Analysis and construction of four-party deterministic operation sharing with a generalized seven-qubit Brown state

Abstract

In this paper, a four-party scheme is presented for remotely sharing a single-qubit operation with the help of LOCC and the generalized seven-qubit Brown state [Formula: see text]. Besides, we consider a theoretical scheme for four-party QOS by using the generalized [Formula: see text]-qubit Brown state [Formula: see text] proposed by Muralidharan and Panigrahi (Phys. Rev. A 77 (2008) 032321). Furthermore, some concrete discussions are made to study its important features, including the scheme determinacy, the sharer symmetry, the scheme security, the nowaday’s experimental feasibility as well as the intrinsic efficiency.

Four-party deterministic quantum operation sharing with a generalized seven-qubit Brown state

“…The necessary operations and classical communications in both the ZBZ and Zhang schemes (in the case that David is chosen as the final reconstructor of the conceivable state) are summarized in table 1. The summary can be directly gained from the figure in this paper and the counterpart in [36]. By the way, in [36] there is a mistake in the subgraph (v), i.e.…”

“…However, in the Zhang scheme, he only needs to measure the qubit and needs not to tell either partner his measurement outcome. Although it looks a little puzzling, in contrast to the ZBZ scheme [36] it is actually a subtle design of the Zhang scheme indeed. One can see this later.…”

“…Shared entanglements are indispensable in QOS [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In all existing QOS schemes, some multi-particle entangled states, such as Bell and GHZ states [25,37], W states [29,31], cluster states [30,32], genuine states [26,38] and so on, have been employed as quantum channels to fulfill QOS.…”

“…This generalized seven-qubit Brown state is different from the generalized seven-qubit GHZ and W states under stochastic LOCC and optimally violates a new Bell inequality. Due to their important features, Brown states have been used to deal with some quantum information processing [26,36,[40][41][42][43]. Particularly, in 2017 utilizing the generalized seven-qubit Brown state in a given qubit distribution, Zhou et al [36] presented an interesting work, i.e.…”

“…Due to their important features, Brown states have been used to deal with some quantum information processing [26,36,[40][41][42][43]. Particularly, in 2017 utilizing the generalized seven-qubit Brown state in a given qubit distribution, Zhou et al [36] presented an interesting work, i.e. they proposed a four-party deterministic QOS scheme (referred to as the ZBZ scheme hereafter).…”