Witnessing Genuine Multipartite Entanglement with Positive Maps

Huber, Marcus; Sengupta, Ritabrata

doi:10.1103/physrevlett.113.100501

Cited by 77 publications

(84 citation statements)

References 34 publications

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“…This insight has led to the concept of PPT mixers [264,265], yielding effective numerical tools for low dimensions. At the same time, this connection can be used to effectively 'lift' bipartite witnesses for multipartite usage [266,267], and to obtain generalisations to maps which are positive on biseparable states [268]. GME witnesses.…”

Section: Contemporary Challenges: Multipartite Entanglementmentioning

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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Section: Contemporary Challenges: Multipartite Entanglementmentioning

confidence: 99%

Entanglement certification from theory to experiment

et al. 2018

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“…The general idea of getting explicit separability for n-qubits system is that we get a sufficient condition, but it might be not necessary as the condition for separabilty might be improved by using different methods. This method is different from those methods in which one gets the condition for entanglement [14][15][16][17][18][19][20][21][22][23]25]. Both methods are important and in the present work we concentrate on finding explicit separability forms for n-qubits systems.…”

Section: Introductionmentioning

confidence: 98%

Separability of 3-qubits density matrices, related tol₁andl₂norms and to unfolding of tensors into matrices

Ben‐Aryeh

Mann

2018

J. Phys. Commun.

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We treat separability of 3 (and more) qubits states. Especially we discuss density matrices with maximally disordered subsystems (MDS), by using Hilbert-Schmidt (HS) decompositions, where in the general case these density matrices include 27 HS parameters. By using 'unfolding methods', the MDS tensors are converted into matrices and by applying singular values decompositions (SVD) to these matrices the number of the parameters for treating full separability, in the general MDS case, is reduced to 9, and under the condition that the sum of the absolute values of these parameters is not larger than 1, we conclude that the density matrix is fully separable. In order to know if density matrices with MDS are separable, one needs to check with 9 parameters at a time and not with all 27 parameters. We use also Frobenius (l 2 ) norms. For treating bi-separability of 3-qubits MDS density matrices, the 27 HS parameters are divided into 9 triads. If the sum of the nine l 2 norms for these triads is not larger than 1, we conclude that the density matrix is bi-separable. We analyze the relations between 3 qubits MDS density matrices and the method of high order singular value decomposition (HOSVD). We demonstrate the use of our methods in examples. For 3-qubits states which are non-MDS the HS decomposition includes up to 63 parameters. If the sum of the absolute values of all the HS parameters is not larger than 1, we conclude that the density matrix is fully separable, and we have explicit expressions for their separability. For the systems of GHZ and W states mixed with white noise we find a simple way to reduce the sum of the absolute values of the HS parameters and get better conditions for their full separability.

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“…Due to the importance of genuine entanglement, numerous approaches have been devoted to detecting genuinely multipartite entanglement. Among the influential ones, the methods using entanglement witness [2][3][4][5][6][7][8][9], generalized concurrence [10][11][12][13][14], and Bell-inequality [15] are very useful. Nevertheless, the problem of detecting genuinely entanglement is far from being solved.…”

Section: Introductionmentioning

confidence: 99%

Uniform Entanglement Frames

et al. 2016

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We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of infinitely many detectors to check genuine multipartite entanglement. We also introduce the concept of k-separable circles via geometric distance for probability vectors, which include at most (k − 1)-separable states. The entanglement witness is also generalized to a universal entanglement witness which is able to detect the k-separable states more accurately.

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Witnessing Genuine Multipartite Entanglement with Positive Maps

Cited by 77 publications

References 34 publications

Entanglement certification from theory to experiment

Entanglement certification from theory to experiment

Separability of 3-qubits density matrices, related tol₁andl₂norms and to unfolding of tensors into matrices

Uniform Entanglement Frames

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Witnessing Genuine Multipartite Entanglement with Positive Maps

Cited by 77 publications

References 34 publications

Entanglement certification from theory to experiment

Entanglement certification from theory to experiment

Separability of 3-qubits density matrices, related tol1andl2norms and to unfolding of tensors into matrices

Uniform Entanglement Frames

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Product

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Separability of 3-qubits density matrices, related tol₁andl₂norms and to unfolding of tensors into matrices