Spectral properties of tensor products of channels

Jaques, Samuel; Rahaman, Mizanur

doi:10.1016/j.jmaa.2018.05.052

Cited by 5 publications

(11 citation statements)

References 32 publications

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“…A uniform upper bound for the multiplicative index may provide an upper bound for this number. In a recent article [8], Theorem 3.8, such a bound for multiplicative index of a channel was proposed. Also analyzing the structure of PPT maps in Section 3, it can be realized that to prove the PPT-squared Conjecture (1.1) it is enough to prove the same for unital and trace preserving PPT maps which have trivial multiplicative domain.…”

Section: Discussionmentioning

confidence: 99%

Eventually entanglement breaking maps

Rahaman

Jaques

Paulsen

2018

Journal of Mathematical Physics

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We analyze linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor product space. If a linear map becomes entanglement breaking after finitely many iterations, we say the map has a finite index of separability. In particular we show that every unital PPT-channel has a finite index of separability and that the class of unital channels that have finite index of separability is a dense subset of the unital channels. We construct concrete examples of maps which are not PPT but have finite index of separability. We prove that there is a large class of unital channels that are asymptotically entanglement breaking. This analysis is motivated by the PPT-squared conjecture made by M. Christandl that says every PPT channel, when composed with itself, becomes entanglement breaking.

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Section: Discussionmentioning

confidence: 99%

Eventually entanglement breaking maps

Rahaman

Jaques

Paulsen

2018

Journal of Mathematical Physics

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“…Grayscale (think of the image as a 3D image of XY) 2. The gamma correction method is used to standardize the color space of the input image in order to adjust the contrast of the image, reduce the influence caused by the local shadow and illumination change of the image [26], and at the same time, suppress the noise interference 3. Calculate the gradient (including size and direction) of each pixel in the image, primarily to capture contour information while further attenuating the interference of light 4.…”

Section: Implementation Of Hog Feature Extraction Algorithmmentioning

confidence: 99%

RETRACTED ARTICLE: Image processing algorithm of Hartmann method aberration automatic measurement system with tensor product model

Fan

2019

J Image Video Proc.

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Nowadays, the society has entered the digital information age, and the information contained in the image is far more than the sum of the information contained in other media. In the Internet industry, image processing technology can be used to quickly find the required picture information. Other applications include disaster prevention, industrial automation production lines, semiconductor, electronics, tobacco, and food industries. After the meter glyph spot image is collected, there are several spots in the image, and the corresponding pixel values are stored in memory. In order to process images, they should be distinguished and marked so that the spot has definite eigenvalues. To this end, this paper proposes an image processing method. Firstly, an image denoising method combining self-snake model and P-M model is introduced. Secondly, the recursive HOSVD dimensionality reduction algorithm based on tensor product model is used to further process the image. The center of the Hartmann aperture image is solved by the centroid of all the spots, and the center overlap algorithm for determining the centroid distance of the aperture image by the symmetry of the centroid of the spot centroid can reduce the number of calculations. The experimental results show that this method can effectively identify and process the spot of the image and greatly reduce the time complexity and computational complexity of the algorithm.

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“…A recent work [8] indicated that if we consider unital quantum memory cell E (E(I) = I) and use the decoherence-free subsystems storing quantum information, then the superactivation of quantum information cannot exist. So checking the existence for general quantum memory cells is also an interesting problem.…”

Section: Discussionmentioning

confidence: 99%

Super-activating Quantum Memory with Entanglement

Guan¹,

Feng²,

Ying³

2017

Preprint

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Noiseless subsystems were proved to be an efficient and faithful approach to preserve fragile information against decoherence in quantum information processing and quantum computation. They were employed to design a general (hybrid) quantum memory cell model that can store both quantum and classical information. In this paper, we find an interesting new phenomenon that the purely classical memory cell can be super-activated to preserve quantum states, whereas the null memory cell can only be super-activated to encode classical information. Furthermore, necessary and sufficient conditions for this phenomenon are discovered so that the super-activation can be easily checked by examining certain eigenvalues of the quantum memory cell without computing the noiseless subsystems explicitly. In particular, it is found that entangled and separable stationary states are responsible for the super-activation of storing quantum and classical information, respectively.

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Spectral properties of tensor products of channels

Cited by 5 publications

References 32 publications

Eventually entanglement breaking maps

Eventually entanglement breaking maps

RETRACTED ARTICLE: Image processing algorithm of Hartmann method aberration automatic measurement system with tensor product model

Super-activating Quantum Memory with Entanglement

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