory cost for generating temporal correlations in classical and quantum systems. The present work is based on the talk given at the Purdue Winer Memorial Lectures 2018: probability and contextuality. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

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“…that of communication cost, has been explored in relation to both Bell nonlocality [24,25] and temporal correlations [26,27]. Similar notions have been explored also in the prepare-and-measure scenario [28][29][30][31][32] and in connection with quantum information tasks such as random access codes [33][34][35].…”

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Memory cost of temporal correlations

2019

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A possible notion of nonclassicality for single systems can be defined on the basis of the notion of memory cost of classically simulating probabilities observed in a temporal sequence of measurements. We further explore this idea in a theory-independent framework, namely, from the perspective of general probability theories (GPTs), which includes classical and quantum theory as special examples. Under the assumption that each system has a finite memory capacity, identified with the maximal number of states perfectly distinguishable with a single measurement, we investigate what are the temporal correlations achievable with different theories, namely, classical, quantum, and GPTs beyond quantum mechanics. Already for the simplest nontrivial scenario, we derive inequalities able to distinguish temporal correlations where the underlying system is classical, quantum, or more general.

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Certifying an Irreducible 1024-Dimensional Photonic State Using Refined Dimension Witnesses

Cited by 44 publications

References 44 publications

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

Contextuality, memory cost and non-classicality for sequential measurements

Memory cost of temporal correlations

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