Entanglement Detection by Violations of Noisy Uncertainty Relations: A Proof of Principle

Zhao, Yuanyuan; Xiang, Guo-Yong; Hu, Xiaomin; Liu, Bi-Heng; Li, Chuan‐Feng; Guo, Guang‐Can; Schwonnek, René; Wolf, Ramona

doi:10.1103/physrevlett.122.220401

Cited by 20 publications

(17 citation statements)

References 42 publications

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“…This optimisation can be solved in three stages, indicated by boxes in ( 16 ): The optimisation within the square bracket [ ] over ρ is an SDP on 4 × 4 matrices, which can be efficiently solved 60 . The optimisation in the curly bracket { } over b is performed by relaxing the continuous optimisation over the (2-norm) unit sphere to a discrete optimisation on a sequence of polygonial approximation (similar to the method used in Schwonnek et al 61 , 62 ). Also this optimisation can be performed with reliable lower bounds to the order of any target precision.…”

Section: Methodsmentioning

confidence: 99%

“…The optimisation in the curly bracket { } over b is performed by relaxing the continuous optimisation over the (2-norm) unit sphere to a discrete optimisation on a sequence of polygonial approximation (similar to the method used in Schwonnek et al 61 , 62 ). Also this optimisation can be performed with reliable lower bounds to the order of any target precision.…”

Section: Methodsmentioning

confidence: 99%

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Device-independent quantum key distribution with random key basis

et al. 2021

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Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an insecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today’s loophole-free Bell experiments. Here, we significantly narrow the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. By using two randomly chosen key generating bases instead of one, we show that our protocol significantly improves over the original DIQKD protocol, enabling positive keys in the high noise regime for the first time. We also compute the finite-key security of the protocol for general attacks, showing that approximately 108–1010 measurement rounds are needed to achieve positive rates using state-of-the-art experimental parameters. Our proposed DIQKD protocol thus represents a highly promising path towards the first realisation of DIQKD in practice.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Device-independent quantum key distribution with random key basis

et al. 2021

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“…Beyond linear witnesses. To improve over linear witnesses, a very useful method which allows for implementations in experiments (see, e.g., [93]) makes use of local uncertainty relations (LURs). The idea to derive entanglement criteria by means of LURs has some analogies with the original EPR-Bell approach in the sense that it considers pairs of non-commuting single party observables, say (A 1 , A 2 ) for party A and (B 1 , B 2 ) for party B.…”

Section: S 2 Gmementioning

confidence: 99%

Entanglement certification from theory to experiment

et al. 2018

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Entanglement is an important resource that allows quantum technologies to go beyond the classically possible. There are many ways quantum systems can be entangled, ranging from the archetypal two-qubit case to more exotic scenarios of entanglement in high dimensions or between many parties. Consequently, a plethora of entanglement quantifiers and classifiers exist, corresponding to different operational paradigms and mathematical techniques.However, for most quantum systems, exactly quantifying the amount of entanglement is extremely demanding, if at all possible. This is further exacerbated by the difficulty of experimentally controlling and measuring complex quantum states. Consequently, there are various approaches for experimentally detecting and certifying entanglement when exact quantification is not an option, with a particular focus on practically implementable methods and resource efficiency. The applicability and performance of these methods strongly depends on the assumptions one is willing to make regarding the involved quantum states and measurements, in short, on the available prior information about the quantum system. In this review we discuss the most commonly used paradigmatic quantifiers of entanglement. For these, we survey state-of-the-art detection and certification methods, including their respective underlying assumptions, from both a theoretical and experimental point of view.In the early twentieth century, the phenomenon of quantum entanglement rose to prominence as a central feature of the famous thought experiment by Einstein, Podolsky, and Rosen [1]. Initially disregarded as a mathematical artefact that showcases the incompleteness of quantum theory, the properties of entanglement were largely ignored until 1964, when John Bell famously proposed an experimentally testable inequality able to distinguish between the predictions of quantum mechanics and those of any local-realistic theory [2]. With the advent of the first experimental tests [3], spearheaded by , emerged the realisation that entanglement constitutes a resource for information processing *

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“…Whether deeper principles underlie quantum uncertainty and nonlocality has been listed as one of the challenging scientific problems on the occasion of celebrating the 125th anniversary of the academical journal Science [8]. Thus it is of fundamental significance to explore the intrinsic uncertainty of given quantum mechanical observables due to its connections with entanglement detection [9,10,11,12,13,14] and quantum nonlocality [15].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty regions of observables and state-independent uncertainty relations

Zhang,

Luo,

Fei

et al. 2021

Preprint

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The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the tight uncertainty relations of variance or deviation via determining the uncertainty regions, which are formed by the tuples of two or more of quantum observables in random quantum states induced from the uniform Haar measure on the purified states. From the analytical formulae of these uncertainty regions, we present state-independent uncertainty inequalities satisfied by the sum of variances or deviations of two, three and arbitrary many observables, from which experimentally friend entanglement detection criteria are derived for bipartite and tripartite systems.

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Entanglement Detection by Violations of Noisy Uncertainty Relations: A Proof of Principle

Cited by 20 publications

References 42 publications

Device-independent quantum key distribution with random key basis

Device-independent quantum key distribution with random key basis

Entanglement certification from theory to experiment

Uncertainty regions of observables and state-independent uncertainty relations

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