Analysis and optimization of quantum adaptive measurement protocols with the framework of preparation games

Weilenmann, Mirjam; Aguilar, Edgar A.; Navascués, Miguel

doi:10.1038/s41467-021-24658-9

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…In the context of Bell's inequalities, similar kinds of probabilistic protocols are constructed for the single‐shot non‐locality detection [ 70 ] and entanglement detection via preparation games. [ 71 ] In the context of quantum state verification, [ 18,72–74 ] a single‐shot entanglement verification naturally arises in bipartite states as long as the dimension of marginal systems becomes sufficiently large. [ 75,76 ] The generalization to the GHZ states can be found in ref.…”

Section: Entanglement Verificationmentioning

confidence: 99%

Quantum Verification and Estimation with Few Copies

et al. 2022

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As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represent one of the main challenges in the employment of such systems for reliable quantum information processing. Though the most complete technique is undoubtedly full tomography, the inherent exponential increase of experimental and post‐processing resources with system size makes this approach infeasible even at moderate scales. For this reason, there is currently an urgent need to develop novel methods that surpass these limitations. This review article presents novel techniques focusing on a fixed number of resources (sampling complexity), and thus prove suitable for systems of arbitrary dimension. Specifically, a probabilistic framework requiring at best only a single copy for entanglement detection is reviewed, together with the concept of selective quantum state tomography, which enables the estimation of arbitrary elements of an unknown state with a number of copies that is low and independent of the system's size. These hyper‐efficient techniques define a dimensional demarcation for partial tomography and open a path for novel applications.

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Section: Entanglement Verificationmentioning

confidence: 99%

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et al. 2022

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Optimized Detection of High-Dimensional Entanglement

Xing

Guo

et al. 2021

Phys. Rev. Lett.

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Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect entanglement within a large class of entangled quantum states, the so-called unfaithful states. In this paper, we introduce a highly flexible automated method to construct optimal tests for entanglement detection given a bipartite target state of arbitrary dimension, faithful or unfaithful, and a set of local measurement operators. By restricting the number or complexity of the considered measurement settings, our method outputs the most convenient protocol to test the entanglement of the target state in the lab. Using the 3-setting protocols generated by our method, we experimentally certify 2-and 3-dimensional entanglement in 4-dimensional unfaithful states. I. INTRODUCTIONEntanglement is the bedrock of most quantum information processing protocols (Gühne and Tóth, 2009; Horodecki et al., 2009). It is a key resource in quantum teleportation (Bennett et al., 1993), entanglement-based quantum key distribution (QKD) (Yin et al., 2017) and quantum communication complexity (Buhrman et al., 2010). Generating high-quality entangled states and detecting them reliably is a crucial prerequisite to conduct any quantum communication task.

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Optimization of Time-Ordered Processes in the Finite and Asymptotic Regimes

Weilenmann,

Budroni,

Navascués

2024

PRX Quantum

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Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through adaptive measurements, computing the maximum average score of a preparation game over a continuous set of target states, and limiting the behavior of a (quantum) finite-state automaton. In this work, we introduce tractable relaxations of this class of optimization problems. To illustrate their performance, we use them to: (a) compute the probability that a finite-state automaton outputs a given sequence of bits; (b) develop a new many-body entanglement-detection protocol; and (c) let the computer an adaptive protocol for magic state detection. As we further show, the maximum score of a sequential problem in the limit of infinitely many time steps is in general incomputable. Nonetheless, we provide general heuristics to bound this quantity and show that they provide useful estimates in relevant scenarios. Published by the American Physical Society 2024

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Analysis and optimization of quantum adaptive measurement protocols with the framework of preparation games

Cited by 4 publications

References 23 publications

Quantum Verification and Estimation with Few Copies

Quantum Verification and Estimation with Few Copies

Optimized Detection of High-Dimensional Entanglement

Optimization of Time-Ordered Processes in the Finite and Asymptotic Regimes

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