Related papers: $k$-Uniform states and quantum information masking

$k$-Uniform states and quantum information masking

URL: http://arxiv.org/abs/2009.12497v2
Date: Tue, 13 Oct 2020 03:42:40 GMT
Title: $k$-Uniform states and quantum information masking
Authors: Fei Shi, Mao-Sheng Li, Lin Chen, and Xiande Zhang
Abstract summary: A pure state of $N$ parties with local dimension $d$ is called a $k$-uniform state if all the reductions to $k$ parties are maximally mixed. We show that when $dgeq 4k-2$ is a prime power, there exists a $k$-uniform state for any $Ngeq 2k$ (resp. $2kleq Nleq d+1$)
Score: 15.308818907018546
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: A pure state of $N$ parties with local dimension $d$ is called a $k$-uniform state if all the reductions to $k$ parties are maximally mixed. Based on the connections among $k$-uniform states, orthogonal arrays and linear codes, we give general constructions for $k$-uniform states. We show that when $d\geq 4k-2$ (resp. $d\geq 2k-1$) is a prime power, there exists a $k$-uniform state for any $N\geq 2k$ (resp. $2k\leq N\leq d+1$). Specially, we give the existence of $4,5$-uniform states for almost every $N$-qudits. Further, we generalize the concept of quantum information masking in bipartite systems given by [Modi \emph{et al.} {Phys. Rev. Lett. \textbf{120}, 230501 (2018)}] to $k$-uniform quantum information masking in multipartite systems, and we show that $k$-uniform states and quantum error-correcting codes can be used for $k$-uniform quantum information masking.

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